Mathematics Objective Mathematics MATHEMATICS DEPARTMENT PAKTURK INTERNATIONAL SCHOOLS AND COLLEGES Intermediate Part I By Engin Baştürk PAKTURK
Mathematics
Objective
MathematicsMATHEMATICS
DEPARTMENT
PAKTURK INTERNATIONAL SCHOOLS AND COLLEGES
Intermediate Part I
By Engin Baştürk
PAKTURK
PAKTURKMATHEMATICS
DEPARTMENT
Copyright PAKTURK MATHS DEPARTMENT, 2015
All rights reserved. No part of this publication may be reproduced,translated, stored in a retrieval system of transmitted, in any form or by any means, without the prior permission of PAKTURK MATHS DEPARTMENT.
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Number System No 1
Q1: a bi can be written also as:
A) a bi B) ,a b
C) a bi D) ,b a
Q2: a bi can be written also as:
A) a bi B) a bi
C) ,a b D) ,a b
Q3: a bi can be written also as:
A) a bi B) a bi
C) ,a b D) a bi
Q4: What is the value of 2
i ?
A) 0 B) -1
C) 1 D) i
Q5: i can be written as:
A) 1,0 B) 0,1
C) 1,0 D) 0, 1
Q6: 2
i can be written as ............
A) 1,0 B) 0,1
C) 1,0 D) 0, 1
Q7: What is the value of 40
i ?
A) 0 B) -1
C) 1 D) i
Q8: The real part of a complex number a bi is .......
A) b B) 0,1
C) a D) 0, 1
Q9: The imaginary part of a complex number a bi is:
A) b B) 0,1
C) a D) 0, 1
Q10: Any real number a can be written as: (as order pair of
complex numbers)
A) ai B) 0,a
C) ,1a D) ,0a
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Q11: , , ?a b c d
A) ,ac bd ad bc B) .ad bc ac bd
C) ,bd ac ad bc D) ,ac bd ad bc
Q12: ?a bi c di
A) ac bd ad bc i
B) bd ac ad bc i
C) ad bc ac bd i
D) ac bd ad bc i
Q13: , , ?a b c d
A) ,a d b c B) ,a c b d
C) 2 ,2a d D) ,b d a c
Q14: ?a bi c di
A) a d b c i B) a c b d i
C) a c b d i D) b d a c i
Q15: , , ?r R r a b
A) ,a b B) ,ra b
C) ,a rb D) ,ra rb
Q16: If 1, .........z a bi z
A) a bi B) a bi
C) 2 2 2 2
a bi
a b a b
D)
2 2 2 2
a bi
a b a b
Q17: If 1, , .........z a b z
A) ,a b B) ,a b
C) 2 2 2 2
,a b
a b a b
D) 2 2 2 2
,a b
a b a b
Q18: If 11,2 , .........z z
A) 1
1,2
B) 1 1
,2 5
C) 1 2
,5 5
D) 1 2
,5 5
Q19: If 15 3 , .........z i z
A) 5 3
34 34i B)
5 3
34 34i
C) 5 3
34 34i D)
5 3
34 34i
Q20: Simplify 4
2 2i
A) 1 i B) 1 i
C) 2i D) i
Answer Key
1 2 3 4 5 6 7 8 9 10
B D A B B C C C A D
11 12 13 14 15 16 17 18 19 20
D A B C D C D D A B
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Number System No 2
Q1: Every real number is also a .............
A) Natural Number B) Complex Number
C) Rational Number D) Whole Number
Q2: If z a bi then z is:
A) a ib B) a ib
C) a ib D) 2 2
a b
Q3: If z a ib , then z a ib is called …...... of z
A) Root B) Inverse
C) Conjugate D) Identity
Q4: The complex number "a "i is called purely:
A) Real B) Complex
C) imaginary D) None
Q5: z is same with ……………
A) z B) z
C) z D) z
Q6: If a+ bz i , then z ________
A)2 2
a b B) 2 2
a b
C) a b D) None of these
Q7: If z a bi then z
A) 2 2
a b B) 2 2
a b
C) 2 2
a b D) 2 2
a b
Q8: Find the modulus of 3 4i
A) 5 B) 5
C) 5 D) 5
Q9: If 7 2z i then z
A) 53 B) 53
C) 53 D) 45
Q10: If 1 5 4z i and 2 5 2z i then 1 2 ...........z z
A) 4i B) 10
C) 10 D) 2i
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Q11: Which of the following is equal to 2
z
A) 2
z B) .z z
C) 2
z D) z
Q12: 81 16 is equal to ………
A) 5i B) 5i
C) 13i D) 12i
Q13: 64 100 is equal to ………
A) 2i B) 2i
C) 18i D) 18i
Q14: 12 144 is equal to ………
A) 12 2 3i B) 12 2 3i
C) 12 2 3i D) 12 4 3i
Q15: The polar form of a complex number is ….
A) tan cotr i B) sin cosr i
C) sec cscr i D) sec cscr i
Q16: 1 3
........2 2
i
A) 3 B) 1
C) 2 D) 0
Q17: 2
............1 i
A) 1 i B) 1 i
C) 2 1 i D) 2 1 i
Q18: 7
5
is ……..
A) 7
5
i
i B)
7
5
C) 7
5i D) None of these
Q19: The additive identity in Complex numbers is:
A) 0,0 B) 1,1
C) 1,0 D) 0,1
Q20: In terms of i , 3 ______.
A) 3i B) 3 i
C) 3 i D) 3i
Answer Key
1 2 3 4 5 6 7 8 9 10
B A C C C B B A A D
11 12 13 14 15 16 17 18 19 20
B A B A B B A C C B
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Number System No 3
Q1: 0 is ................
A) Positive Integer B) Irrational Number
C) Negative Number D) Complex Number
Q2: If z a bi then z z
A) 2a B) 2a bi
C) 2 2a bi D) 2bi
Q3: If z a bi then z
A) a bi B) a bi
C) a bi D) a bi
Q4: If 2 3z i then z
A) 2 3i B) 2 3i
C) 2 3i D) 3 2i
Q5: A complex Number is called zero complex number if ............x y
A) B) 0
C) Non-zero D) Equal
Q6: 22,z C z z
A) Imaginary B) Real
C) Zero D) Negative
Q7: , cos sin ......n
n Z i
A) sin cosn i n B) tan cotn i n
C) cos sinn i n D) cos sinn i n
Q8: The numerical value of 2
i is ________
A) 1 B) 1 C) i D) 1
Q9: The product of two imaginary no is always:
A) Imaginary B) Real
C) Negative D) None of these
Q10: The quotient of two imaginary numbers in simplest
form is always ….
A) Real number B) Imaginary number
C) Positive D) negative
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Q11: The value of 56
i is ………..
A) i B) -1 C) 1 D) i
Q12: Simplify 3
2 2i
A) 1 i B) 1 i C) 2i D) 3 3
4
i
Q13: Simplify 4 1 1i i
A) 8 B) 8i C) 4i D) 8
Q14: Simplify 4 4
1
i
i
A) 8 B) 8i C) 4i D) 4i
Q15: Simplify 31 i
A) 1 i B) 2 1 i
C) 1 i D) 2 1 i
Q16: 31 ?i
A) 3 3i B) 2 2i
C) 2 2i D) 2 2i
Q17: Simplify 21 i
A) 2 B) 1 C) 2i D) 2i
Q18: Simplify 21 i
A) 0 B) 1 C) 2i D) 4i
Q19: Simplify 21 2i i
A) 0 B) 2i C) 4i D) 2i
Q20: 112 ?i
A) 1 B) 0 C) 1 D) 2
Answer Key
1 2 3 4 5 6 7 8 9 10
D A C A B B D B B A
11 12 13 14 15 16 17 18 19 20
B D A C B D D C B C
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Number System No 4
Q1: 7 is ........
A) an irrational number B) a prime number
C) a rational number D) a whole number
Q2: Golden rule of fraction is that for 0, ...........a
kb
A) ab
k B)
k
ab
C) kb
ka D)
ka
kb
Q3: Whicf of the following sets has closure property with
respect to addition?
A) 1,1 B) 1
C) 1 D) 0
Q4: Whicf of the following sets has closure property with
respect to multiplication?
A) 1,1 B) 1
C) 1,0 D) 0,2
Q5: For , , , , 0, 0a b c d R b d then a c
b d
A) ac bd
bd
B)
ab cd
bd
C) ad bc
bd
D) abcd
Q6: Rational Numbers expressed in the form of ……..
A) a
b B)
a
b
C)
2
2
a
b D) ab
Q7: For any two real No’s , 0x y x y the x and y
are …………. of each other.
A) Identity B) Inverse
C) Reciprocal D) None of these
Q8: For any two real numbers , . 1x y x y , this property
is called as …………..
A) Multiplicative Identity B) Multiplicative inverse
C) additive inverse D) none of these
Q9: The property used in 11 11 0 is said to be:
A) Additive Inverse B) Additive identity
C) Inverse D) None of These
Q10: For , ,a b c a c b c a b , this
property is called _________ property w.r.t to addition.
A) Additive B) Multiplicative
C) Cancelation D) None of these
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Q11: Which of the following sets has closure property w.r.t
multiplication ________?
A) 0 B) 0,1
C) 1,1
D) 0, 1
Q12: The value of 2 is …………
A) Rational Number B) Irrational number
C) Natural number D) None of these
Q13: Which of the following sets has closure property w.r.t
multiplication ________?
A) 2, 1,0 B) 2,0,1
C) 0, 1,1
D) 0, 1
Q14: The additive identity of real numbers is always ….
A) Two B) Three
C) One D) Zero
Q15: The property used in
, ,x y z x y z x z y z is ……… property.
A) Distributive B) Commutative
C) Associative D) None
Q16: The sum of Real and Imaginary numbers is known as
….
A) Real Number B) Complex Number
C) Rational Number D) Irrational Number
Q17: Which of the following is associative property of real
numbers?
A) A B B A
B) A B C A B C
C) A B B A
D) A B C A B A C
Q18: Which of the following is commutative property of real
numbers?
A) A B B A
B) 3 4 5 3 4 5
C) 2 2 0
D) 4 1 4
Q19: Which of the following is additive property of real
numbers?
A) 4 4a b a b B) 4 4a b a b
C) 0a a D) 1
1aa
Q20: The sum of multiplicative identity and its multiplicative
inverse is:
A) 1 B) 0
C) 1 D) 2
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Number System No 5
Q1: , , 0, 0, .......a b R a b a b
A) a b B) a b
C) 1 1
a b D)
1 1
a b
Q2: 1 1
, , 0, 0, .......a b R a ba b
A) a b B) a b
C) 1 1
a b D) a b
Q3: , , 0, 0, .......a b R a b a b
A) a b B) a b
C) a b D) a b
Q4: If 0a then ..............
A) 0a B) 0a
C) 1
0a D)
10
a
Q5: If 0a then ..............
A) 0a B) 0 a
C) 1
0a D)
10
a
Q6: If a b b c c d then .................
A) a d B) a d
C) a d D) c a
Q7: If1 1
,a b
then ………….
A) a b B) a b
C)1 1
a b D) a b
Q8: If a b ,then …………..
A) a b B) a b
C)1 1
a b D) a b
Q9: What is the name of property used in
4 3 1 0
A) Multiplicative B) Additive
C) Identity D) None
Q10: , ,a b c R either a b and b c then a c . The
given property is called:
A) Trichotomy B) Transitive
C) Reflexive D) Symmetric
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Q11: ,a b R either a b or a b or a b . The given
property is called:
A) Trichotomy B) Transitive
C) Reflexive D) Symmetric
Q12: What is the property used in 3 2 0 1
A) Additive property B) Multiplicative property
C) Transitive property D) Multiplicative Identity
Q13: What is the property used in 5 4 20 16
A) Additive property B) Multiplicative property
C) Multiplicative Identity D) Transitive property
Q14: What is the property used in 1 1 3 5
A) Additive property B) Multiplicative property
C) Transitive property D) Multiplicative Identity
Q15: What is the property used in 0 0a a
A) Additive property B) Multiplicative property
C) Transitive property D) Multiplicative Identity
Q16: What is the property used in 1 1
a ba b
A) Additive property B) Multiplicative property
C) Transitive property D) Multiplicative Identity
Q17: What is the property used in a b a b
A) Additive property B) Multiplicative property
C) Transitive property D) Multiplicative Identity
Q18: What is the property used in 20 40 100 120
A) Additive property B) Multiplicative property
C) Transitive property D) Multiplicative Identity
Q19: What is the property used in 1 2 1 2
A) Additive property B) Multiplicative property
C) Multiplicative Identity D) Transitive property
Q20: What is the property used in a b b a
A) Additive property B) Multiplicative property
C) Transitive property D) Multiplicative Identity
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Number System No 6
Q1: , , 0, 0, .......a b R a b a b
A) a b B) a b
C) 1 1
a b D)
1 1
a b
Q2: 1 1
, , 0, 0, .......a b R a ba b
A) a b B) a b
C) 1 1
a b D) a b
Q3: , , 0, 0, .......a b R a b a b
A) a b B) a b
C) a b D) a b
Q4: If 0a then ..............
A) 0a B) 0a
C) 1
0a D)
10
a
Q5: If 0a then ..............
A) 0a B) 0 a
C) 1
0a D)
10
a
Q6: If a b b c c d then .................
A) a d B) a d
C) a d D) c a
Q7: If1 1
,a b
then ………….
A) a b B) a b
C)1 1
a b D) a b
Q8: If a b ,then …………..
A) a b B) a b
C)1 1
a b D) a b
Q9: What is the name of property used in
4 3 1 0
A) Multiplicative B) Additive
C) Identity D) None
Q10: , ,a b c R either a b and b c then a c . The
given property is called:
A) Trichotomy B) Transitive
C) Reflexive D) Symmetric
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Q11: ,a b R either a b or a b or a b . The given
property is called:
A) Trichotomy B) Transitive
C) Reflexive D) Symmetric
Q12: What is the property used in 3 2 0 1
A) Additive property B) Multiplicative property
C) Transitive property D) Multiplicative Identity
Q13: What is the property used in 5 4 20 16
A) Additive property B) Multiplicative property
C) Multiplicative Identity D) Transitive property
Q14: What is the property used in 1 1 3 5
A) Additive property B) Multiplicative property
C) Transitive property D) Multiplicative Identity
Q15: What is the property used in 0 0a a
A) Additive property B) Multiplicative property
C) Transitive property D) Multiplicative Identity
Q16: What is the property used in 1 1
a ba b
A) Additive property B) Multiplicative property
C) Transitive property D) Multiplicative Identity
Q17: What is the property used in a b a b
A) Additive property B) Multiplicative property
C) Transitive property D) Multiplicative Identity
Q18: What is the property used in 20 40 100 120
A) Additive property B) Multiplicative property
C) Transitive property D) Multiplicative Identity
Q19: What is the property used in 1 2 1 2
A) Additive property B) Multiplicative property
C) Multiplicative Identity D) Transitive property
Q20: What is the property used in a b b a
A) Additive property B) Multiplicative property
C) Transitive property D) Multiplicative Identity
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Sets, Functions and Groups No 1
Q1: If A B , then the complement of B is ..........
A) A B B) U B C) A B D) A B
Q2: A set contaning only one element is called ........
A)Null set B) Empty Set
C) Singleton set D) Inverse set
Q3: 0 is ...........
A)Empty Set B) Singleton Set
C) Null Set D) Solution Set
Q4: If n A k , then ..........nP A
A) 2k B)
22 k C) 2k D)
2k
Q5: The set of students of PAKTURK is ..............
A) Infinite Set B) Finite Set
C) Empty Set D) Null Set
Q6: The set 1,2,3 is:
A) Infinite Set B) Singleton set
C) Empty Set D) Three point Set
Q7: If A , then ...........P A
A)Empty Set B) 0 C) D) None
Q8: The number of subsets of a set of 5 elements is ...........
A)32 B) 16 C) 4 D) 25
Q9: The set 1,2,3 , 1,2 has ............
A) Two elements B) Five element
C) Infinite elements D) One element
Q10: The union of two sets A and B is ..............
A) A B B) B A C) A B D) A B
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Q11: The intersection of two sets A and B is ..............
A) A B B) B A C) A B D) A B
Q12: If A and B are disjoint sets, then ............
A) A B B) B A A
C) A B D) A B
Q13: If A and B are overlapping sets, then ...........
A) A B B) B A A
C) A B D) A B
Q14: ..........A B
A) B A B) B A C) A B D) B A
Q15: ..........A B
A) B A B) B A C) A B D) B A
Q16: ..........A B C
A) A B C B) A B C
C) A B C D) B A B
Q17: ..........A B C
A) A B C B) A B C
C) A B C A D) A B C
Q18: ..........A B C
A) A B A C B) A B A C
C) A B A C D) A B A C
Q19: ..........A B C
A) A B A C B) A B A C
C) A B A C D) A B A C
Q20: ..........A A B
A) B B) A B C) A B D) A
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Sets, Functions and Groups No 2
Q1: ..........A A B
A) B B) A B C) A B D) A
Q2: For a set A and the universal set U , C
A A
A) A B) C
A C) D) U
Q3: For a set A and the universal set U , CC
A
A) A B) C
A C) D) U
Q4: For a set A and the universal set U ,C
A A
A) A B) C
A C) D) U
Q5: For any subsets A and B of U , CA B
A) A B B) C C
A B C) C C
A B D)
Q6: For any subsets A and B of U , CA B
A) A B B) C C
A B C) C C
A B D)
Q7: ..........C
C CA B
A) A B B) C C
A B C) A B D) C C
A B
Q8: ..........C
C CA B
A) A B B) C C
A B C) A B D) C C
A B
Q9: If B A , then the shaded region represents ……
A) A B B) C C
A B C) A B D) C C
A B
Q10: The number of subsets of a set having three elements is
……………
A)4 B) 6 C) 8 D) 10
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Q11: If B A , then the shaded region represents ……
A) A B B) C C
A B C) A B D) C C
A B
Q12: A subset of A A is called a ……..
A) Relation from A to B B) Relation from B to A
C) Relation in A D) Relation in B
Q13: A subset of B B is called a ……..
A) Relation from A to B B) Relation from B to A
C) Relation in A D) Relation in B
Q14: The range of , ,1 , 0,3f m y n is ……..
A) ,1,3y B) , ,m n o
C) , ,3, ,1,3m n o
D) m
Q15: The domain of ,1 ,2f a b is ……..
A) ,a b B) 1,2,3 C) , ,1,2a b D) a
Q16: The cancellation laws hold in ………….
A) Sets B) Numbers
C) Group D) Abelian Group
Q17: If p is any proposition its negation is denoted by
………
A) p B) p C) p D) p
Q18: If p is true, then p is ………………….
A) True B) has no information
C) False D) equivalent to p
Q19: If p is true, then p is ………………….
A) True B) has no information
C) False D) equivalent to p
Q20: The conjunction of two statements p and q is denoted
by ………………….
A) p q B) p q C) p q D) p q
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Sets, Functions and Groups No 3
Q1: p q represents ……………
A) Disjunction B) Conjunction
C) Conditional D) Quantifier
Q2: A conjunction of two statements p and q is true only
if ..
A) p is true B) Both p and q are true
C) q is true D) Both p and q are false
Q3: p: Islamabad is a capital of Pakistan and q: Lohore is
not a city of Pakistan, the conjunction p q is ………..
A) True B) not valid C) False D) unknown
Q4: p: Islamabad is a capital of Pakistan and q: Multan is a
city of Pakistan, the conjunction p q is ………..
A) True B) not valid C) False D) unknown
Q5: : 4 7, : 7 11p q , then the conjunction p q is
………..
A) True B) not valid C) False D) unknown
Q6: :3 5, : 7 4p q , then the conjunction p q is
………..
A) True B) not valid C) False D) unknown
Q7: : 4 7, : 7 11p q , then the conjunction p q is
……
A) True B) not valid C) False D) unknown
Q8: p: Islamabad is a capital of Pakistan and q: Lahore is
not a city of Pakistan, the conjunction p q is ………..
A) True B) not valid C) False D) unknown
Q9: The disjunction of two statements p and q is denoted
by ………………….
A) p q B) p q C) p q D) p q
Q10: A disjunction of two statements p and q is false only
if ……………
A) p is true B) Both p and q are true
C) q is true D) Both p and q are false
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: A compound statement of the form “ if p then q ” is called an ………..
A)Implication B) Hypothesis C) Conclusion D) Unknown
Q12: An implication or conditional “ if p then q ” is denoted by ……………..
A) p q B) . p q . C) p q D) p q
Q13: An implication or conditional “ if q then p ” is denoted by ……………..
A) p q B) q p C) q p D) p q
Q14: In a statement “ if q then p ” p is ……………….
A) Implication B) Hypothesis
C) Conclusion D) Unknown
Q15: In a statement “ if q then p ” q is ……………….
A) Implication B) Hypothesis
C) Conclusion D) Unknown
Q16: A conditional is regarded as false only when the
antecedent is true and consequent is …………
A) True B) Known
C) False D) Unknown
Q17: A subset of A B is called a ……..
A) Relation from A to B B) Relation from B to A
C) Relation in A D) Relation in B
Q18: A subset of B A is called a ……..
A) Relation from A to B B) Relation from B to A
C) Relation in A D) Relation in B
Q19: If A then A is called ………………… set.
A) Sub B) Empty C) Singleton D) Null
Q20: The set of real numbers between 1 and 2 is …………..
A) Finite B) Empty
C) Infinite D)Non-Empty
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 1
For more news and updates visit pakturkmaths.com
CL
AS
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XI
For any question mail us at [email protected]
Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Sets, Functions and Groups No 4
Q1: For , ,a A b B then r a b is ………
A) Relation from A to B B) Relation from B to A
C) Relation in A D) Relation in B
Q2: For , ,a A b B then r b a is ………A)
Relation from A to B B) Relation from B to A
C) Relation in A D) Relation in B
Q3: The set of the first elements of the ordered pairs
forming a relation is called its ……………….
A) Relation in A B) Relation in B
C) Range D) Domain
Q4: The set of the second elements of the ordered pairs
forming a relation is called its ……………….
A) Relation in A B) Relation in B
C) Range D) Domain
Q5: The domain of ,1 , 2 , ,3f a a a is ……..
A) a B) 1,2,3 C) ,2,3a D) 2
Q6: The inverse of a relation ,1 , , 2 , ,3x y z is
…………..
A) ,1 , , 2 , ,3x y z B) 1, , 2, , 3,x y z
C) 1 1 1
,1 , ,2 , ,3x y z
D) , , , , ,x x y y z z
Q7: The inverse of an identity relation is ……….
A) Not an identity relation B) Not a relation
C) an identity relation D) An empty set
Q8: A subset f of A B is said to be a function from A
to B if domain of f is A and first elements of order pairs of f
………….
A) Do not repeat B) Do not exist
C) The members of B D) Repeat
Q9: Which one is a function from A to B if , ,A a b c
and 1,2,3B
A) ,1 , ,1 , , 2a b c B) ,1 , ,1 , ,3a b b
C) ,1 , ,1 , , 2a b a D) ,1 , ,1 , , 2a b b
Q10: A function in which the second elements of the order
pairs are distinct is called ………..
A) Onto function B) One-one function
C) Identity function D) Inverse function
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: A function from A to B is called the onto function if its
range is ………
A) A B) B
C) Neither A nor B D) Both A and B
Q12: A function whose range consists of just one element is
called ………..
A) One-one function B) Constant function
C) Onto function D) Identity function
Q13: If , ,A a b c , 1,2,3B and
,1 ,1 , ,1f a b c is ………………
A) One-one function B) Constant function
C) Onto function D) Identity function
Q14: The range of ,1 ,1 , ,1f a b c is ……..
A) , ,a b c B) 1
C) , , ,1a b c
D) a
Q15: The domain of ,1 , 2 , ,3f a b c is ……..
A) , ,a b c B) 1,2,3 C) ,2,3a D) a
Q16: The function ,f x y y mx c is ……..
A) Quadratic function B) Constant function
C) Cubic function D) Linear function
Q17: The graph of a linear function represents ………..
A) Triangle B) Straight Line
C) Circle D) Parabola
Q18: The function 2,f x y y ax bx c is ……..
A) Quadratic function B) Constant function
C) Cubic function D) Linear function
Q19: The function 2, 3 5f x y y x x is ……..
A) Quadratic function B) Constant function
C) Cubic function D) Linear function
Q20: The function , 11f x y y is ……..
A) Onto function B) Constant function
C) One-one function D) None of these
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 1
For more news and updates visit pakturkmaths.com
CL
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XI
For any question mail us at [email protected]
Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Sets, Functions and Groups No 5
Q1: If A B then A B ……………….
A) A B) B C) U D)
Q2: A bijective function is ……..
A) Onto but not one-one B) One-one but not onto
C) One-one and onto D) Only onto
Q3: A set which has no element is called ……..
A) Power set B) Empty set
C) Non-empty set D) Subset
Q4: Every set is ……………. of itself.
A) an empty B) an improper set
C) proper Subset D) None of these
Q5: If A B and A B , then A is ………….. of B .
A) Proper Subset B) Improper subset
C) Super set D) Power set
Q6: The two sets and A B are said to be …………… if they have equal number of elements.
A) Equal B) Finite Set
C) Equivalent set D) Singleton set
Q7: A set consisting of only one element is called
………………
A) Equal B) Finite Set
C) Equivalent set D) Singleton set
Q8: Power set is a set which consists of all the possible
…………….. of a given set.
A) Subsets B) Super sets
C) Elements D) None of these
Q9: The power set of an empty set i.e. P is ……….
A) Singleton Set B) Empty Set
C) Non-empty Set D) Infinite set
Q10: If A B then A B ……………….
A) A B) B C) U D) c
A
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: If A B then A B …………………
A) A B) B C) U D) c
A
Q12: A set whose last element is known and which is a
containable set is called ………………
A) Singleton set B) Infinite set
C) Finite set D) Non-empty
Q13: If A B then …………………
A) c c
A B B) c c
B A C) c
A B D) c
B A
Q14: If , cA A then
cA A …………..
A) A B) C) U C) c
A
Q15: If and , then c cA A A A …………..
A) A B) U C) B D) c
A
Q16: If A and B are two sets then A B =………………..
A) /x x A x B B) /x x A x B
C) /x x A x B D) /x x A x B
Q17: The two sets A and B are said to be …………. if they have the same elements.
A) Equivalent B) Equal
C) Empty D) None of these
Q18: The set of all the members under consideration is called
………………
A) Subset B) Power set
C) Universal set D) None of these
Q19: If A U then c
A =…………….
A) A U B) U A
C) U A D) None of these
Q20: If B A , then c
B A ………………
A) U B) B C) A D)
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 1
For more news and updates visit pakturkmaths.com
CL
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XI
For any question mail us at [email protected]
Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Sets, Functions and Groups No 6
Q1: The statement " "p q is called ………..
A) Conditional B) Implication
C) Bi-conditional D) Conjunction
Q2: p q q p is equal to …………..
A) p q B) q p
C) p q D) p q
Q3: p q is equal to ………..
A) p q B) p q C) p q D) p q
Q4: For any two sets, A B B A if ………..
A) A
B) B
C) A B D) A B
Q5: The Cartesian product of A B is defined as …..
A) ,x y x A y B B) ,x y y A x B
C) ,x y x A y B D) ,x y x B y A
Q6: For any three sets; A , B andC , A B C
………..
A) A B C B) A B C
C) A B C D) None of these
Q7: c c cA B A B is called ________ law.
A) Commutative B) Associative
C) De Morgan’s D) Complementation
Q8: A ________.
A) A B) c
A C) U D)
Q9: The Tabular form of set 2 16 0x x x R is__________.
A) 4 B) 4 C) D) 1
Q10: The presentation of sets through the diagrams is called
________
A) Argand Diagram B) Venn Diagram
C) Circular Diagram D) None of these
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: If c
A B A then A B _______
A) A B B) c
A C) D) None
Q12: ?c cA B
A) U A B B) U A B
C) U A B D) None of these
Q13: The number of elements of a set is …… if it has 31 subsets.
A) 3 B) 4
C) 5 D) All of these
Q14: The set of first co-ordinates of A B is called:
A) Range B) Function
C) Domain D) Binary function
Q15: A function of the type f : x 2x is called:
A) Quadratic B) Linear
B) Trigonometric C) None of these
Q16: If as Set A has m elements and set B has n elements
then A B has _______ elements.
A) 2 2
m n B) 2
m C) 2
n D) n m
Q17: The function which is both one-to-one and onto is
called _______
A) Onto function B) Onto one function
C) Bijective function D) Into function
Q18: The number of subsets of set having 9 elements is:
A) 128 B) 256 C) 420 D) 512
Q19: If " "p is false then p is:
A) True B) False C) Both D) None
Q20: The number of elements of a set having 128 subsets is:
A) 4 B) 5 C) 7 D)8
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 1
For more news and updates visit pakturkmaths.com
CL
AS
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XI
For any question mail us at [email protected]
Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Matrices and Determinants No 1
Q1: The list of numbers within a square bracket is
called ………..
A) Determinant B) Set
C) Matrix D) Equation
Q2: m n represent ……….. of a Matrix
A) Row B) Columns
C) Order D) None
Q3: A matrix of the form
4
1
4
A
is called ….Matrix
A) Column B) Row
C) Square D) Zero
Q4: A matrix of the form B a b c is called … matrix
A) Column B) Row
C) Square D) None
Q5: A matrix is said to be rectangular matrix if its order
is …………
A) m n B) m n
C) 2m D) 3n
Q6: What is the additive identity of matrices (2x2)
A) 0 0
0 0
B) 1 0
0 1
C) 1 0
0 0
D) None of these
Q7: A,B and C are three matrices then If AB C what
is A?
A) 1CB
B) CB
C) C
A D) none
Q8: Which of the following is false
A) 1.A A I B) 1.B B I
C) .A I A D) .0A I
Q9: If
1
3
7
A
then A is
A) 1 2 B) 2 3 C) 3 1 D) 1 3
Q10: If 3 9
1 3A
then which of the following is true
A) 18A B) A is a singular matrix
C) A is non singular matrix D) A is a scalar matrix
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: A matrix of the form 1 2
3 4A
is called …….
matrix
A) Rectangular B) Square
C) Identity D) Row
Q12: The order of matrix aij is ……….. If 1,2i and
1,2,3j
A) 2x2 B) 3x2
C) 2x3 D) 3x3
Q13: A matrix “A” will be a square matrix if ………
A) m n B) 2 2m n
C) m n D) m n
Q14: A matrix of the form
5 0 0
0 7 0
0 0 8
is called …….
A) Identity B) Scalar
C) Rectangular D) Diagonal
Q15: If 1 0
0 1A
then A is not called ………. Matrix
A) Scalar B) Identity
C) Rectangular D) Diagonal
Q16: If a b
Ac d
and 1 5 4B then .......
A) A B B) TA B C) B I D) A B
Q17: The two matrices are said to be conformable for
addition. If ………..
A) Both are square matrices B) Both are row matrices
C) Both are column matrices D) Both are in same order
Q18: A matrix
0 0 0
0 0 0
0 0 0
A
is called ….. matrix
A) Rectangular B) Identity
C) Null D) Rectangular
Q19: The identity matrix in the matrix addition is ……
A) Column matrix B) Square matrix
C) Null matrix D) None of them
Q20: If A nad B are two matrices of the same order such
that 0A B B A , then ..........B
A) –B B) Zero matrix
C) –A D) A
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 1
For more news and updates visit pakturkmaths.com
CL
AS
S
XI
For any question mail us at [email protected]
Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Matrices and Determinants No 2
Q1: The two matrices A and B are said to be additive
inverse of each other if ………
A) A B I B) 0A B C) AB I D) 0AB
Q2: The two matrices A and B are said to be
multiplicative inverse of each other if ………
A) AB BA B) BA A C) AB BA I D) 0AB
Q3: If “A” is a matrix of order mxn and “B” is a matrix of order pxq, their product AB is defined if ……..
A) m=q B) n=p C) n=q D) m=p
Q4: If 2 5
2 0A
and 1 0
1 2A
then, .....AB
A) 2 0
2 0
B) 7 10
2 0
C) 10 0
0 2
D) 7 2
10 0
Q5: 1 0
0 9
is a …………….
A) Diagonal B) Identity C) Scalar D) Zero
Q6: If m n
Ak l
then, AdjA is …..
A) l k
n n
B) l k
n m
C) l n
k m
D) m k
n l
Q7: 3 5 4 9 ... ...
A) 1 14 B) 1 14 C) 7 14 D) 7 14
Q8: If A and B are the two matrices of the same order
then AB BA if …………
A) A B B) A B C) A B I D) B A
Q9: If “B” is diagonal matrix and 11 22 33...... nn
a a a a k then “B” is called …… matrix of order “n” where 0,1k
A) Identity B) Rectangular
C) Square D) Scalar
Q10: If “B” is diagonal matrix and 11 22 33...... 1
nna a a a then “B” is not called …… matrix.
A) Scalar B) Rectangular
C) Unit D) Square
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Q11: If A aij then aji is called …… matrix
A) Symmetric B) Transpose
C) Identity D) Scalar
Q12: If A is any square matrix, then the matrix obtained
by the interchange of rows and columns of A is called
…….. of A
A) Scalar B) Symmetric
C) Transpose D) None of these
Q13: If tA A then A is known as ……… matrix
A) Transpose B) Scalar
C) Symmetric D) Identity
Q14: If tA A , then A is known as ………… matrix
A) Symmetric B) Skew symmetric
C) Transpose D) Zero matrix
Q15: Transpose of identity matrix tI is ……
A) Scalar B) Symmetric
C) Identity D) Zero matrix
Q16:
0 0
0 0
0 0
a
a
a
is a ………… if 0,1a
A) Scalar matrix B) Unit Matrix
C) Zero Matrix D) Diagonal matrix
Q17: If A is order of m n , then the order of tA is
…….
A) m n B) n m C) m m D) n n
Q18:
4 5 6
5 3 2
6 2 8
is ………………………………
A) Rectangular Matrix B) Diagonal Matrix
C) Square Matrix D) Scalar Matrix
Q19: If A A , then A is called ………
A) Real Matrix B) Symmetric Matrix
C) Hermitian Matrix D) Skew Hermitian Matrix
Q20: If t
A A , then A is called ………
A) Transpose B) Symmetric Matrix
C) Hermitian Matrix D) Skew Hermitian Matrix
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 1
For more news and updates visit pakturkmaths.com
CL
AS
S
XI
For any question mail us at [email protected]
Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Matrices and Determinants No 3
Q1: Which of the following is conjugate matrix?
A) 1 5
5 6
B) 2 6
9 4
C) 3 5
6 7
i i
i i
D) 0 0
0 0
Q2: Transpose of a square matrix is ……………
A) Rectangular Matrix B) Scalar Matrix
C) Square Matrix D) Identity matrix
Q3: If t
A A , then A is called ………
A) Transpose B) Symmetric Matrix
C) Hermitian Matrix D) Skew Hermitian Matrix
Q4: The additive inverse of cos sin
tan cot
is
………..
A) sin cos
cot tan
B) cos sin
tan cot
C) cos sin
tan cot
D) sin cos
cot tan
Q5: If two rows or two columns of a square matrix A
are identical then ...........A
A) 1 B) -1
C) 0 D) Non-zero
Q6: Find adjoint matrix of 2 3
3 2
A) 2 3
3 2
B) 2 3
3 2
C) 2 3
3 2
D) 2 3
3 2
Q7: The determinant of
2 1 3
1 1 0
2 3 4
is ………
A) 11 B) 10 C) -10 D) -11
Q8: If ij
A a is any square matrix, then co-factor of
an element ij
a is ………….
A) 1i j
ijM
B) 1i j
ijM
C) 1i j
jiM
D) 1i j
jiM
Q9: Which of the following is a not scalar matrix?
A)
5 0 0
0 5 0
0 0 5
B)
1 0 0
0 1 0
0 0 1
C)
4 0 0
0 4 0
0 0 16
D)
0 0 0
0 0 0
0 0 0
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Q10: If A and B are of the same order then which one is
always true
A) AB BA B) A B B A
C) AB BA D) None of these
Q11: What is determinant of zero matrix
A) 1 B) 0
C) -1 D) Not possible
Q12: 1...........AB
A) 1 1A B B) AB
C) BA D) 1 1B A
Q13: ...........t
AB
A) t tA B B) AB
C) BA D) t tB A
Q14: If AB BA then which of the following is correct?
A) A I or B I B) ,A I B I
C) 2 2A B D) None of these
Q15: A and B are of the same order and AB BA I
then ……………
A) A B B) B I
C) A I D) 1A B
Q16: If A is non-singular matrix then …………….
A) 0A B) 0A
C) 1A D) A is zero matrix
Q17: A is a square matrix then 11
A is equal to
………….
A) 1A B) A C) t
A D) I
Q18: Determinant of
3 4 2
1 7 3
0 0 0
is equal to …………
A) 12 B) 0 C) 15 D) 1
Q19: Determinant of
1 2 9
3 7 8
1 2 9
is equal to …………
A) 9 B) -3 C) 13 D) 0
Q20: Inverse of a square matrix “A” exists if ………….
A) 0A B) 0A
C) 1A D) A is zero matrix
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 1
For more news and updates visit pakturkmaths.com
CL
AS
S
XI
For any question mail us at [email protected]
Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Matrices and Determinants No 4
Q1: Determinant of A is possible only when A is
………….
A) Symmetric Matrix B) Rectangular Matrix
C) Square matrix D) None of these
Q2: A is a square matrix, then tA is equal to ………..
A) tA B) A C) t
A D) A
Q3: The value of
cos 0 sin
1 1 0
sin 0 cos
is equal to ….
A) 0 B) 1 C) -1 D)
Q4: A is a non-singular matrix then 1t
A is equal to
….
A) 1A B) 1
tA
C) t
A D) None
Q5: The matrix
0 1 2 4
0 0 1 3
0 0 0 4
0 0 0 0
is ……………..
A) In reduced form B) In echelon form
C) In rank form D) In Identity form
Q6: The number of non-zero rows in the Echelon form
is called …………… of the matrix
A) Transpose B) Determinant
C) Rank D) Adjoint
Q7: The rank of
1 4 2
0 1 3
0 0 0
is equal to …….
A)1 B) 2 C) 3 D) 0
Q8: For what value of the matrix
2 6 5
4 4 6
0 1
A
is
a singular matrix
A) 0 B) 1 C) -2 D) -1
Q9: The order of A is 4 4 then what will be the order
of 1A
A) 5 5 B) 6 6 C) 4 4 D) None
Q10: If any two rows or columns of a square matrix A
interchanged then determinant will be equal to …………
A) A B) A C) 2
A D) A
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: The product of ac d
b
is equal to …..
A) ab cd B) ac ad
bc bd
C) ac bd D) None of these
Q12: The solution set 0,0,0 is called ……….. for homogeneous system of linear equations
A) Non-trivial B) Trivial
C) Unique D) Infinite
Q13: If a system , 0AX B B is called ……. If it has unique or infinite many solutions
A) Trivial B) Non-trivial
C) Consistent D) Inconsistent
Q14: The system of linear equations is said to be ….. if it has no solution
A) Trivial B) Non-trivial
C) Consistent D) Inconsistent
Q15: Those equations whose solution is common are
called …………..
A) Quadratic Equations B) Linear Equations
C) Simultaneous Equations D) Homogeneous Equations
Q16: A system 0AX has non-trivial solution if
…………
A) 0A B) 0A
C) A A D) A A
Q17: C and D are two non singular matrices then
11 1
C D is equal to …………
A) 1 1D C
B) CD C) DC D) 1 1C D
Q18: The ratio of the adjoint and determinant of non
singular matrix is ……………. of the matrix
A) Inverse B) Transpose
C) Co-factor D) None of these
Q19: Cramer’s Rules is applicable on AX B if ….
A) 0A B) 0A C) 0A D) 0A
Q20: The value of
1
1
1
y z x
z x y
x y z
is equal to ……
A) 1 B) 0 C) x y z D) xyz
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 1
For more news and updates visit pakturkmaths.com
CL
AS
S
XI
For any question mail us at [email protected]
Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Matrices and Determinants No 5
Q1: The square of a scalar matrix is a …………..
A) Identity Matrix B) Rectangular Matrix
C) Scalar Matrix D) Identity Matrix
Q2: A is a unit matrix , then A is equal to …………
A) 0 B) 1 C) -1 D) 2
Q3: Order of 3 5 is ……….
A) 1x1 B) 1x2 C) 2x1 D) 2x2
Q4: 1 0
0 1
is a …………….. matrix
A) Singular B) Zero C) Unit D) None
Q5: If 1AA I
, then 1A is ……….. of matrix A
A) Adjoint B) Multiplicative inverse
C) Additive inverse D) Transpose of A
Q6: If matrix 4 16
8n
is singular, then ...n
A) -2 B) 2 C) 4 D) -4
Q7: If A,B and C are three matrices which are
conformable for multiplication, then ...........A BC
A) AC B B) BC A C) AB C D) CA B
Q8: 31 4 .............
5
A) 2 3
4 5
B) 3 12
5 20
C) 2 12
4 25
D) 12 3
16 8
Q9: 2...........
3x y
A) 3x y B) 3x y C) 2 3x y D) 3x y
Q10: 5 0
0 5
is a …………. Matrix
A) Zero B) Identity C) Unit D) Scalar
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: If4 2 92
6 5 12 2 25
m
, then ...........m
A) 3 B) 5 C) 7 D) 9
Q12: The matrix of co-efficient for the equations
3 12x y and 3 2 8x y is ………………..
A) 1 3
3 2
B) 1 12
3 8
C) 3 12
2 8
D) 3 1
3 2
Q13: If 2 3
2 1A
then A is …….
A) -4 B) 4 C) -5 D) 5
Q14: If 1 0
0 1A
then, 1 ..........A
A) 1 0
0 1
B) 1 0
0 1
C) 1 0
0 1
D) None
Q15: If the number of rows and columns in a matrix are
not equal, then the matrix is called....
A) Square matrix B) Zero matrix
C) Unit matrix D) Rectangular matrix
Q16: If 5 3
12 2 5A
then A is …….
A) -4 B) 4 C) -5 D) 5
Q17: Matrix 0 0
0 0
is a ………. matrix
A) Zero B) Unit
C) Column D) Row
Q18: Which of the following is false
A) 1AA I
B) tI I C) t
tA A D) 1t
A A
Q19: If 1 0
0 1A
then, which of the following is false
A) A is scalar matrix B) A is unit matrix
C) A is zero matrix D) A is diagonal matrix
Q20: What is the multiplicative identity of matrices
(2x2)?
A) 0 0
0 0
B) 1 0
0 1
C) 1 0
0 0
D) none
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Matrices and Determinants No 6
Q1: 1 0
0 1
is ……………………..
A) not unit matrix B) additive identity
C) zero matrix D) multiplicative identity
Q2: 3
5A
and 2
7B
then A+B=?
A) 1
12
B) 5
12
C) 1
2
D) 1
12
Q3: 10
5A
and 2
6B
then A-B=?
A) 8
11
B) 8
11
C) 12
1
D) 12
11
Q4: Which of the following is a zero matrix
A) 0 0
0 1
B) 21 1 2 4
2 2 0
C) 2 2 0
0 3 1
D) 0 0
0 11
Q5: Which of the following is a scalar matrix
A) 2 0
0 2
B) 7 0
0 17
C) 5 0
0 25
D) 1 0
0 1
Q6: Which of the following is a unit matrix
A) 5 4 0
0 1
B) 0 0
0 0
C) 0 0
0 1
D) 0 1
1 0
Q7: Which of the following is row matrix
A) 3 4 B) 3 0
2 1
C) 0 0
0 1
D) None of these
Q8: 3 9 is a ……….
A) Row matrix B) Column matrix
C) Scalar matrix D) Zero matrix
Q9:
0
0
0
is a ………………
A) unit matrix B) zero matrix
C) scalar matrix D) diagonal matrix
Q10: 1 0
0 1
is a …………….
A) unit matrix B) row matrix
C) zero matrix D) None of these
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: If 2 4
1 8A
then ?A
A) 10 B) -12 C) 12 D) 0
Q12: If 2 4
4 8A
then which of the following is true
A) A is a non singular matrix B) A is a singular matrix
C) A is scalar matrix D) A is unit matrix
Q13: If 2 4
1 8A
then ?A
A) 2 B) -2 C) 4 D) -4
Q14: Which of the following is diagonal matrix
A) 1 0
0 1
B) 1 9
0 1
C) 1 1.2
0.8 1
D) 1 5
5 1
Q15: If 1 0
0 1A
then which of the following is false
A) A is a unit matrix B) A is a scalar matrix
C) A is a diagonal matrix D) A is a zero matrix
Q16: If 4
12
x y
x y
then which of the following is true
A) 1 1 12
1 1 4
x
y
B)
1 1 12
1 0 4
x
y
C) 1 1 4
1 1 12
x
y
D)
1 1 4
1 1 12
x
y
Q17: Which of the following is false
A) If A is a singular matrix then 0A
B) If B is a zero matrix then all terms are o
C) If A is unit matrix then 1A
D) Unit matrix is a zero matrix
Q18: What is the additive inverse of 2 9
5 4
A) 2 5
9 4
B) 2 9
5 4
C) 0 0
0 0
D) None of these
Q19: If 1 2
3 4A
then ...........tA
A) 4 2
3 1
B) 1 3
2 4
C) 4 3
2 1
D)4 3
2 1
Q20: If 4
2 2
xA
is a singuler matrix then
.............x
A) 4 B) -2 C) 2 D) -4
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Matrices and Determinants No 7
Q1: Which of the following matrix is symmetric matrix?
A) 3 4
4 3
B) 1 0
0 1
C) 3 3
0 3
D) 0 4
4 0
Q2: If
2 1 2
0 3 3
1 2 4
, then what is 23A ?
A) 3 B) 5 C) 3 D) 5
Q3: If
2 1 2
0 2 1
1 3 4
, then what is 33M ?
A) 3 B) 4 C) 3 D) 4
Q4: 21 22 23
21 22 23
4, 3, 7?
2, 1, 3
a a aA
A A A
A) 18 B) 12 C) 16 D) 21
Q5: 31 32 33
31 32 33
2, 3, 5?
2, 1, 4
a a aA
M M M
A) 13 B) 21 C) 14 D) 19
Q6: Find x if
1 4 7
0 1 8
2 30 0
4
x
has unique solution.
A) 3
8 B)
3
2 C)
2
3 D)
8
3
Q7: If 1 2
334 3
x
x
, then what is x ?
A) 3 B) 2 C) 3 D) 1
Q8:
5 0 0
3 2 1 ?
1 2 3
A) 15 B) 20 C) 10 D) 15
Q9: If 4
94
x
x , then what is x ?
A) 5,5 B) 5,5 C) 5,5 D) 5,5
Q10:
5 15 20
7 14 21 ?
4 8 12
A) 140 B) 75 C) 1 D) 0
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: Find x and y if 3 1 2 1
3 2 3 2
x
A) 2 B) 3 C) 1 D) 0
Q12: Find .x y if 3 1 7 1
3 3 4 3 11
x
y
A) 12 B) 9 C) 15 D) 21
Q13: If 1 2 3
1 0 2A
and 0 3 2
1 1 2B
, then find
4 3A B
A) 4 5 6
1 3 2
B) 4 5 6
1 3 2
C) 4 5 6
1 3 2
D) 4 3 6
1 4 2
Q14: Find 2
A if 1 2
3 0A
A) 7 2
3 6
B) 7 2
0 6
C) 7 2
0 6
D) 7 2
3 6
Q15: If 1 1 2
0 3 1A
and 2 3 0
1 2 1B
, then find
tA B
A)
3 1
3 4
1 0
B)
3 1
2 3
2 1
C)
3 1
2 5
2 0
D)
4 1
2 3
2 0
Q16: Find the multiplicative inverse of 2 1
1 1
A) 1 1
1 2
B) 1 1
1 2
C) 1 1
1 2
D) 1 1
1 2
Q17: 2 7
..........3 5
A) 2 7
3 5
B) 5
2
C) 9
8
D) 9
8
Q18: 2 2 0 3
....3 3 1 2
A) 2 5
2 1
B) 2 1
2 1
C) 2 5
2 1
D) 0
Q19: What is the value of A B if 1A B
A) 0 B) A C) I D) B
Q20: Determinant of unit matrix is ...............
A) Unit Matrix B) Scalar matrix
C) Diagonal matrix D) Zero matrix
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
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XI
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Quadratic Equations No 1
Q1: 21 ............
A) 1 B) 0 C) 1 D)
Q2: 1 ............
A) 1 B) 2 C)
2 D) 0
Q3: 21 ............
A) 1 B) C) D) 0
Q4: 50 ............
A) 1 B) 2 C) D) 1
Q5: 3 ............
A) 1 B) 2 C)
2 D) 0
Q6: 1 ............
A) 1 B) 3 C)
2 D) 2
Q7: Solve 2 5 4 0x x
A) 1, 4 B) 1,4 C) 1,3 D) 2,4
Q8: Solve 2 36 0x
A) 6 B) 6 C) 6i D)
Q9: Solve 2 4 0x
A) 4 B) 2 C) 4i D) 2i
Q10: Solve 2 3 0x x
A) 2, 3 B) 3, 2 C) 2 D) 3
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: If 2 1 3
2
i , then what is the value of
A) 1 3
2
i B)
1 3
4
i C)
1 3
2
i D)
1 3
2
i
Q12: If 1 3
2
i , then what is the value of
2
A) 1 3
2
i B)
1 3
2
C)
1 3
2
i D)
1 3
2
i
Q13: Find the cube root unity of 3 125x
A) 25,5 ,5 B)
25, 5 , 5
C) 25, 5 ,5 D)
2 35,5 ,5
Q14: 46 47 48 ...........
A) B) 3 C)
2 D) 0
Q15: Find the product of roots of 23 7 12 0x x
A) 12
3 B)
12
3 C)
7
3 D)
7
3
Q16: Find the sum of roots of 22 5 3 0x x
A) 5
2 B)
5
2 C)
3
2 D)
3
2
Q17: Solve 4 16 0x
A) 2, 2,2 , 2i i B) 4, 4,4 , 4i i
C) 8, 8,8 , 8i i D) 16, 16,16 16i i
Q18: What is the sum of roots of 4 81 0m
A) 12i B) 12i C) 12 D) 0
Q19: What is the product of roots of 4 256 0x
A) 64 B) 256 C) 16 D) 128
Q20: 4 4
1 3 1 3 ...............
A) 16 B) 16 C) 8 D) 8
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
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XI
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Quadratic Equations No 2
Q1: 1, 1, ,i i is called.......................
A) The cube roots of unity B) The fourth roots of unity
C) The fifth roots of unity D) None of these
Q2: Which of the following is false?
A) The complex fourth roots of unity are conjugate of each
other
B) The real fourth roots of unity are inverse of each other
C) Sum of all the four fourth roots of unity is zero
D) Product of all the fourth roots of unity is 1
Q3: Product of all the fourth roots of unity is equal to
.............
A) 1 B) i C) 1 D) i
Q4: Find the solution set of 2 1 0x
A) 1, 1 B) 0, 1 C) 1,0 D) ,i i
Q5: Find the solution set of 2 1 0x
A) 1, 1 B) 0, 1 C) 1,0 D) ,i i
Q6: Evaluate 821
A) 256 B) 128 C) 256 D) 128
Q7: Evaluate 28 29 1
A) 1 B) 0 C) D) 2
Q8: Evaluate 2 21 1
A) 4 B) 4 C) 4 D) 4
Q9: Evaluate
7 7
1 3 1 3
2 2
A) B) C) 1 D) 1
Q10: Evaluate 5 5
1 3 1 3
A) 32 B) 32 C) 32 D) 32
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: The highest power of a polynomial function is called
.....
A) Degree B) Power C) Monomial D) Binomial
Q12: What is the sum of roots of 4 1 0x
A) 1 B) 2 2i C) 0 D) 2
Q13: What is the sum of roots of 3 1 0x
A) 1 B) 2 C) 0 D) 2 3
Q14: What is the product of roots of 3 1 0x
A) 1 B) 2 C) 0 D) 2 3
Q15: What is the sum of real roots of 4 16 0x
A) 1 B) 1 C) 0 D) 2 3
Q16: 2 .............
A) 0 B) 1 C) 1 D)
Q17: Find the remainder when 3 2 2 4 0x x x is
divided by 1x
A) 1 B) 2 C) 2 D) 0
Q18: Find the numerical value of k if 3 2 2 6 0x x kx
has a remainder of12 , when divided by 1x
A) 1 B) 2 C) 4 D) 0
Q19: If 2 0ax bx c and
2 4 0b ac then the roots
will be....................
A) real and equal B) complex and equal
C) real and unequal D) complex and unequal
Q20: If 2 0ax bx c and
2 4 0b ac and not a perfect
number, then the roots will be....................
A) real and equal B) complex and equal
C) real and unequal D) complex and unequal
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
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CL
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Quadratic Equations No 3
Q1: Find the solutions set of 2 7 12 0x x
A) 3,4 B) 4,1
C) 4, 3 D) 4,3
Q2: Find the solutions set of 2 2x x
A) 1, 2 B) 1,2
C) 3, 4 D) 1,2
Q3: Which of the following is a radical equation?
A) 2 4 0x B) 3 1x
C) 2x D) 2 1 12x
Q4: Find the solutions set of 2 1 0x
A) 1x B) 1
2x
C) 2x D) 2x
Q5: Find the three cube roots of 8 if 1 3
2 .
A) 22, 2 , 2 B)
22, ,
C) 2 D) 22,2 ,2
Q6: Find the three cube roots of -8 if 1 3
2 .
A) 22, 2 , 2 B)
22, ,
C) 2 D) 22,2 ,2
Q7: Find the three cube roots of 27 if 1 3
2 .
A) 23,3 ,3 B)
23,3 ,3
C) 3,3 D) 21,3 ,6
Q8: 3 3 ...............a b
A) 2 2a b a ab b B) 2 2
a b a ab b
C) 2 22a b a ab b D) 2 2a b a ab b
Q9: 3 3 ...............a b
A) 2 2a b a ab b B) 2 2
a b a ab b
C) 2 22a b a ab b D) 2 2a b a ab b
Q10: 2 2 ...............a b
A) a b a b B) a b a b
C) a b a b D) 2 2
a ab b
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: 2
2
1.............x
x
A)
21
2xx
B)
21
4xx
C)
21
2xx
D)
21
2xx
Q12: 2
2
1.............x
x
A)
21
2xx
B)
21
4xx
C)
21
4xx
D)
21
2xx
Q13: 100 200 300 ?
A) 2 B)
C) 1 D) 0
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
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XI
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Partial Fractions No 1
Q1:
3
2 3x x can be written in the form of partial
fractions as ...............
A) 2 3
A B
x x
B)
232
A B
xx
C) 2
2 3
A B
x x
D)
2 3
A B
x x
Q2: If the degree of the polynomial P x is less than the
degree of the polynomial Q x in a rational fraction
P x
Q x,
then the fraction is called ..................
A) Improper Rational Fraction B) Proper Rational Fraction
C) Improper Rational Equation D) Proper Rational Equation
Q3: If the degree of the polynomial P x is equal to or
greater than the degree of the polynomial Q x in a rational
fraction
P x
Q x, then the fraction is called ........
A) Improper Rational Fraction B) Proper Rational Fraction
C) Improper Rational Equation D) Proper Rational Equation
Q4: Which of the following is quadratic factor?
A) 2 4x B)
2 1x
C) 2 2 1x x D)
2 5 4x x
Q5: Which of the following is not quadratic factor?
A) 2 4x B)
2 1x
C) 2 1x x D)
2 2x x
Q6: Which of the following is a linear factor
A) 2
x ax B) 2
x bx C) ax b D) 3 1x
Q7: Which of the following is a proper fraction?
A)
2 2 3
2 .2
x x
x x
B)
3 2 8
9
x x
x
C)
1 1 3
1 1 4
x x x
x x x
D) 1
x
Q8: Which of the following is an improper fraction?
A)
2 2 3
2 . 1 . 1
x x
x x x
B)
3
4
2 8
9
x x
x
C) x a x b x c
x a x b x c
D)
2
3
1
1
x
x
Q9: The partial fraction of 2
1
1x is ............
A)
1 1
2 1 2 1x x
B)
1 1
2 1 2 1x x
C)
1 1
2 1 2 1x x
D)
1 1
2 1 2 1x x
Q10: To resolve a combined fraction into its pars is
called………….
A) Partial Fractions B) Proper Fraction
D) Improper Fraction D) Combined Fraction
Q11: The form of partial fractions of
2
1
1 4x x is:
A) 21 4
A B
x x
B)
21 4
A Bx C
x x
C) 1 2 2
A B C
x x x
D)
2
1
1 4
A
x x
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q12: The form of partial fractions of 2
4
3 4
x
x x is:
A) 2
4
1 4
x
x x
B)
21 4
A B
x x
C) 3 2 2
A B C
x x x
D)
23 4
A Bx C
x x
Q13: The form of partial fractions of 2 2
1
1 4
x
x x
is:
A) 2 21 4
A B
x x
B)
2 21 4
Ax B Cx D
x x
C)
2
2 21 4
Ax B Cx Dx
x x
D)
2 21 4
Ax B Cx D
x x
Q14: The form of partial fractions of
2
2 2
1
1 3
x
x x
is:
A) 2 21 31
A Bx C Dx E
x xx
B) 2 21 31
A B C
x xx
C) 2 21 31
A B Cx D
x xx
D) 2 2
1 31 3
A B C D
x xx x
Q15: The form of partial fractions of
1
1
x
x x
is:
A) 1
A B
x x
B)
1
A Bx C
x x
C) 1 1
1x x
D)
1
A B
x x
Q16: Resolve 3
2
1x
A) 2
2
1 1
x
x x x
B)
2
2 2
1 1
x
x x x
C) 2
2 2
1 1
x
x x x
D)
2
1 2
1 1
x
x x x
Q17: Resolve 3
11
1x
A) 2
11 11 22
3 1 3 1
x
x x x
B)
2
11 11 22
1 1
x
x x x
C) 2
11 11 22
3 1 3 1
x
x x x
D)
2
11 22 11
3 1 3 1
x
x x x
Q18: Partial fractions of 2
1
1x are equivalent to:
A)
1 1
2 1 2 1x x
B)
1 1
2 1 2 1x x
C)
1 1
4 1 4 1x x
D)
1 1
2 1 2 1x x
Q19: Partial fractions of 2
1
4x are equivalent to:
A)
1 1
4 1 4 1x x
B)
1 1
2 1 2 1x x
C)
1 1
4 2 4 2x x
D)
1 1
4 2 4 2x x
Q20: Partial fractions of 2
1
9x are equivalent to
……………
A)
1 1
9 3 9 3x x
B)
1 1
3 3 3 3x x
C)
1 1
6 3 6 3x x
D)
1 1
4 1 4 1x x
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 1
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CL
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For any question mail us at [email protected]
Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Sequences and Series No 1
Q1: An arrangement of number formed according to some
definite rule is called:
A) Series B) Polynomial
C) Sequence D) Equation
Q2: A sequence is a function whose domain is the set of:
A) Integers B) Real No.
C) Natural no. D) Even No.
Q3: The sequence whose difference between every two
consecutive terms is a same is called:
A) G.P B) H.P C) Binomial D) A.P
Q4: The general term of .A P is:
A) 1
1
n
na a r
B) 1 1n
a a n d
C) 1 1n
a a n d D) 1
2n
n na
Q5: The general term of the sequence 1,1, 1,1,..... is:
A) 1n
na B) n
a n
C) 11
n
na
D) 11
n
na
Q6: The sequence whose general term is
1 2n
n
na
n
is:
A) 1 1
1,0, ,3 2
B)
1 11,0, ,
3 2
C) 1 1
1,0, ,3 2
D)
1 11,0, , ,...
3 2
Q7: The sequence whose general term is
1 1n
na n is:
A) 2,3, 4,5 B) 2,3, 4,5
C) 2, 3,4,5 D) 2,3,4, 5
Q8: If 1 5a and 3d ,then 10 ?a
A) 30 B) -32 C) 31 D) 32
Q9: If , ,a A b are in A.P , then ?A
A) Geometric Mean B) Arithmetic Mean
C) Harmonic Mean D) None of these
Q10: The .A M between 4 5 & 2 5 is:
A) 2 5 B) 5
3 C) 3 5 D)
6 5
7
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: The10thterm of the sequence
52, ,3,....
2is:
A) 13
2 B)
13
2
C)
11
2 D)
2
13
Q12: The A.M between 2 3x y and8 5x y is:
A) 5x y B) 3x y C) 5x y D) 3x y
Q13: Which term of the .A P3 13
,2, ,...4 4
is98
4?
A) 21st B) 19th
C) 20th D) 18th
Q14: The 8th term of A.P
3 13,2, ,...
4 4 is:
A) 39
4 B)
38
4 C)
37
4 D)
43
4
Q15: The A.M between the two numbers 5 4 and
5 4 is:
A) 5 B) 2 5 C) 4 5 D) 5
Q16: How many terms are in A.P if 30,n
a 25,d
5a ?
A) 1 B) 2 C) 3 D) 4
Q17: The A.M between a and b is:
A) 2
a b B)
2ab
a b C)
2
a b D) ab
Q18: The H.M between a and b is:
A) 2
a b B)
2
a b C)
2
a b
ab
D)
2ab
a b
Q19: The G.M between a and b is:
A) a b B) ab C) a b D) 2
a b
Q20: The Sum of the terms of a sequence is called:
A) Sequence B) Series C) Function D) Fraction
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 1
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Sequences and Series No 2
Q1: The sum for 1 2 3 4 ..... n is:
A) 1 1a n d B) 1
2
n n
C) 1
2
n n D) NONE
Q2: 1 1 1 12 ... 1 ?a a d a d a n d
A) 1 12
na n d B) 12 1n a n d
C) 12 12
na n d D) 12 1
2
na n d
Q3: Which formula is used for arithmetic series?
A) 1 12
n
nS a n d B) 1
2n n
nS a a
C)
1
1
1
n
n
rS a
r
D) NONE
Q4: The sum of 1st 100 positive even integers is:
A) 10000 B) 10111 C) 10101 D) 10100
Q5: The sum of the series 5 9 13 ... 41 is:
A) 220 B) 230 C) 240 D) 280
Q6: The sum of the series 8 6 4 ... up to 10 terms is:
A) -8 B) 8 C) 10 D) -10
Q7: How many terms of the series
11 7 3 ... will sum up 304?
A) 19
2n
B) 15n C) 16n D) 17n
Q8: The sequence 1 2 3
1 1 1 1 1, , , ,..., na a r a r a r a r is called …
A) A sequence B) H.P
C) G.P D) A.P
Q9: The H.M between 9 and 11is:
A) 9
10 B)
7
10
C) 99
10 D) None of these
Q10: The positive G.M between 4 and 64 is:
A) 4 B) 16 C) 32 D) 64
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: In G.P 1
1
n
na a r
where r is:
A) Common difference B) Common Ratio
C) Common Factor D) NONE
Q12: If the 1st three terms of G.P are 1,
3,
4
9
16 then the 6th
term is:
A) 242
257 B)
241
1024 C)
243
1024 D) None
Q13: The 7th term of the G.P 5,15,.... is:
A) 3544 B) 3645 C) 3646 D) 3640
Q14: The general term of a G.P is:
A)1
n
na a r B)
1
1
n
na a r
C) 1
1
n
na a r
D) 1na a r
Q15: If 1r then the G.S is called as:
A) Convergent B) Divergent C) Finite D) Constant
Q16: If 1r then the infinite G.S is called as:
A) Divergent B) Convergent C) Finite D) Constant
Q17: If , ,a G b are in G.P then G is called:
A) Geometric Progression B) Geometric mean
C) A.M D) Harmonic Mean
Q18: If 1 44, 256,a a then r is:
A) 2 B) 3 C) 4 D) 1
2
Q19: The geometric mean between 1
22
and 1
122
is:
A) 5 5
3 B)
5
2 C)
5 2
2 D)
5 5
2
Q20: The sum of the series 1 2 3 1
1 1 1 1 1, , , ,..., na a r a r a r a r
if 1r
is:
A)
1 1
1
na r
r
B)
1
1
a
r
C)
1 1
1
na r
r
D)
1
1
nr
r
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 1
For more news and updates visit pakturkmaths.com
CL
AS
S
XI
For any question mail us at [email protected]
Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Sequences and Series No 3
Q1: If 1r then, the sum of the finite Geometric Series is:
A)
1 1
1
na r
r
B)
1 1
1
na r
r
C) 1
2
n n D) 1
2n
na a
Q2: For finite geometric series which statement is not true?
A) 1r B) 1r C) 2r D) 1r
Q3: If 1 3a , 2r then 6 .............S
A) -93 B) -102 C) -190 D) -189
Q4: How many terms are in G.P: 1 1 1
1, , ,...,2 4 1024
A) 10 B) 11 C) 12 D) None
Q5: Find the last term of 1 3 2 7 3 11 .....
A) . 1n n B) . 1n n C) . 4 1n n D) . 4 1n n
Q6: The sum of the 1st 16 terms of the Geometric Series
1 1 1 1 1 1 1.... is:
A) 1 B) -1 C) 0 D) 2
Q7: The sum of the infinite geometric series is:
A) 1
1
a
r B) 12
1
a
r C) 1
1
a
r D)
1 1
1
na r
r
Q8: The sum of the series 1 1 1
1 ....3 9 27
is:
A) 2
3 B)
2
3 C)
3
2 D)
3
2
Q9: Is the series 2 8 32 128 ... convergent?
A) Yes B) No C) Neither D) None
Q10: The series 1 1 1 1 1 ... is:
A) Convergent B) Divergent
C) Finite D) Does not converge
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: 2.410 in the common fraction is:
A) 410
999 B)
2308
999 C)
2408
999 D) None
Q12: If the first three terms of G.P are 4 3,8 3,16 3,...
then 4a is:
A) 15 3 B) 3 16 C) 16 3 D) 32 3
Q13: The reciprocal of A.P is called:
A) G.P B) G.M C) A.M D) H.P
Q14: If 1 1 1
, , ,...3 8 13
is H.P, then 12a is:
A) 1
54 B)
1
55 C)
1
59 D)
1
58
Q15: If 1 1 1 1 1 1 1 ... is a sequence to n terms
then , what is n
S if n is even.
A) 1 B) -1 C) 0 D) 2
Q16: If 1
125 2, , 8,
8 5a r n then 8 _____a
A) 16
625 B)
625
16 C)
17
125 D) NONE
Q17: The series 3 3
6 3 ...2 4
is _____
A) Divergent B) Convergent C) G.P. D) Constant
Q18: The series 1 2
1 1 1 .....a a r a r has a sum 1
1
a
r if:
A) 1r B) 1r C) 1r D) 2
3r
Q19: The sum of 2 1 1 2 1 .... is____
A) 2 B) 1
2 2
C) Possible D) Impossible
Q20: The common difference fraction of 1.321 is:
A) 44
33 B)
440
333 C)
40
33 D)
441
331
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 1
For more news and updates visit pakturkmaths.com
CL
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XI
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Sequences and Series No 4
Q1: If 2 3
2 3
1 1 1.....
3 3 3y x x x then x is:
A) 2
1
y
y B)
1
y
y C)
3
1
y
y D) NONE
Q2: If
1 1 1
8 16 3216 16 16 .....y then y is:
A) 4 B) 2 C) 3 D) 2
Q3: If A,G & H are the . , . . A M G M and H M between a
& b , then which one of the following is true:
A) A G H B) A G H
C) H A G D) G A H
Q4: The sum of the series 3 3 3 31 2 3 ......n is:
A) 22 1
4
n n B)
22 1
2
n n C)
23 1
4
n n D) NONE
Q5: The general term of the sequence 2 4 6 8, , ,.....x x x x
is:
A) 21n n
na x B) 1
1n n
na x
C) 31n n
na x D) 2n
na x
Q6: If 1 1 1
, ,a b c
are in a H.P, then b is:
A) 2ab
a b B)
2ac
a c C)
2
a c D)
2
a b
ac
Q7: If 1 1 1
,2 1 4 1
andk k k
are in H.P, then k is:
A) 1 B) 3 C) 2 D) 5
Q8: The 7th term of H.P
1 1 1, , ,.....
3 5 7 is:
A) 15 B) 1
14 C)
1
15 D)
1
10
Q9: If .G G M , .A A M and .H H M then:
A) 2 2 2.G A H B) .G A H
C) 2 .G A H D)
2.G A H
Q10: Which one is H.P?
A) 3,6,9,... B) 1 1 1
, , ,...2 5 11
C) 1 1 1
, , ,...3 6 9
D) NONE
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: If ,2 2,3 3,...y y y is a G.P, then y is:
A) 1,4 B) 1,4 C) 1, 4 D) 1, 4
Q12: 1 2 3 .............. ?n
A) 1n n B) 1
2
n n C)
1
2
n n D)
2 1
2
n n
Q13: 2 2 2 21 2 3 .............. ?n
A) 1 2 1
3
n n n B)
1 2 1
2
n n n
C) 1 2
3
n n n D)
1 2 1
6
n n n
Q14: 3 3 3 31 2 3 .............. ?n
A) 2
1
2
n n
B) 2
1
2
n n
C) 3
1
2
n n
D) 2
1
3
n n
Q15: 0
1 ?n
n
k
S
A) 1 B) n C) 1n D) 2
n
Q16: 0
?n
n
k
S k
A) 1n n B) 1
2
n n C)
1
2
n n D)
2 1
2
n n
Q17: 2
0
?n
n
k
S k
A) 1 2 1
3
n n n B)
1 2 1
6
n n n
C) 1 2
3
n n n D)
1 2
6
n n n
Q18: 3
0
?n
n
k
S k
A) 2
1
2
n n
B) 2
1
2
n n
C) 3
1
2
n n
D) 2
1
3
n n
Q19: The difference of two consecutive terms of an A.P is
called its:
A) A.M B) G.M
D) Common Difference D) Common Ratio
Q20: 5,15,20,25 ... is:
A) A.M B) G.M D) H.M D) NONE
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 1
For more news and updates visit pakturkmaths.com
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XI
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Sequences and Series No 5
Q1: 2,8,32,...............is ..........................
A) A.M B) G.M D) H.M D) None
Q2: (n-1) th term of an A.P is ..................
A) 1 1a n d B) 12 1a n d
C) 1 2a n d D) 12 2a n d
Q3: The common difference of the sequence
3,15,27,.............. is ...........
A) 2 B) 12 D) 6 D) None
Q4: Find the common ratio of the sequence 0.5, 0.25,
0,125,............
A) 10 B) 5 D) 0.5 D) 1.5
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 1
For more news and updates visit pakturkmaths.com
CL
AS
S
XI
For any question mail us at [email protected]
Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Permutation, Combination and Probability No 1
Q1: The product of all positive integers equal to or less
than ‘ n ’ is called ……………….. of n.
A) Factor B) Factorial
C) Sequence D) Series
Q2: If ‘ n ’ is a positive integer then !n is:
A) 2 3 ....2.1n n n B) 4 5n n n
C) 1 2 ....3.2.1n n n D) .5.4.3.2.1n
Q3: 0! ?
A) 0 B) 2 C) 1 D) -1
Q4: The arrangement of finite No of objects taken
some or all at a time in certain order is called:
A) Probability B) Factorial
C) Permutation D) Combination
Q5: 5! ?
A) 24 B) 120 C) 720 D) -120
Q6: ?n
rP
A) !
!
n
r B)
!
! !
n
r n r
C)
1 !
! !
n
r n r
D)
!
!
n
n r
Q7: ?n
nP
A) 0 B) 1 C) n D) !n
Q8: 0 ?nP
A) 0 B) 1 C) n D) !n
Q9: 10
3 ?P
A) 10!
3! B) 5040 C) 720 D)
10!
7!3!
Q10: If 3 4
n nP P , then n is:
A) 5 B) 0 C) 1 D) 4
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: Total number of words formed from the letter
“TRIANGLE” using all the letters is:
A) 41320 B) 4320
C) 40320 D) None of these
Q12: If 11 990n
P , then n is:
A) 11 B) 4 C) 19 D) 3
Q13: The numbers of signals that can be given by six
flags of different colors using three flags at a time are:
A) 6 B) 120 C) 24 D) 18
Q14: If 1 30n
P , then n is:
A) 24 B) 15 C) 30 D) 120
Q15: 16
2 ?P
A) 250 B) 240 C) 120 D) 230
Q16: 7!
?2!3!
A) 120 B) 400 C) 420 D) 24
Q17: How many words can be formed from the letter
ARTICLE using all the letters ………………..
A) 5040 B) 5050 C) 5000 D) 720
Q18: If 1
4 3: 9 :1n nP P
, then n is:
A) 8 B) 9 C) 10 D) 5
Q19: If 4 36n n
P P then n is:
A) 11 B) 10 C) 9 D) 15
Q20: The number of words can be formed from the letter
“MISSISSIPPI” using all the letters is:
A) 34650 B) 34600 C) 35650 D) None
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 1
For more news and updates visit pakturkmaths.com
CL
AS
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XI
For any question mail us at [email protected]
Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Permutation, Combination and Probability No 2
Q1: Total number of words can be formed from the letters
of the word ‘mathematics’ using all letters is:
A) 4889600 B) 4889660
C) 48899600 D) 4899660
Q2: In how many different ways can seven female be seated
at around table?
A) 750 B) 120 C) 24 D) 720
Q3: How many 7-digit numbers can be formed from
2,2,3,3,3,4,4 ?
A) 200 B) 220 C) 210 D) 720
Q4: How many different numbers greater than 3 million can
be formed from the digits 1,1,1,1,2,2,3?
A) 16 B) 15 C) 20 D) 24
Q5: How many different ways are possible of the letter
‘SOME’ ?
A) 2! B) 3! C) 4! D) 5!
Q6: ?n
rC
A)
!
!
n
n r B)
!
!
n
r
C)
!
1 !
n
r D)
!
! !
n
n r r
Q7: 1 ?n
nC
A) !n B) 1n C) n D) !n
Q8: 0 ?n
C
A) 1 B) 0 C) n D) !n
Q9: 1 ?nC
A) 1 B) !n C) 0 D) n
Q10: ?n
nC
A) 0 B) n C) 1 D) !n
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: ?n
n rC
A) n
nC B)
!
! !
n
n r r C)
!
!
n
n r D)
!
1 !
n
r
Q12: If 5
nC =
7
nC than .............n
A) 7 B) 5
C) 12 D) None of these
Q13: Which one of the following is true?
A) n
rP = ! n
rr C B)
n
rC = !n
rP r
C) n
rC =
n
rP D) !n n
r rC r P
Q14: 1 1
1 ?n n
r rC C
A) 1n
rC
B)
1
n
rC C)
n
rC D)
n
rP
Q15: If 1
3 23 7n nC C
then ?n
A) 5n B) 4n C) 6n D) 10n
Q16: If 4
nC = 5
nC then ...........n
A) 10n B) 9n C) 6n D) 8n
Q17: If 6. 4
nC =
3
nP , then ?n
A) 6 B) 7 C) 8 D) 5
Q18: If 220n
rC and 1320n
rP , then the values of n
and r are:
A) 12n , 2r B) 11, 3n r
C) 12, 3n r D) None
Q19: The total No of the diagonals in a ten sided figure is:
A) 40 B) 30 C) 35 D) 20
Q20: 16 16
10 11 ?C C
A) 16
12C B) 16
10C C) 16
15C D) 17
11C
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 1
For more news and updates visit pakturkmaths.com
CL
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XI
For any question mail us at [email protected]
Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Permutation, Combination and Probability No 3
Q1: In how many ways can ‘6’ questions be selected out of 10 questions?
A) 220 B) 120 C) 250 D) 210
Q2: If2 2
8 4: 7 :6n nC P
, then ?n
A) 50 B) 10
C) 200 D) None of these
Q3: Number of different committees of 3 men and 4 woman
out of 8 men and 6 woman are:
A) 800 B) 720
C) 840 C) None of these
Q4: The prediction of the chances that an event will occur is
called:
A) Combination B) Permutation
C) Probability D) Event
Q5: The set of all possible outcomes of an experiment is:
A) Sample space B) Permutation
C) Probability D) Event
Q6: Any subset of a sample space “S” called:
A) Event B) Element
C) Probability D) Experiment
Q7: What is the probability of selecting a prime number
from first 10 whole numbers?
A) 2
5 B)
3
10 C)
1
2 D)
3
4
Q8: An event “A”is called sure or absolute certain event if ?P A
A) 200 B) 20 C) 0 D) 1
Q9: If “S” is sample space, then ?P S
A) 0 B) 1 C) 2 D) 1/2
Q10: The two events A and B are said to be mutually
exclusive or disjoint if ?A B
A) A B) A B C) B D)
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: If B S then ?P B
A)
n B
n S B)
n S
n B
C) n B n S D) n S n B
Q12: If 0P A , then event “A” is called:
A) absolute impossible event B) favorable event
C) possible event D) sure event
Q13: The two events A and B are said to be mutually
exclusive or disjoint if A B is:
A) P A B B) P A P B
C) .P A P B D) 1
Q14: If for two events A and B,
P A B P A P B P A B , then the events A
and B are called:
A) Mutually exclusive B) Disjoint
C) Not mutually exclusive D) Sure
Q15: A dice is rolled, the probability of an event shown even
and odd number is:
A) 0 B) ½ C) 5/6 D) 1
Q16: If “A” is an event that occurs, then P not A is:
A) P A B) 1P A
C) 1P A D) 1 P A
Q17: Which of the following is true, for an event “A”
A) 0 100P A B) 0 1P A
C) 1 2P A D) 0 0.5P A
Q18: The probability of selecting a prime number from a list
of natural number 1,2,3,4,.....,33 is:
A) 1/2 B) 1 C) 1/4 D) 1/3
Q19: If there are 6 red balls out of 15 in a box, then the
probability that one ball drawn is red is:
A) 1/2 B) 2/5 C) 3/4 D) 5/2
Q20: If A and B are mutually disjoint events then
?P A B
A) P A B B) P A P B
C) .P A P B D) None of these
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 1
For more news and updates visit pakturkmaths.com
CL
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For any question mail us at [email protected]
Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Permutation, Combination and Probability No 4
Q1: cP A is equal to:
A) P A B) 1P A C) 1P A D) 1 P A
Q2: If 1,2,3,4,5,6S then probability of an event A
which denotes numbers less than 4 is:
A) 1
3P A B) 1
2P A
C) 3
4P A D) None of these
Q3: The probability that a three digit number taken at
random is divisible by 5 is:
A) 1/4 B) 11/5 C) 3/4 D) 1/5
Q4: If three coins are tossed, then what is the number of
elements in the sample space?
A) 90 B) 6 C) 8 D) 10
Q5: How many distinct permutations of the letter ENGIN
are possible?
A) 24 B) 120 C) 100 D) 96
Q6: The number of comities of 7 persons formed from a
group of 10 persons is:
A)130 B) 720 C) 120 D) 900
Q7: A dice is thrown, then the probability to get a number
divisible by 2 is:
A) 2/3 B) 1/3 C) 1/2 D) 3/5
Q8: How many distinct words are possible of the letters in
the word “PULLY”?
A) 50 B) 60 C) 120 D) 0 730
Q9:
3 !?
2 !
n
n
A) 2 !n B) 3 !n C) 3n D) 1n
Q10: 2 1 ?n n n
A) !n B) 2 !n C)
1 !
2 !
n
n
D)
2 !
1 !
n
n
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: 1
?4.3.2.1
n n
A) !n B) 4! 2 !
!
n
n
C)
!
4! 2 !
n
n D)
2 !
4! !
n
n
Q12: 10.9.8.7.6 ?
A) 10! 5! B) 10! 5! C) 10!
5! D)
5!
10!
Q13: 8.7.6
?3.2.1
A) 8!
3!5! B)
5!3!
8! C)
10!
2!8! D) 10!
Q14: 3 . 2 . 1 ........3.2.1 ?n n n
A) !n B) 1 !n
C) 3 !n D) 3 ! 3!n
Q15: 5 persons can be seated at a round table in:
A) 25 ways B) 24 ways
C) 20 ways D) 120 ways
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 1
For more news and updates visit pakturkmaths.com
CL
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S
XI
For any question mail us at [email protected]
Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Mathematical Induction and Binomial Theorem No 1
Q1: Which of the following is equal to 4a b ?
A) 4 3 2 2 3 44 6 4a a b a b ab b
B) 4 3 2 2 3 44 6 4a a b a b ab b
C) 4 3 2 2 3 44 12 4a a b a b ab b
D) 4 3 2 2 3 44 12 4a a b a b ab b
Q2: Which of the following is the binomial coefficients?
A) , , ,....,1 2 3
n n n n
n
B) , , ,....,0 1 2
n n n n
n
C) 1 2 3
, , ,....,n
n n n n
D) , , ,....,0 1 2
n n n n
n
Q3: The number of terms in the expansion 7a b is
equal to:
A) 7 B) 8 C) 6 D) 1n
Q4: The number of terms in the expansion n
a b is
....................... its index
A) one smaller than B) equal to
C) one greater than D) None of these
Q5: The sum of exponents of a and b in each term of the
expansion n
a b is equal to its:
A) 1n B) n C) 1n D) !n
Q6: The exponent of a in the expansion n
a b ............
from index to zero
A) increases B) decreases
C) doubled D) None of these
Q7: ?n
r
A) 1
n
r
B) 1
n
r
C) n
n r
D) n
n r
Q8: ?n
n r
A) 1
n
r
B) 1
n
r
C) n
r
D) n
r n
Q9: 11
?6
A) 11
5
B) 12
5
C) 10
5
D) 11
10
Q10: 3
nC exist when n is:
A) 2n B) 3n C) 3n D) 3n
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: 11
rC exist when r is:
A) 11r B) 12r
C) 11r D) Only when 11r
Q12: 11 11
4 3 ?C C
A) 11
4C B) 12
3C C) 12
4C D) 11
7C
Q13: The inequality 4 3 4n n is valid if:
A) 2n B) 2n C) 2n D) 2n
Q14: .... ?0 1 2
n n n n
n
A) !n B) 2n
C) 1
n n
n n
D) 1 !n
Q15: The inequality 2 2 1nn is valid if:
A) 3n B) 3n C) 3n D) 2n
Q16: If n is any positive integer, then 2 2 2 21 2 3 ..... ?n
A) 1 2 1
6
n n n B)
1 2 1
2
n n n
C) 1 2
6
n n n D)
1 2 1
3
n n n
Q17: If n is any positive integer, then
1 2 3 .......... ?n
A) 1
3
n n B)
1
2
n n
C) 2 1
3
n n D)
2 1
2
n n
Q18: If n is any positive integer, then 3 3 3 31 2 3 .......... ?n
A) 2
1
3
n n
B) 2
1
2
n n
C) 2
2 1
3
n n
D) 2
2 1
2
n n
Q19: If n is any positive integer, then
4 8 12 .......... 4 ?n
A) 4 1n n B) 2 1n n
C) 2 2 1n n D) 2 1n n
Q20: The inequality ! 2 1nn is valid if:
A) 3n B) 3n C) 4n D) 4n
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Mathematical Induction and Binomial Theorem No 2
Q1: The inequality 1! 3n
n is valid if ........
A) 5n B) 5n C) 3n D) 3n
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Fundamentals of Trigonometry No 1
Q1: The union of two non-collinear rays which have a
common endpoint is called:
A)Angle B) Radian
C) Degree D) Minute
Q2: The common end point of two rays is called:
A)Radian B) Degree
C) Vertex D) None of these
Q3: If the circumference of a circle is divided into 360
congruent parts, the angle subtended by one part at the centre of
the circle is called:
A)Angle B) Radian
C) Degree D) Minute
Q4: One degree is denoted by :
A)1 radian B) 1 C) 1 D) 01
Q5: The 60th part of one degree is called one:
A) Second B) Radian C) Degree D) Minute
Q6: One minute is denoted by:
A)1 radian B) 1 C) 1 D) 01
Q7: 01 is equal to:
A) 60 B) 60 C) 3600 D) 360
Q8: The 60th part of one minute is called one:
A) Second B) Radian
C) Degree D) Minute
Q9: One second is denoted by:
A) 1 radian B) 1 C) 1 D) 01
Q10: 1 is equal to:
A) 60 B) 60 C) 3600 D) 360
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Q11: A right angle is the angle of measure:
A) 90 B) 90 C) 090 D)
0360
Q12: The system of measurement in which the angle is
measured in degrees, and its sub units, minutes and seconds is
called:
A) Circular System B) Sexagesimal System
C) M K S System D) CGS System
Q13: Which of the following trigonometric ratio is positive
in third quadrant?
A) Sin B) Cosine C) Tangent D) Secant
Q14: Which of the following is false?
A) sin 23 sin 23 B) cos 20 cos20
C) tan0 0 D) cot 0 undefined
Q15: 2 2sin cos ?x x
A) 1 B) 0
C) 1 D) undefined
Q16: 2sec 1 ?x
A) 2cot x B)
2tan x
C) 1 D) 2tan x
Q17: Which of the following is false?
A) 2 2tan 1 secx x B)
2 2cot 1 cscx x
C) 2 2tan cot 1x x D)
2 2sin cos 1x x
Q18: Which of the following trigonometric ratio is negative
in second quadrant?
A) Sine B) Cosine
C) Cosecant D) Nome of them
Q19: tan 45 cot 45 ?
A) 1 B) 2
C) 1 D) undefined
Q20: Which of the following is positive?
A) sin171 B) cos187
C) tan91 D) sin 30
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Fundamentals of Trigonometry No 2
Q1: sin0 ..............
A) B) 0 C) 1 D) 1
Q2: sin30 ..............
A) 1 B) 3
2 C) 3 D)
1
2
Q3: sin 45 ..............
A) 2 B) 1
2 C)
2
2 D)
3
2
Q4: cos60 sin30 ?
A) 1 B) 2
2 C) 3 D)
1
2
Q5: sin ..............2
A) 1 B) 0
C) 1 D) Undefined
Q6: cos0 ..............
A) 1 B) 0
C) 1 D) Undefined
Q7: cos30 ..............
A) 1 B) 3
2 C) 3 D)
1
2
Q8: cos45 ..............
A) 2
2 B)
1
3 C)
2
2 D)
1
2
Q9: cos60 ..............
A) 2 B) 1
2 C)
2
2 D)
3
2
Q10: cos90 ..............
A) 1 B) 0
C) 1 D) Undefined
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Q11: tan0 ..............
A) 1 B) 0
C) 1 D) Undefined
Q12: tan30 ..............
A) 2 B) 3 C) 2
2 D)
3
3
Q13: tan 45 ..............
A) 1 B) 3 C) 1 D) 2 3
Q14: tan60 ..............
A) 2 B) 3 C) 2
2 D)
3
3
Q15: tan90 ..............
A) 1 B) 0
C) 1 D) Undefined
Q16: cot 0 ..............
A) 1 B) 0
C) 1 D) Undefined
Q17: cot30 ..............
A) 2 B) 3 C) 2
2 D)
3
3
Q18: cot 45 ..............
A) 1 B) 3
C) 1 D) 2 3
Q19: cot 60 ..............
A) 2 B) 3 C) 2
2 D)
3
3
Q20: cot90 ..............
A) 1 B) 0
C) 1 D) Undefined
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Fundamentals of Trigonometry No 3
Q1: sec0 ..............
A) 1 B) 0
C) 1 D) Undefined
Q2: sec30 ..............
A) 2 B) 3
2 C)
2
3 D) 2 3
Q3: sec45 ..............
A) 1 B) 2 C) 2
2 D) 2 2
Q4: sec60 ..............
A) 2 B) 3
2 C)
1
2 D) 2 3
Q5: sec90 ..............
A) 1 B) 0
C) 1 D) Undefined
Q6: csc0 ..............
A) 1 B) 0
C) 1 D) Undefined
Q7: csc30 ..............
A) 2 B) 3
2 C)
2
3 D)
1
2
Q8: csc45 ..............
A) 1 B) 2 C) 2
2 D) 2 2
Q9: csc60 ..............
A) 2 B) 3
2 C)
2
3 D) 2 3
Q10: csc90 ..............
A) 1 B) 0
C) 1 D) Undefined
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Q11: sin180 ..............
A) 1 B) 0
C) 1 D) Undefined
Q12: sin 270 ..............
A) 1 B) 0
C) 1 D) Undefined
Q13: sin360 ..............
A) 1 B) 0
C) 1 D) Undefined
Q14: cos180 ..............
A) 1 B) 0
C) 1 D) Undefined
Q15: cos270 ..............
A) 1 B) 0
C) 1 D) Undefined
Q16: cos360 ..............
A) 1 B) 0
C) 1 D) Undefined
Q17: tan180 ..............
A) 1 B) 0
C) 1 D) Undefined
Q18: tan 270 ..............
A) 1 B) 0
C) 1 D) Undefined
Q19: tan360 ..............
A) 1 B) 0
C) 1 D) Undefined
Q20: cot180 ..............
A) 1 B) 0
C) 1 D) Undefined
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Fundamentals of Trigonometry No 4
Q1: cot360 ..............
A) 1 B) 0
C) 1 D) Undefined
Q2: sec180 ..............
A) 1 B) 0
C) 1 D) Undefined
Q3: sec270 ..............
A) 1 B) 0
C) 1 D) Undefined
Q4: sec360 ..............
A) 1 B) 0
C) 1 D) Undefined
Q5: csc180 ..............
A) 1 B) 0
C) 1 D) Undefined
Q6: csc270 ..............
A) 1 B) 0
C) 1 D) Undefined
Q7: csc360 ..............
A) 1 B) 0
C) 1 D) Undefined
Q8: sin .............
A) P
H B)
B
H C)
P
B D)
B
P
Q9: cos .............
A) P
H B)
B
H C)
P
B D)
B
P
Q10: tan .............
A) P
H B)
B
H C)
P
B D)
B
P
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Q11: cot .............
A) P
H B)
B
H C)
P
B D)
B
P
Q12: sec .............
A) P
H B)
B
H C)
H
B D)
B
P
Q13: csc .............
A) P
H B)
B
H C)
P
B D)
H
P
Q14: sin720 ..............
A) 1 B) 0
C) 1 D) Undefined
Q15: cos210 ..............
A) 3
2 B)
3
2 C)
1
2 D)
1
2
Q16: tan300 ..............
A) 3 B) 3 C) 3
2 D)
3
2
Q17: cot120 ..............
A) 3 B) 3 C) 3
3 D)
3
3
Q18: sec450 ..............
A) 1 B) 0
C) 1 D) Undefined
Q19: csc150 ..............
A) 2 B) 2 C) 3
2 D)
3
2
Q20: tan3690 ..............
A) 1 B) 0
C) 1 D) Undefined
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Fundamentals of Trigonometry No 5
Q1: sin 300 ..............
A) 1
2 B)
3
2 C)
3
2 D) 2
Q2: cos 330 ..............
A) 1
2 B)
3
2 C)
3
2 D) 2
Q3: tan 120 ..............
A) 3 B) 3
3 C) 3 D)
3
3
Q4: cot 135 ..............
A) 1 B) 3 C) 1 D) 3
Q5: sec 225 ..............
A) 2 3
4 B) 2 C) 2 D) 2
Q6: csc 390 ..............
A) 1 B) 0 C) 2 D) 2
Q7: In which quadrant sin is positive?
A) I and II B) I and III
C) I and IV D) All
Q8: In which quadrant cos is positive?
A) I and II B) I and III
C) I and IV D) All
Q9: In which quadrant tan is positive?
A) I and II B) I and III
C) I and IV D) All
Q10: In which quadrant cot is positive?
A) I and II B) I and III
C) I and IV D) All
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: In which quadrant sec is positive?
A) I and II B) I and III
C) I and IV D) All
Q12: In which quadrant csc is positive?
A) I and II B) I and III
C) I and IV D) All
Q13: In which quadrant sin is negative?
A) II and II B) II and IV
C) III and IV D) All
Q14: In which quadrant cos is negative?
A) II and II B) II and IV
C) III and IV D) All
Q15: In which quadrant tan is negative?
A) II and II B) II and IV
C) III and IV D) All
Q16: In which quadrant cot is negative?
A) II and II B) II and IV
C) III and IV D) All
Q17: In which quadrant sec is negative?
A) II and II B) II and IV
C) III and IV D) All
Q18: In which quadrant csc is negative?
A) II and II B) II and IV
C) III and IV D) All
Q19: In which quadrant cos and tan are negative?
A) II B) III
C) IV D) I and II
Q20: In which quadrant all the trigonometric functions are
positive?
A) I-II-III and IV B) II and IV
C) III and IV D) All
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Fundamentals of Trigonometry No 6
Q1 What is the circular measure of the angle between the
hands of a watch at 4 O’clock?
A) 120 B) 150 C) 90 D) 180
Q2: What is the length of the arc intercepted on a circle of
radius 14 cm by the arms of a central angle of 45
A) 11cm B) 22cm C) 26cm D) 6cm
Q3: If 12
sin13
and the terminal arm of the angle is in
first quadrant, then cos is:
A) 12
13 B)
5
13 C)
13
5 D)
5
12
Q4: If 12
sin13
and the terminal arm of the angle is in
first quadrant, then tan :
A) 12
5 B)
5
13 C)
13
5 D)
5
12
Q5: If 1
sin2 2
and the terminal arm of the angle is in
first quadrant, then cot :
A) 7
2 B) 7 C)
1
7 D)
2
7
Q6: If 5
sin13
and the terminal arm of the angle is in
first quadrant, then sec :
A) 12
13 B)
5
13 C)
13
12 D)
5
12
Q7: If 1
cos3
and the terminal arm of the angle is in
first quadrant, then sec :
A) 2 2 B) 3 C) 3
2 D)
1
3
Q8: If tan 1 and the terminal arm of the angle is in
fourth quadrant, then sin :
A) 2 2 B) 2 C) 1
2 D)
1
2
Q9: If 1
cos2
and the terminal arm of the angle is in
fourth quadrant, then tan :
A) 2 B) 0 C) 1 D) 1
Q10: If 9
cos41
and the terminal arm of the angle is in
fourth quadrant, then cot :
A) 9
40 B)
9
40 C)
40
9 D)
40
41
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Q11: If 1
tan7
and terminal arm of the angle is not in
quad. III, then 2sec 1x :
A) 7 B) 1
7 C)
1
7 D) 7
Q12: 0 0 0 0sin 60 cos30 cos60 sin 30 :
A) sin30 B) sin 45 C) sin60 D) sin90
Q13: 0 01
2sin 45 csc 452
is:
A) 3 2
4 B) 3 2 C)
3
2 D)
4 2
3
Q14:
tan tan3 6
1 tan tan3 6
is:
A) 3
6 B)
3
3 C)
3
3 D)
3
3
Q15: if 2 0 2 0 0 0 0tan 45 cos 60 sin 45 cos 45 tan 60x Find
the value of x .
A) 1 B) 3 2 C) 3
2 D) 2
Q16: cos 330 ?
A) 1
2 B)
3
2 C)
1
2 D)
3
2
Q17: sin 765 ?
A) 2 B) 2 C) 1
2 D)
1
2
Q18: sin 675 ?
A) 2 2 B) 2 C) 1
2 D)
1
2
Q19: Which of the following is the circumference of a circle?
A) 2 r B) 2r C) r D)
22 r
Q20: Which of the following is the area of a circle?
A) 2 r B) 2r C) r D)
22 r
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Fundamentals of Trigonometry No 7
Q1: tan cot ?
A) cos B) csc sec C) sin cos D) sin
Q2: cos tan sin ?
A) 1
cos B)
1
sin C) tan D) cot
Q3:
2
2
sin?
1 cos
A) 1 B) 1 C) sin D) cos
Q4: 2
2 tan?
1 tan
A) cot 2 B) tan 2 C) tan D) cot
Q5: 1 sin 1 sin ?
A) cos B) cos C) sin D) sin
Q6: sec tan sec tan
A) sec B) 1 C) 1 D) 0
Q7: tan cos .............
A) sin B) cos C) sec D) csc
Q8: sin 45 cos45 .............
A) 2
4 B) 2 2 C) 2 D)
2
2
Q9: 1
sin .............sin
A) tan cot B) cos tan
C) cos csc D) cos cot
Q10: 2 2tan cot 2 ?x x
A) 2 2sec cscx x B)
2 2sec cscx x
C) 2 2sec cscx x D)
2 2sec cscx x
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Q11: What is the value of sin 47 if cos43 m ?
A) m B) 2 1m
C) 2 1m D)
21 m
Q12: In fourth quadrant psoitive functions are:
A) sin and csc B) cos and sec
C) tan and cot D) sin and cos
Q13: Value of 2 2 3cos sin cot
3 6 4
is:
A) 2
3 B)
3
2 C) 3 D) 2
Q14: Value of tan cot ?4 4
is:
A) 4 B) 1
2 C)
3
2 D) 2
Q15: 1
sin ?sin
x
x
A) 1
csccsc
x
x
B) 1
secsec
x
x
C) sec cscx x D) 1
coscos
x
x
Q16: Which of the following angles are coterminal?
A) 5
,3 3
B)4
,3 3
C) 17
,3 3
D) 13
,3 3
Q17: If cos 4r and sin 3r then r is:
A) 25 B) 5 C) 25 D) 25
Q18: 54 45 is ....... radians
A) 0.958 B) 0.0175
C) 0.65 D) None of these
Q19: If 3
cos2
and terminal side of the angle is not in
3rd quadrant then sin is:
A) 1
2 B)
1
2 C)
3
2 D)
3
2
Q20: If 2
tan5
and 02
then 2sec 1 is:
A) 8
5 B)
4
5 C)
4
25 D)
2
7
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Trigonometric Identities No 1
Q1: Which of the following is the distance formula?
A) 2 2
1 2 1 2d x x y y
B) 2 2
1 2 1 2d x x y y
C) 1 2 1 2d x x y y
D) 2 2
1 1 2 2d x y x y
Q2: Find the distance between 3,8A and 5,6B
A) 6 B) 2 2 C) 2 D) 2 3
Q3: cos .............x y
A) cos cos sin .sinx y x y B) cos sin sin .cosx y x y
C) cos cos sin .sinx y x y D) sin cos cos .sinx y x y
Q4: cos .............x y
A) cos sin sin .cosx y x y B) cos cos sin .sinx y x y
C) cos cos sin .sinx y x y D) sin cos cos .sinx y x y
Q5: sin .............x y
A) sin cos cos .sinx y x y B) cos sin sin .cosx y x y
C) cos cos sin .sinx y x y D) sin cos cos .sinx y x y
Q6: sin .............x y
A) sin cos cos .sinx y x y B) cos sin sin .cosx y x y
C) cos cos sin .sinx y x y D) sin cos cos .sinx y x y
Q7: Find the value of cos12
A) 3 1
2
B)
3 1
2 2
C)
3 1
2 2
D)
3 1
2
Q8: cos ...............2
A) sin B) cos C) sin D) cos
Q9: cos ...............2
A) sin B) cos C) sin D) cos
Q10: cos ...............
A) sin B) cos C) sin D) cos
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Q11: cos ...............
A) sin B) cos C) sin D) cos
Q12: 3
cos ...............2
A) sin B) cos C) sin D) cos
Q13: 3
cos ...............2
A) sin B) cos C) sin D) cos
Q14: cos 2 ...............
A) sin B) cos C) sin D) cos
Q15: cos 2 ...............
A) sin B) cos C) sin D) cos
Q16: sin ...............2
A) sin B) cos C) sin D) cos
Q17: sin ...............2
A) sin B) cos C) sin D) cos
Q18: sin ...............
A) sin B) cos C) sin D) cos
Q19: sin ...............
A) sin B) cos C) sin D) cos
Q20: 3
sin ...............2
A) sin B) cos C) sin D) cos
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Trigonometric Identities No 2
Q1: 3
sin ...............2
A) sin B) cos C) sin D) cos
Q2: sin 2 ...............
A) sin B) cos C) sin D) cos
Q3: sin 2 ...............
A) sin B) cos C) sin D) cos
Q4: tan ...............2
A) tan B) cot C) tan D) cot
Q5: tan ...............2
A) tan B) cot C) tan D) cot
Q6: tan ...............
A) tan B) cot C) tan D) cot
Q7: tan ...............
A) tan B) cot C) tan D) cot
Q8: 3
tan ...............2
A) tan B) cot C) tan D) cot
Q9: 3
tan ...............2
A) tan B) cot C) tan D) cot
Q10: tan 2 ...............
A) tan B) cot C) tan D) cot
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Q11: tan 2 ...............
A) tan B) cot C) tan D) cot
Q12: Express sin5 sin7x x as a produc
A) 2sin3 cosx x B) 2sin cos6x x
C) 2sin6 cosx x D) sin cos6x x
Q13: cot ...............2
A) tan B) cot C) tan D) cot
Q14: cot ...............2
A) tan B) cot C) tan D) cot
Q15: cot ...............
A) tan B) cot C) tan D) cot
Q16: cot ...............
A) tan B) cot C) tan D) cot
Q17: 3
cot ...............2
A) tan B) cot C) tan D) cot
Q18: 3
cot ...............2
A) tan B) cot C) tan D) cot
Q19: cot 2 ...............
A) tan B) cot C) tan D) cot
Q20: cot 2 ...............
A) tan B) cot C) tan D) cot
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Trigonometric Identities No 3
Q1: sec ...............2
A) sec B) sec C) csc D) csc
Q2: sec ...............2
A) sec B) sec C) csc D) csc
Q3: sec ...............
A) sec B) sec C) csc D) csc
Q4: sec ...............
A) sec B) sec C) csc D) csc
Q5: 3
sec ...............2
A) sec B) sec C) csc D) csc
Q6: 3
sec ...............2
A) sec B) sec C) csc D) csc
Q7: sec 2 ...............
A) sec B) sec C) csc D) csc
Q8: sec 2 ...............
A) sec B) sec C) csc D) csc
Q9: csc ...............2
A) sec B) sec C) csc D) csc
Q10: csc ...............2
A) sec B) sec C) csc D) csc
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: csc ...............
A) sec B) sec C) csc D) csc
Q12: csc ...............
A) sec B) sec C) csc D) csc
Q13: 3
csc ...............2
A) sec B) sec C) csc D) csc
Q14: 3
csc ...............2
A) sec B) sec C) csc D) csc
Q15: csc 2 ...............
A) sec B) sec C) csc D) csc
Q16: csc 2 ...............
A) sec B) sec C) csc D) csc
Q17: 2
is in:
A) First Quadrant B) Second Quadrant
C) Third Quadrant D) Fourth Quadrant
Q18: 2
is in:
A) First Quadrant B) Second Quadrant
C) Third Quadrant D) Fourth Quadrant
Q19: is in:
A) First Quadrant B) Second Quadrant
C) Third Quadrant D) Fourth Quadrant
Q20: is in:
A) First Quadrant B) Second Quadrant
C) Third Quadrant D) Fourth Quadrant
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
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XI
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Trigonometric Identities No 4
Q1: 3
2
is in ..............
A) First Quadrant B) Second Quadrant
C) Third Quadrant D) Fourth Quadrant
Q2: 3
2
is in ..............
A) First Quadrant B) Second Quadrant
C) Third Quadrant D) Fourth Quadrant
Q3: 2 is in ..............
A) First Quadrant B) Second Quadrant
C) Third Quadrant D) Fourth Quadrant
Q4: 2 is in ..............
A) First Quadrant !B) Second Quadrant
C) Third Quadrant D) Fourth Quadrant
Q5: cos315 ..................
A) 1
2 B) 2 C)
1
2 D) 3
Q6: sin540 ..................
A) 1 B) 2
2 C) 1 D) 0
Q7: tan 135 ..................
A) 1 B) 1 C) 0 D) 3
Q8: sec 300 ..................
A) 2 B) 2 C) 3 D) 3
Q9: Express sin196 as a trigonometric function of
an angle of positive degree measure less than 45
A) sin16 B) cos16 C) sin16 D) cos16
Q10: Express cos147 as a trigonometric function
of an angle of positive degree measure less than 45
A) cos33 B) cos33 C) sin33 D) sin33
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: Express sin319 as a trigonometric function of an
angle of positive degree measure less than 45
A) sin 41 B) cos41 C) sin 41 D) cos41
Q12: Express cos254 as a trigonometric function of an
angle of positive degree measure less than 45
A) cos16 B) cos16 C) sin16 D) sin16
Q13: Express tan 294 as a trigonometric function of an
angle of positive degree measure less than 45
A) cot 24 B) tan 24 C) cot 24 D) tan 24
Q14: Express cos728 as a trigonometric function of an
angle of positive degree measure less than 45
A) sin8 B) cos8 C) sin8 D) cos8
Q15: Express sin 625 as a trigonometric function of an
angle of positive degree measure less than 45
A) sin5 B) cos5 C) cos5 D) sin5
Q16: Express cos 435 as a trigonometric function of an
angle of positive degree measure less than 45
A) 2 B) 2 C) sin15 D) 3
Q17: Express sin150 as a trigonometric function of an
angle of positive degree measure less than 45
A) 2 B) 2 C) 3 D) sin30
Q18: sin 180 sin 90 .............
A) sin cos B) sin cos
C) sin sin D) cos cos
Q19: sin780 sin 480 .............
A) 3
4 B)
1
4 C)
3
2 D)
1
2
Q20: cos120 sin30 .............
A) 1
4 B)
1
4 C)
1
2 D)
1
2
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Trigonometric Identities No 5
Q1: cos11 sin11
............cos11 sin11
A) cot56 B) tan56 C) tan56 D) cot56
Q2: 2 2sin cos ..........
A) 1 B) 1 C) 0 D) cos2
Q3: sin .................
A) 21 cos B)
21 cos
C) 1 cos D) 1 cos
Q4: cos .................
A) 21 sin B)
21 sin
C) 1 sin D) 1 sin
Q5: 2 2sin 2 cos 2 ..........
A) 2 B) 1 C) 0 D) cos4
Q6: 2 2sin 20 cos 20 ..........
A) 1 B) 1 C) 0 D) 2
Q7: sin 45 ..............
A) 1sin cos
2 B) 1
sin cos2
C) 1sin cos
2 D) 1
sin cos2
Q8: cos 45 ..............
A) 1sin cos
2 B) 1
sin cos2
C) 1cos sin
2 D) 1
cos sin2
Q9: tan ...........
A) tan tan
1 tan .tan
B)
tan tan
1 tan .tan
C) tan tan
1 tan .tan
D)
tan tan
1 tan .tan
Q10: tan ...........
A) tan tan
1 tan .tan
B)
tan tan
1 tan .tan
C) tan tan
1 tan .tan
D)
tan tan
1 tan .tan
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: tan 2 ...........
A) 2
tan 2
1 tan
B) 2
tan 2
1 tan
C) 2
2 tan
1 tan
D) 2
2 tan
1 tan
Q12: sin cos ...........6 3
A) cos B) sin
C) sin D) cos
Q13: cos8 sin8
............cos8 sin8
A) cot37 B) tan37 C) tan37 D) cot37
Q14: sin 2 ............
A) sin cos B) sin cos
C) 2sin cos D) 4sin cos
Q15: cos2 ............
A) 2 2cos sin B)
2 2cos sin
C) 22sin 1 D)
21 2cos
Q16: cos2 ............
A) 2 2cos sin B) cos sin
C) cos sin D) 22cos 1
Q17: cos2 ............
A) 21 2sin B) cos sin
C) cos sin D) 2 2cos 2sin
Q18: cos ............2
A) 1 sin
2
B)
1 cos
2
C) 1 cos
2
D)
1 sin
2
Q19: sin ............2
A) 1 sin
2
B)
1 cos
2
C) 1 cos
2
D)
1 sin
2
Q20: tan ............2
A) 1 sin
sin
B)
1 cos
1 cos
C) 1 cos
1 cos
D)
1 sin
sin
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Trigonometric Identities No 6
Q1: cot :2
A) 1 sin
sin
B)
1 cos
cos
C) 1 cos
cos
D)
1 sin
sin
Q2: sin3 :
A) 33sin 4sin B)
33sin sin
C) 34sin sin D)
34sin 3sin
Q3: cos3 :
A) 34cos 3cos B)
33cos 4cos
C) 34cos 3cos D)
33cos 4cos
Q4: tan3 :
A)
3
2
tan 3tan
1 3tan
B)
3
2
tan 3tan
3 tan
C)
3
2
3tan tan
3 tan
D)
3
2
3tan tan
1 3tan
Q5: 2sin cos :
A) sin sin B) sin sin
C) cos cos D) cos cos
Q6: 2cos sin ............
A) sin sin B) sin sin
C) D) cos cos
Q7: 2cos cos ............
A) sin sin B) sin sin
C) cos cos D) cos cos
Q8: 2sin sin ............
A) sin sin B) sin sin
C) cos cos D) cos cos
Q9: sin sin :A B
A) 2sin cos2 2
A B A B B) 2cos sin
2 2
A B A B
C) 2cos cos2 2
A B A B D) 2sin sin
2 2
A B A B
Q10: sin sin :A B
A) 2sin cos2 2
A B A B B) 2cos sin
2 2
A B A B
C) 2cos cos2 2
A B A B D) 2sin sin
2 2
A B A B
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: cos cos :A B
A) 2sin cos2 2
A B A B B) 2cos sin
2 2
A B A B
C) 2cos cos2 2
A B A B D) 2sin sin
2 2
A B A B
Q12: cos cos :A B
A) 2sin cos2 2
A B A B B) 2cos sin
2 2
A B A B
C) 2cos cos2 2
A B A B D) 2sin sin
2 2
A B A B
Q13: 2 2sin cos ?
2 2
x x
A) 1
2 B) 2 C) 1 D) x
Q14: 2sin cos ?2 2
x x
A) sin 2x B) cos2x C) sin x D) cos x
Q15: 2 sin15 cos15 ?
A) 3 1
2
B)
3 1
2
C)
3
2 D)
1
2
Q16: 2 2cos 15 sin 15 ?
A) 3 1
2
B)
3 1
2
C)
3
2 D)
1
2
Q17: sin
sin 2 ?cos
x ax
x b
A) ab B) a b C) 2ab D) a
b
Q18:
2 2cos sin?
2sin cos
x x
x x
A) tan 2x B) tan x C) cot 2x D) cot x
Q19: 2
?sec cscx x
A) sin 2x B) cos2x C) sin x D) cos x
Q20: sin15 sin30 sin70 (cos20 cos75 ?
A) 2
3 B)
1
4 C)
3
2 D)
1
2
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Trigonometric Functions and Their Graphs No 1
Q1: Which of the following is the domain of sine in real
numbers?
A) R
B) 2 1 ,2
R x x k k Z
C) ,R x x k k Z
D) None of them
Q2: Which of the following is the domain of cosine in real
numbers?
A) R
B) 2 1 ,2
R x x k k Z
C) ,R x x k k Z
D) None of them
Q3: Which of the following is the domain of tangent in real
numbers?
A) R
B) 2 1 ,2
R x x k k Z
C) ,R x x k k Z
D) None of them
Q4: Which of the following is the domain of cotangent in
real numbers?
A) R
B) 2 1 ,2
R x x k k Z
C) ,R x x k k Z
D) None of them
Q5: Which of the following is the domain of secant in real
numbers?
A) R
B) 2 1 ,2
R x x k k Z
C) ,R x x k k Z
D) None of them
Q6: Which of the following is the domain of cosecant in
real numbers?
A) R
B) 2 1 ,2
R x x k k Z
C) ,R x x k k Z
D) None of them
Q7: Which of the following is the range of sine in real
numbers?
A) 1 1x x R x
B) R
C) 1 1R x x
D) 1, 1R
Q8: Which of the following is the range of cosine in real
numbers?
A) 1 1x x R x
B) R
C) 1 1R x x
D) 1, 1R
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q9: Which of the following is the range of tangent in real
numbers?
A) 1 1x x R x
B) R
C) 1 1R x x
D) 1, 1R
Q10: Which of the following is the range of cotangent in real
numbers?
A) 1 1x x R x
B) R
C) 1 1R x x
D) 1, 1R
Q11: Which of the following is the range of secant in real
numbers?
A) 1 1x x R x
B) R
C) 1 1R x x
D) 1, 1R
Q12: Which of the following is the range of cosecant in real
numbers?
A) 1 1x x R x
B) R
C) 1 1R x x
D) 1, 1R
Q13: A function is said to be ................. if x p D where
p is positive number f x p f x
A) Periodic function B) Range
C) Domain D) None of these
Q14: Which one of the following is periodic of sin
A) B) 2 C) 3 D) 2
Q15: Which one of the following is periodic of cos
A) B) 2 C) 3 D) 2
Q16: Which one of the following is periodic of tan
A) B) 2 C) 3 D) 2
Q17: Which one of the following is periodic of cot
A) B) 2 C) 3 D) 2
Q18: Which one of the following is periodic of sec
A) B) 2 C) 3 D) 2
Q19: Which one of the following is periodic of csc
A) B) 2 C) 3 D) 2
Q20: Find the period of sin3x
A) 2 B) 2
3
C)
3
2
D)
2
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
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XI
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Trigonometric Functions and Their Graphs No 2
Q1: Find the period of cos2x
A) 2
B)
2
3
C) D) 2
Q2: Find the period of tan 4x
A) 3
2
B)
2
C) D)
4
Q3: Find the period of cot2
x
A) 2
B)
2
3
C) D) 2
Q4: Find the period of sin3
x
A) B) 2 C) 4 D) 6
Q5: Find the period of csc4
x
A) 8 B) 6 C) 4 D) 4
Q6: Find the period of sin5
x
A) 12 B) 10 C) 5 D) 6
Q7: Find the period of cos6
x
A) B) 6 C) 12 D) 16
Q8: Find the period of tan7
x
A) 3 B) 5 C) 7 D) 14
Q9: Find the period of cot8x
A) 3
B)
5
C)
4
5
D)
8
Q10: Find the period of sec9x
A) B) 2
9
C)
9
D)
3
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: Find the period of csc10x
A) B) 5
C) 5 D) 15
Q12: Find the period of 3sin x
A) B) 2 C) 4 D) 6
Q13: Find the period of 2cos x
A) 2 B) C) 3 D) 4
Q14: Find the period of 3cos5
x
A) 12 B) 10 C) 5 D) 6
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
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XI
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Application of Trigonometry No 1
Q1: Find the value of sin38 24
A) 0.6262 B) 0.6211 C) 0.6112 D) 0.6012
Q2: Find the value of sin38 28
A) 0.6212 B) 0.6240 C) 0.6220 D) 0.6230
Q3: Find the value of sin65 30
A) 3.1235 B) 0.900 C) 1.1943 D) 0.909
Q4: If sin 0.5100x , find x
A) 30 40 B) 20 30 C) 10 45 D) 14 55
Q5: Find the value of sin53 340
A) 0.0856 B) 0.6580 C) 0.5680 D) 0.8056
Q6: Find the value of cos36 20
A) 0.3456 B) 0.3541 C) 0.8055 D) 0.3241
Q7: Find the value of cot33 50
A) 1.4950 B) 1.4357 C) 2.0103 D) 3.1276
Q8: Find the value of tan65 30
A) 3.1235 B) 2.1943 C) 1.1943 D) 2.1345
Q9: If sin 0.5791 , find
A) 35 23 B) 33 22 C) 31 45 D) 34 51
Q10: If cos 0.5257 , find
A) 55 43 B) 55 26 C) 58 17 D) 58 51
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: If tan 1.705 , find
A) 45 43 B) 59 59 C) 59 36 D) 56 54
Q12: Find the value of c in ABC if 3.2a , 5.74b
and 90
A) 9.18 B) 6.73 C) 5.91 D) 6.98
Q13: Find the measure of 6.73 in given triangle?
A) 16 B) 4 2 C) 8 2 D) 16 2
Q14: Find the measure of 6.73 in given triangle?
A) 12 3 B) 9 3 C) 8 3 D) 4 3
Q15: A vertical pole is 8 m high and the length of its shadow
is 6 m. What is the angle of elevation of the Sun at that
moment?
A) 51 B) 52 C) 53 D) 54
Q16: A ladder leaning against a vertical wall makes an angle
of 24 with the wall. Its foot is 5 m from the wall. Find the
length.
A) 12.29m B) 12.12m C) 11.49m D) 10.64m
Q17:
tan2 ..................
tan2
A) b c
b c
B) a c
a c
C) b c
b c
D) a b
a b
Q18:
tan2 ..................
tan2
A) 2c
a b B)
a b
a b
C) 2
a b
c
D)
a b
a b
Q19:
tan2 ..................
tan2
A) c a
c a
B) c b
c b
C) a b
a b
D) a c
a c
Q20: Which of the following is the law of sines?
A) sin sin sin
a b c
B)
sin sin sin
b c a
C) 3 2 1
sin sin sin D)
sin 2 sin 2 sin 2
a b c
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
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CL
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XI
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Application of Trigonometry No 2
Q1: If sin sin
a x
, then ?x
A) c B) 1 C) 0 D) b
Q2: Which of the following is the law of cosine?
A) 2 2 2 2 cosa b c bc B)
2 2 2 2 cosb a c bc
C) 2 2 2 cos2a b c bc D)
2 2 2 cosa b c bc
Q3: 2 2 2 cos ...............b c bc
A) a B) 2
a C) 3
a D) a
Q4: cos ...............
A)
2 2 2
2
c a b
ac
B)
2 2 2
2
a b c
ab
C)
2 2 2
2
b c a
bc
D)
2 2 2
2
c a b
abc
Q5: cos ...............
A)
2 2 2
2
c a b
ac
B)
2 2 2
2
a b c
ab
C)
2 2 2
2
b c a
bc
D)
2 2 2
2
c a b
abc
Q6: cos ...............
A)
2 2 2
2
c a b
ac
B)
2 2 2
2
a b c
ab
C)
2 2 2
2
b c a
bc
D)
2 2 2
2
c a b
abc
Q7: cos ...............2
A) s s a
bc
B)
s s b
ac
C) s s c
ab
D)
s s a
ac
Q8: cos ...............2
A) s s a
bc
B)
s s b
ac
C) s s c
ab
D)
s s a
ac
Q9: cos ...............2
A) s s a
bc
B)
s s b
ac
C) s s c
ab
D)
s s a
ac
Q10: ...............s
A) 2 a b c B) 2
a b c
C) 3
a b c D) 3 a b c
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: a b c
A) 2
s B) 2s C) 3s D) 4s
Q12: 2
a b c
A) s B) 2s C) 3s D) 4s
Q13: tan ............2
A)
s c s a
s s b
B)
s a s b
s s c
C)
s b s c
s s a
D)
.
s b s c
s a
Q14: tan ............2
A)
s c s a
s s b
B)
s a s b
s s c
C)
s b s c
s s a
D)
.
s b s c
s a
Q15: tan ............2
A)
s c s a
s s b
B)
s a s b
s s c
C)
s b s c
s s a
D)
.
s b s c
s a
Q16: tan ............2
A) r
s a B)
s a
r
C) r D) R
Q17: tan ............2
A) r
s b B)
s b
r
C) r D) R
Q18: tan ............2
A) r
s c B)
s c
r
C) r D) R
Q19: Area of ABC is ......
A) 1
sin4
bc B) 1
sin2
bc
C) sinbc D) 2 sinbc
Q20: Area of ABC is ......
A) 1
sin4
ac B) 1
sin2
ac
C) sinac D) sinac
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
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XI
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Application of Trigonometry No 3
Q1: Area of ABC is ......
A) 1
sin4
ab B) 1
sin2
ab
C) sinab D) sinab
Q2: Area of ABC is ......
A) 2 sin sin
2sina
B) sin sin
2sina
C) 4 sin sin
2sina
D) sin sin
2sin
Q3: Area of ABC is ......
A) 2 sin sin
2sinb
B) sin sin
2sinb
C) 4 sin sin
2sinb
D) sin sin
2sin
Q4: Area of ABC is ......
A) 2 sin sin
2sinc
B) sin sin
2sinc
C) 4 sin sin
2sinc
D) sin sin
2sin
Q5: ............R
A) 2sin
a
B)
sin
a
C) sina D)
sin
r
Q6: ............R
A) 2sin
b
B)
sin
b
C) sinb D)
sin
r
Q7: ............R
A) 2sin
c
B)
sin
c
C) sinc D)
sin
r
Q8: ............r
A) s
B)
s a
C) s b
D) s c
Q9: 1 ............r
A) s
B)
s a
C) s b
D) s c
Q10: 2 ............r
A) s
B)
s a
C) s b
D) s c
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: 3 ............r
A) s
B)
s a
C) s b
D) s c
Q12: ............
A) s a s b s c B) s s a s b s c
C) s s a s b s c D) s a s b s c
Q13: Find the area of a triangle if 3cm , 4cm and 5cm
A) 6 B) 6 6 C) 6 2 D) 6 3
Q14: Which of the following is the area of an equilateral if
one side of the triangle is a cm?
A)
43
4
a B)
23
4
a C)
23
4
a D)
23
2
a
Q15: 1 1 1
.............ab bc ac
A) 1
2rR B)
1
r C)
1
rR D)
1
R
Q16: Find R if 13a , 14b and 15c
A) 8.13 B) 7.89 C) 8.90 D) 7.48
Q17: Find 1r if 13a , 14b and 15c
A) 7.5 B) 8.5 C) 10.5 D) 9.5
Q18: Find 2r if 13a , 14b and 15c
A) 10 B) 11 C) 12 D) 13
Q19: Find 3r if 13a , 14b and 15c
A) 14.4 B) 14.2 C) 14 D) 13.12
Q20: Find 2
3
r
r if 13a , 14b and 15c
A) 11
14 B)
6
7 C)
7
6 D)
13
14
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Application of Trigonometry No 4
Q1: 1 2 3 ............rrr r
A) B) 2 C) D)
4
Q2: 1 2 3 ............rr r
A) rs B) 2
rs C) 3
rs D) 4
rs
Q3: s
A) r B) 1r C) 2r D) 3r
Q4: s a
A) r B) 1r C) 2r D) 3r
Q5: s b
A) r B) 1r C) 2r D) 3r
Q6: s c
A) r B) 1r C) 2r D) 3r
Q7: ...............4
abc
A) R B) S C) r D) rR
Q8: 4 ...............R
A) 4abc B) abc C) abcR D) R
Q9: 2 ...............S
A) a b c B) 2
a b c C) abc D) 4abc
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 1
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XI
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Inverse Trigonometric Functions No 1
Q1: Evaluate 1sin 1 in the interval 0,
2
A) 2
B)
2
C)
3
D)
6
Q2: Evaluate 1sin 1 in the interval ,2 2
A) 3
B)
2
C)
3
D)
2
Q3: Evaluate 1 3
cos2
in the interval 0,
A) 3
B)
6
C)
6
D)
3
Q4: Evaluate 1 1
tan3
in the interval ,2 2
A) 3
B)
3
C)
6
D)
6
Q5: Evaluate 1 1
cos2
in the interval 0,
A) 3
B)
3
C)
6
D)
6
Q6: Evaluate 1 1
tan3
in the interval ,2 2
A) 3
B)
3
C)
6
D)
6
Q7: Evaluate 1cot 1 in the interval 0,
A) 3
B)
4
3
C)
3
4
D)
3
4
Q8: Evaluate 1 2
csc3
in the interval ,2 2
A) 3
B)
4
3
C)
3
4
D)
3
4
Q9: Evaluate 1 1
sin2
in the interval ,2 2
A) 3
B)
3
C)
4
D)
4
Q10: Find the value of 1 1
cos sin2
A) 1
2 B)
1
2 C) 2 D) 2
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: Find the value of 1 3
tan cos2
A) 1
3 B)
1
3 C) 3 D) 3
Q12: 1 1sin sin ................A B
A) 1 2 2sin 1 1A B B A
B) 1 2 2sin 1 1A B B A
C) 1 2 2sin 1 1A A B B
D) 1 2 2sin 1 1A B B A
Q13: Find the value of 1tan tan 1
A) 1 B) 1 C) 0 D) 3
Q14: Find the value of 1 1
sin sin2
A) 1
2 B)
1
2 C) 2 D) 2
Q15: 1 1cos cos ................A B
A) 1 2 2cos 1 1AB A B
B) 1 2 2cos 1 1AB A B
C) 1 2 2cos 1 1AB A B
D) 1 2 2cos 1 1AB A B
Q16: Find the value of 1sin tan 1
A) 1
2 B)
1
2 C) 2 D) 2
Q17: Find the value of 1 1
sec sin2
A) 2
3 B)
2
3 C)
2
2 D)
2
3
Q18: 1 1sin sin ................A B
A) 1 2 2sin 1 1A B B A
B) 1 2 2sin 1 1A B B A
C) 1 2 2sin 1 1A A B B
D) 1 2 2sin 1 1A B B A
Q19: Find the value of 1 1
tan sin2
A) 1
3 B)
1
3 C)
3
6 D)
2
3
Q20: 1 1cos cos ................A B
A) 1 2 2cos 1 1AB A B
B) 1 2 2cos 1 1AB A B
C) 1 2 2cos 1 1AB A B
D) 1 2 2cos 1 1AB A B
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Inverse Trigonometric Functions No 2
Q1: 1 1tan tan ................A B
A) 1
A B
AB
B) 1
A B
AB
C) .
1
A B
A B D)
.
1
A B
A B
Q2: 1 1tan tan ................A B
A) 1
A B
AB
B) 1
A B
AB
C) .
1
A B
A B D)
.
1
A B
A B
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
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CL
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XI
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Solution of Trigonometric Functions No 1
Q1: Factorize 2cos sin 1x x
A) sin sin 1 0x x B) sin cos 1 0x x
C) sin sin 1 0x x D) sin cos 1 0x
Q2: Find the solution set of sin 0x
A) n B) 2
n
C) 3
2
n
D) 2 1n
Q3: Find the solution set of sin 1 0x
A) 24
n
B) 3
n
C) n D) 22
n
Q4: Find the solution set of cos 0x
A) 24
n
B) 2
n
C) n D) 2n
Q5: Find the solution set of 1
cos 02
x
A) 2 4
2 23 3
n n
B) 4
2 23 3
n n
C) 2 3
2 23 2
n n
D) 2 4
3 3n n
Q6: Find the solution set of 3
sin2
x in 0,2
A) 4 5
,3 3
B) 3 3
,4 5
C) 4
,3 3
D) 2
,3
Q7: Find the solution set of csc 2x in 0,2
A) 4 7
,6 6
B) 5
,3 3
C) 5
,6 6
D) 5 2
,6 5
Q8: Find the solution set of 1
cot3
x in 0,2
A) 2 5
,3 3
B) 2
,3 3
C) 2 4
,3 3
D) 4
,3 3
Q9: What is the period of sin x in order to find the solution
set of any trigonometric equation?
A) B) 2 C) 2
D)
3
2
Q10: What is the period of cos x in order to find the solution
set of any trigonometric equation?
A) B) 2 C) 2
D)
3
2
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: What is the period of sec x in order to find the solution
set of any trigonometric equation?
A) B) 2 C) 2
D)
3
2
Q12: What is the period of csc x in order to find the solution
set of any trigonometric equation?
A) B) 2 C) 2
D)
3
2
Q13: What is the period of tan x in order to find the solution
set of any trigonometric equation?
A) B) 2 C) 2
D)
3
2
Q14: What is the period of cot x in order to find the solution
set of any trigonometric equation?
A) B) 2 C) 2
D)
3
2
Q15: What is the period of sin 2x in order to find the
solution set of any trigonometric equation?
A) B) 2 C) 2
D)
3
2
Q16: What is the period of cos2x in order to find the
solution set of any trigonometric equation?
A) B) 2 C) 2
D)
3
2
Q17: What is the period of sin3x in order to find the
solution set of any trigonometric equation?
A) B) 2 C) 2
3
D)
3
2
Q18: What is the period of cos3x in order to find the
solution set of any trigonometric equation?
A) B) 2 C) 2
2
D)
3
2
Q19: How many roots does 1
sin2
x have in the interval
0,2 ?
A) 1 B) 2 C) 3 D) 4
Q20: Find the solution set of 1
sin2
x in the interval
0,2 ?
A) 5
,6 6
B) 2
,3 3
C) 11
,6 6
D) 17
,6 6
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 1
For more news and updates visit pakturkmaths.com
CL
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XI
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Past Papers Year 2009
Q1: 1 1 i i is:
A) 1 B) 1 C) i D) i
Q2: Modulus of 8 15i is:
A) 8 B) 15 C) 17 D) 8 15i
Q3: If A has 3 elements and B has 6 elements, then
minimum number of elements in A B is:
A) 3 B) 6 C) 9 D) 18
Q4: A matrix whose determinant value is zero is known as:
A) Zero matrix B) Singular matrix
C) Non singular matrix D) identity matrix
Q5: If the sum of the roots of the equation 2 2 2 0ax x a is equal to their product, then the value of a
is:
A) 1 B) 2 C) 3 D) 4
Q6: The quotient of two polynomials
P x
Q x where
0Q x with no common factors is called a:
A) Rational fraction B) Irrational fraction
C) Polynomial D) None of these
Q7: The sum of series 2 7 12 ............... up to 12 terms
is:
A) 3 72
nn B) 3 7
2
nn
C) 3 33
nn D) None of these
Q8: What is the probability of getting a 3 when one die is
thrown?
A) 1
6 B)
1
2 C)
1
4 D)
1
3
Q9: An expression consisting or two terms is called:
A) Monomial B) Trinomial
C) Binomial D) None of these
Q10: Value of 2 2 3cos sin cot
3 6 4
is:
A) 2
3 B)
3
2 C) 3 D) 2
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: In fourth quadrant psoitive functions are:
A) sin and csc B) cos and sec
C) tan and cot D) None of these
Q12: cos cos ......................
A) 2cos sin B) 2sin cos
C) 2cos cos D) 2sin sin
Q13: tan 2 ...................
A) tan B) tan
C) cot D) cot
Q14: In any triangle ABC , 1 2 3 ......................r r r r
A) B) 2 C)
3 D) 4
Q15: 1tan ...................x
A) 1cot
2x
B) 1tan
2x
C) 1cot
2x
D) 1tan
2x
Q16: sin is .............
A) Odd function B) Even function
C) Both even and odd D) None of these
Q17: Roots of the equation 2 0ax bx c are rational if:
A) 2 4 0b ac B)
2 4 0b ac
C) 2 4 0b ac D)
2 4b ac is perfect
Q18: G.M between 5 and 80 are:
A) 85
2 B)
800
85
C) 20 D) None of these
Q19: 10
7 ..................P
A) 604800 B) 60400
C) 60000 D) None of these
Q20: If A and B are any two matrices then:
A) 0AB B) AB BA
C) AB I D) AB may not be defined
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
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XI
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Past Papers Year 2010
Q1: A decimal which has only finite number of decimal places is called ................. dcimal. A) Terminating B) Non terminating C) Recurring D) Non recurring
Q2: , ,a b c R , a b b c a c , this
inequality property of real number is ................. A) Reflexive B) Trichotomy C) Transitive D) Symmetric Q3: Multiplicative inverse of non zero complex number
,a b is:
A) 2 2 2 2
,a b
a b a b
B)2 2 2 2
,a b
a b a b
C) 2 2 2 2
,a b
a b a b
D) 2 2 2 2
,a b
a b a b
Q4: For the numbers a and b , 2
G is:..,,,444
A) A H B) A H
C) A H D) A
H
Q5: 9
2P i equal to:
A) 91 B) 6 C) -6 D) 72
Q6: An equation of the form ax by k is
homogeneous linear equation when:
A) 0, 0, 1a b k B) 0, 1, 2a b k C) 0, 0, 0a b k D) 0, 0, 0a b k
Q7: Number of roots contaning non zero imajinary part of cube roots of unity are: A) One B) Two C) Three D) Four
Q8: Partial fractions of
1
1x x are:
A) 1 1
1x x
B)
1 1
1x x
C) 1 2
1x x
D)
1 2
1x x
Q9: 1
5 and
1
8 are two terms of an H.P and their sum is
13
40, then sum of the corresponding terms of A.P will be:
A) 40
13 B)
1
13
C) 13 D) None of these
Q10: The inequality ! 2 1nn is true for integral
values of:
A) 1n B) 2n C) 3n D) 4n
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Q11: Which of the following angles are coterminal?
A) 5
,3 3
B)4
,3 3
C) 17
,3 3
D) 13
,3 3
Q12: If cos 7r and sin 3r then r is:
A) 9 B) 58 C) 58 D) 49
Q13: If is the period of tan x then period of tan3
x is:
A) 3 B) 2 C) D) 2
Q14: The circle passing through the vertices of a triangle is called a/an: A) In-circle B) Circum-circle C) Ex-circle D) Semi-circle Q15: For any equilateral triangle having sides measures
a , the value of S is:
A) 3
2
a B)
3
2
a C)
3
a D)
2
3
4a
Q16: s a
is the value of:
A) R B) r C) 1r D) 2r
Q17: Factorial form of 1n n is:
A)
1 !
2 !
n
n
B)
1 !
2 !
n
n
C)
1 !
1 !
n
n
D)
!
1 !
n
n
Q18: The matrix A is Skew Hermition when t
A is:
A) A B) A C) A D) tA
Q19: 1 1tan tan ?A B
A) 1tan1
A B
AB
B) 1tan1
A B
AB
C) 1 1
1 1
tan tan
1 tan tan
A B
A B
D) 1 1
1 1
tan tan
1 tan tan
A B
A B
Q20: Number of elements in the power set of set containing n elements is:
A) n n B) 2n C) 2n n D) 2n
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 1
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CL
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XI
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Past Papers Year 2011
Q1: Multiplicative inverse of i is:
A) i B) i C) 1 D) 1 Q2: Contra positive of i is:
A) p q B) q p
C) p q D) None of these
Q3: If A is a matrix of order m n and B is a matrix
of order n p , the order of AB will be:
A) p m B) p n
C) m p D) None of these
Q4: When polynomial 3 24 2 5x x x is divided by
1x , the remainder is:
A) 6 B) 4 C) 8 D) 0
Q5: Partial fractions of
1
1x x are:
A) 1 1
1x x
B)
1 1
1x x
C) 1 2
1x x
D)
1 2
1x x
Q6: For what value of n , 1 1
n n
n n
a b
a b
is the positive
geometric mean between a and b ?
A) 1n B) 1 C) 1
2 D) 0
Q7: Factorial form of 1 1
3.2.1
n n n is:
A) 1 !
3!.2!
n B)
1 !
3! 2 !
n
n
C)
!
3! 2 !
n
n D) None of these
Q8: The sum of coefficients in the Binomial expansion is equal to:
A) 2n B) 2 1n C) 2n D) 0
Q9: 54 45 is ....... radians
A) 0.958 B) 0.0175 C) 0.65 D) None of these
Q10: For two mutually exclusive events A and B , we have:
A) A B B) A B
C) A B A B D) None of these
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Q11: What is the middle term in the expansion of
na b for even values of n ?
A) 1
2
n B)
3
2
n
C) 2
n D) 1
2
n
Q12: Period of 3cos5
x is:
A) 10 B) 2 C) D) None of these
Q13: sin 2 ?
A) 2
2
1 tan
1 tan
B) 2
2 tan
1 tan
C) 2
2 tan
1 tan
D) None of these
Q14: The value of C in the given triangle is:
A) 4 2 B) 16
C) 8 2 D) None of these Q15: Hero's Formula is used to calculate: A) Area of triangle B) Sides of triangle C) Angles of triangle D) None of these
Q16: 12tan ?A
A) 1
2tan
1
A
A
B)
21tan1
A
A
C) 1
2
2tan
1
A
A
D) None of these
Q17: Solution set of equation 1 cos 0x is:
A) n B) 2 n
C) 2n D) 3
2n
Q18: Harmonic Mean between a and b is:
A) 2ab
a b B)
2
a b
C) 2
a b
ab
D) ab
Q19: If and are the roots of 2 0ax bx c , then
2 2 is:
A) b
a
B)
2
2
2b ac
a
C) 2
2
4b ac
a
D) None of these
Q20: A bijective function is: A) Both one-one and onto B) One-one but not onto C) Onto, but not one-one D) Neither one-one nor onto
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 1
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CL
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XI
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Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Past Papers Year 2012
Q1: 18 ?i
A) 3 B) 2 C) 1 D) 1
Q2: 4
1 i is:
A) 1 i B) 1 i C) 2 1 i D) 2 1 i
Q3: C C
x y is:
A) X Y B) X Y
C) CX Y D) None of these
Q4: If 5 2 1 5
2 1 12 3X
, then X is:
A) 1 3
2 1
B) 1 3
2 1
C) 2 3
1 1
D) 2 3
1 1
Q5: For what value of m , the roots of the equation
21 2 3 8 0m x m x m are equal?
A) 1
2
B)
2
3
C) 1
3
D) None of these
Q6: If is the cube roots of unity, then a quadratic
equation whose roots are 2 and 22 is:
A) 2 2 4 0x x B)
2 2 4 0x x
C) 2 4 0x x D)
2 2 4 0x x
Q7: If degree of P x is 3 and degree of Q x is 4, then
P x
Q x will be:
A) Proper Rational Fraction B) Improper Rational Fraction
C) Polynomial D) None of these
Q8: If a , b , c are in G.P and 0a , 0b , 0c , then
the reciprocals of a , b , c form:
A) A.P B) G.P
C) H.P D) None of these
Q9: If a , b , c are in A.P , then the common difference is:
A) 2
a c
ac
B)
2ac
a c
C) 2
a c
ac
D)
2ac
a c
Q10: A card is drawn from a pack of 52 cards at random.
What is the probability that it is either a heart or a king?
A) 4
13 B)
1
13 C)
9
13 D)
2
13
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: The middle terms in the expansion of
12
2
2
2
x
x
will
be:
A) 5th term B) 7th term
C)8th term D) 6th term
Q12: Circular measure of the angle between the hands of a
watch at 4'O clock is :
A) 6
radians B)
2
3
radians
C) 3
4
radians D)
3
radians
Q13: If 2
tan5
and 02
then 4cos 3sin
cos sin
is:
A) 14
3 B)
26
3
C) 13
7 D) None of these
Q14: The angles 90 , 180 , 270 360
are the ...... angles
A) Composite B) Half
C) Quadrantal D) Allied
Q15: The period of 3cos5
x is:
A) 5 B) 2 C) 10 D) 6
Q16: The in-radius 3cos5
x of a triangle is given by:
A) s B) s
C) s
D) None of these
Q17: 1 3
sin cos ?2
A) 0 B) 1
2 C)
1
6 D)
3
2
Q18: If and are the roots of the equation
2 1 0x p c then 1 1 is:
A) 1 c B) 2c
C) c D) None of these
Q19: Which term of 64,60,56,52,....... is zero?
A) 16th B) 17th
C) 14th D) 15th
Q20: Multiplicative inverse of 1 2i is:
A) 1 2
5
i B)
1 2
5
i
C) 1 2
4
i D) None of these
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 1
For more news and updates visit pakturkmaths.com
CL
AS
S
XI
For any question mail us at [email protected]
Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Past Papers Year 2012
Q1: 20 ?i
A) 3 B) 2 C) 1 D) 0
Q2: 2
?1 i
A) 1 i B) 1 i C) 2 1 i D) 2 1 i
Q3: If A has 3 elements, B has 5 elements then maximum
number of elements in A B is:
A) 5 B) 3 C) 2 D) 8
Q4: If 1 1
Aa b
and 2
A I then a and b are:
A) 0, 1a b B) 1, 0a b
C) 2, 1a b D) 3, 0a b
Q5: For what value of k , the sum of roots of the equation 2 4 0x kx is equal to the product of its roots?
A) 1 B) 4 C) 4 D) 4
Q6: If the roots of 2 0x px q differ by unity then
2 4p q is:
A) 0 B) 1 C) 2 D) 1
Q7: The rational fraction
P x
Q x, where 0Q x , is
Proper Rational Fraction if:
A) Deg DegP x Q x B) Deg DegP x Q x
C) Deg DegP x Q x D) None of these
Q8: If 2 2 2, ,a b c are in A.P, then a b , c a ,b c are in:
A) A.P B) G.P
C) H.P D) None of these
Q9: If 1 1 1
, ,2 1 4 1k k k
are in H.P, then the value of k is:
A) 3 B) 2 C) 1 D) 4
Q10: A die is rolled, what is the probability of getting a
number which is even and greater than 2?
A) 1
2 B)
1
3 C)
1
6 D)
2
3
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: The expansion of 1
31 2x is valid if:
A) 1x B) 1x
C) 1
2x D)
1
2x
Q12: 1 is equal to:
A) radian180
B)
180radian
C) 1
radian180
D) 180 radian
Q13: If 3
cos2
and terminal side of the angle is not in
3rd quadrant then sin is:
A) 1
2 B)
1
2
C) 3
2 D) None of these
Q14: A reference angle is always:
A) 02
B) 2
C) 0 D) None of these
Q15: The period of 5cos3
x is:
A) 3 B) 2 C) 6 D) 5
2
Q16: The in-radius 2 of a triangle is given by:
A) s
B)
4
abc
C) 2sin
c
r D)
1sin
2bc A
Q17: 1cos 2sin x
is equal to:
A) 21 2x B)
21 2x
C) 22 1x D)
21 x
Q18: If the roots of 2 0ax bx c are real an unequal
then:
A) 2 4 0b ac B)
2 4 0b ac
C) 2 4 0b ac D)
2 4 0b ab
Q19: 12 1 .........i
i
is in:
A) .A P B) .G P
C) .H P D) None of these
Q20: If 1 1 2z i and 2 2z i , then 1 2z z is:
A) 4 3
5
i B)
4 3
5
i
C) 5i D) None of these
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 1
For more news and updates visit pakturkmaths.com
CL
AS
S
XI
For any question mail us at [email protected]
Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Past Papers Year 2013
Q1: If a complex number 1 3z i then z is:
A) 4 B) 2 C) 3 D) 2i
Q2: If 1, 1, ,S i i , then set " "S is an abelian group
with respect to:
A) Addition B) Multiplication
C) Subtraction D) Division
Q3: The system of linear equations has unique solution if:
A) 0A B) 0A C) 0A D) 0A
Q4: If ij m n
A a
is a square matrix t
A A then A is:
A) Symmetric B) Skew Symmetric
C) Hermition D) None of these
Q5: The sum of cube roots of unity is:
A) 0 B) 1 C) 2 D) 3
Q6: If 2 4 0b ac then the roots of equation are:
A) Rational B) Distinct
C) Real and Equal D) Imaginary
Q7: A rational fraction
P x
Q x in which the degree of
P X is less than the degree of Q x is called:
A) Improper Fraction B) Proper Fraction
C) Common Fraction D) None of these
Q8: A.M between 2 and 3 2 is:
A) 4 2 B) 2 2
C) 6 D) None of these
Q9: The sum of infinite G.P 2, 2,1,......... is:
A) 3 2 2 B) 2 2 2
C) 4 2 2 D) 5 2 2
Q10: The number of diagonals of a 6 sided figure is:
A) 9 B) 10 C) 11 D) 12
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: In expansion of Binomial Theorem, the general term is:
A) n r
na b
r
B) n r r
na b
r
C) r r
na b
r
D) None of these
Q12: 1
2sin 45 csc452
is equal to:
A) 3
2 B)
1
2 C) 2 D)
5
2
Q13: The measure of or 3
2
lies in the .......
quadrant
A) I B) II C) III D) IV
Q14: sin sin is equal to:
A) 2cos sin B) 2sin cos
C) 2cos cos D) 2sin sin
Q15: The period of tan3
x is:
A) 2 B) C) 3 D) 4
Q16: In a triangle ABC if vertex A is at origion then the law
of cosine is:
A) 2 2 2 2 cosa b c bc B)
2 2 2 2 cosa b c bc
C) 2 2 2 2 cosb a c ac D)
2 2 2 2 cosa b c bc
Q17: In a triangle ABC if one side c and two angles ,
are given then area will be:
A)
2 sin sin
2sin
a
B)
2 sin sin
2sin
b
C)
2 sin sin
2sin
c
D)
2 sin sin
2sin
c
Q18: Circum-centre of a circle is the point of intersection of
the:
A) Perpendiculars B) Right Bisectors
C) Angle Bisectors D) Sides Bisectors
Q19: Range of 1tan x
is:
A) 2 2
x B) 0 x
C) 0 x D) None of these
Q20: If 1
cot3
x then ...................x in interval
0,2
A) 4
,3 3
B)
5,
6 6
C) 2
3
D)
5
6
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 1
For more news and updates visit pakturkmaths.com
CL
AS
S
XI
For any question mail us at [email protected]
Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Past Papers Year 2013-2
Q1: Multiplicative inverse of non zero complex number
,a b is:
A) 2 2 2 2
,a b
a b a b
B)2 2 2 2
,a b
a b a b
C) 2 2 2 2
,a b
a b a b
D) 2 2 2 2
,a b
a b a b
Q2: If 2 3z i , then z z is:
A) 4 B) 6i C) 6i D) 4i
Q3: Contra positive of p q is:
A) q p B) p q
C) q p D) None of these
Q4: The set 1, 1, ,i i possess Closure Property with
respect to:
A) Addition B) Multiplication
C) Division D) Subtraction
Q5: If all elements in a square matrix ijA a below the
principal diagonal are zero i.e. 0ija i j is called:
A) Upper Triangular Matrix B) Triangular Matrix
C) Lower Triangular Matrix D) None of these
Q6: In a square matrix ijA a , if 0ija i j and
ija K , then matrix A is called:
A) Diagonal Matrix B) Scalar Matrix
C) Unit Matrix D) Null Matrix
Q7: 1 1 i i is:
A) 1 B) i C) i D) 1
Q8: If Discriminant 2 4b ac is a perfect square, then roots
are:
A) Irrational B) Rational
C) Imaginary D) Repeated Equal
Q9: If 1 2n na a n and 1 2a , then 3 ?a
A) 6 B) 4 C) 11 D) 17
Q10: The positive Geometric Mean of -2 and 8 is:
A) 4i B) 4i C) 4 D) 4
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: If a die is rolled, then the probability of the dots on the
top are greater than 4 is:
A) 1
6 B)
1
3 C)
1
4 D)
1
2
Q12: The sum of co-efficients in the binomial expansion is:
A) 12n B)
12n C) 1 2n
n D) 2n
Q13: 12n and
12n lie in ................. quadrant
A) I B) II C) III D) IV
Q14: Value of 2 2 3cos sin cot
3 6 4
is:
A) 2
3 B)
3
2 C) 3 D) 2
Q15: The angles associated with basic angles of the measure
to a right angle or its multiple are called ....... angles
A) Supplementary B) Complementary
C) Obtuse D) Allied
Q16: sin cos6 3
is equal to:
A) cos B) sin
C) sec D) csc
Q17: The period of trigonometric function 3cos5
x is:
A) 2 B) 10
C) 5 D) None of these
Q18: In any triangle ABC , 1 2 3 ......................r r r
A) 2
rs B) 2
s C) 2 D)
2r
Q19: The value of 1 3
sin cos2
is:
A) 3
2 B)
1
2 C)
1
2 D)
1
3
Q20: The solution set of trigonometric equation
1 cos 0x is:
A) 2n B) 2n
C) 2 n D) None of these
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 1
For more news and updates visit pakturkmaths.com
CL
AS
S
XI
For any question mail us at [email protected]
Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Past Papers Year 2014
Q1: , ,a b R a b b a , this property is called:
A) Transitive B) Symmetric C) Reflexive D) Additive
Q2: 22 .......................i
A) i B) i C) 1 D) 1
Q3: If A B , then .................A B
A) A B) B C) D) X
Q4: If order of a matrix A is 2x3 and of matrix B is 3x3 the order of 'AB' is: A) 3x2 B) 2x2 C) 3x3 D) 2x3 Q5: The discriminate for equal roots is: A) >0 B) <0 C) =0 D) Perfect square
Q6: If 3 2 5ma n , its nth term is:
A) 2n+1 B) 2n+3 C) 2n-2 D) 2n-8 Q7: If a, A, b are in A)P) then 2A is:
A) a b B) 2
a b C) a b D) a b
Q8: The number of terms in the expansion of
____________n
a x
A) n+1 B)n-1 C) n D) 2n
Q9: 2!n n is true for integral value of n is:
A) 1 B) 2 C) 3 D) 4
Q10: If , , are the angles of a triangle than
tan tan ......................
A) 0 B) 1 C) 2 D) None of these
PAKTURK Success is a ladder you cannot climb with your hands in your pockets 2
Q11: cos11 sin11
...............cos11 sin11
A) tan11 B) cot11 C) tan56 D) cot56
Q12: Sine is a periodic function and its period is:
A) B) 2
C) 2 D) None of these
Q13: Geometric Means between -2 and 8 is:
A) 2 B) 8
C) 4 D) None of these Q14: All trigonometric functions are positive in quadrant:
A) I B) II C) III D) IV Q15: In a triangle ABC, the measures of the sides opposite to three angles are denoted by:
A) 1,2,3 B) A,B,C
C) , , D) a,b,c
Q16: 1 2 3. . . ............r r r r
A) s B) s-a C) D) 2
Q17: 1tan 1 ...............
A)4
B)
2
C)
4
D)
Q18: The graph of 1siny x is along the:
A) x-axis B) y-axis C) Both A and B D) None of these
Q19: In the binomial expansion of n
a b , n is called:
A) Root B) Element C) Index D) None of these
Q20: If 1r , then 1 ?n P
A) !n B) n
C) 1n D) None of these
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20