MATHS N METHODS SECTOR 10, DWARKA,NEW DELHI 110075 9811160442 [email protected]1/5/2014 Mr. Mukesh Kumar,Msc.(Maths),B.Sc.Maths(H),University Of Delhi He has hands on experience of more than 20 years in teaching and guiding students and teachers for class IX, X, XI, XII, engineering entrance exam etc. Because of wide experience exposure with all categories of students, he understands the psychological aspects of students apart from intricacies of math. MATHEMATICS FOR CLASS XI BY MATHS N METHODS
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M A T H S N M E T H O D S
S E C T O R 1 0 , D W A R K A , N E W
D E L H I 1 1 0 0 7 5
9 8 1 1 1 6 0 4 4 2
M A T H S . K M R @ G M A I L . C O M
1 / 5 / 2 0 1 4
Mr. Mukesh Kumar,Msc.(Maths),B.Sc.Maths(H),University Of Delhi He has hands on experience of more than 20 years in teaching and
guiding students and teachers for class IX, X, XI, XII, engineering
entrance exam etc. Because of wide experience exposure with all
categories of students, he understands the psychological aspects of
students apart from intricacies of math.
MATHEMATICS FOR
CLASS XI BY
MATHS N METHODS
Class XI (Mathematics) www.mathsNmethods.in
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Ch1 Sets
For 1 mark 1. If A and B are two sets such that n(A∩B)=10,n(A)=28 and n(B)=32,find n(A∪B).
1. If A and B are two sets such that n(A∪B)=50,n(A)=28 and n(B)=32,find n(A∩B).
2. How many subsets will be of a set containing 3 elements?
3. Find no. of elements in power set of A, if A= {1, 2, 4} ?
4. Find no. of elements in P(A) if A = {1,2,3}
5. Find P (A) if A= {2}.
6. Draw Venn diagram of B-A.
7. Find no. of elements in P(A) if A = {1,2,3}
8. Write in set builder form for the set A = {a,e,i,o,u}
9. Write in set builder form for the{�� , �
� , �� , �
� , � ,
}.
10. If A = {ø}, then find � ���, �� ��� ������� ����� ��� �� �.
11. Write the set {x: x2<4, x is an integer} in roster form.
12. If A = {ø}, then find ����� ��� �� �.
For 4 marks
1. A college awarded 38 medals in football, 15 in basketball and 20 in cricket. If these medals went to
a total of 58 men and only 3 men got medals in all the 3 sports, how many received medals in
exactly 2 0f the 3 sports ?
2. Write all subsets of the set {ø,1,2}.
3. Write all subsets of the set {ø,1,0}.
4. In a committee, 60 people speak French, 20 speak Spanish and 10 speak both Spanish and French.
How many speak at least one of the 2 languages?
5. In a committee, 50 people speak French, 20 speak Spanish and 10 speak both Spanish and French.
How many speak at least one of the 2 languages?
6. A and B are 2 sets If A∩X = B∩X =ø and AUX =BUX for some set X, prove that A=B.
7. For A = {1,3,5,7} , B= {1,2,3,4}, U={1,2,3,4,5,6,7,8,9}. Find (a) A-B (c) A-ø (c) A’ B
’
8. For A ={3,4,6,7} , B= {2,4,6,8} verify that (A B)’=A’U B’ for U={1,2,3,4,5,6,7,8}.
9. Verify De Morgan’s law by Venn diagram.
10. If U = {1,2,3, . . . , 10 } , A = {1,2,3} and B = { 3,4,5} then find (a) A – B (b) (A U B)’
(c) (A ∩ B)’ (d) B - A
11. For any sets A and B, show that
P(A ∩ B) = P(A) ∩ P(B)
For 6 marks
Class XI (Mathematics) www.mathsNmethods.in
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1. In a survey of 100 people, it was found that 28 people read newspaper H, 30 people read
newspaper T, 42 people read newspaper I, 8 read both H and T, 10 read both H and I, 5 read both T
and I, 3 read all three newspapers. Find the no. of people who read (a) at least one of the
newspapers and (b) newspaper I only.
2. In a survey of 60 people, it was found that 25 people read newspaper H, 26 people read newspaper
T, 26 people read newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I, 3
read all three newspapers. Find the no. of people who read at least one of the newspapers.
3. A college awarded 38 medals in football, 15 in basketball and 20 in cricket. If these medals went to
a total of 58 men and 0nly 3 men got medals in all the three sports, how many received medals in
exactly (a)1 of 3 sports (b)2 of 3 sports .
Class XI (Mathematics) www.mathsNmethods.in
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Ch2 Relation and Functions For 1 mark
1.Find the domain of the function defined by f(x) = ����√���.
2. Find the domain of the function f(x)=� !��!� � ���!�
3. If A={1,2}, B={2,4,5}, then find A X B
4. If A={1,2}, B={3,4}, then find A X (B X ø ).
5. Let f=((1,1),(2,3),(0,-1),(-1,-3)} be a linear function from Z into Z. Find f(x).
6. Define modulus function .
7. If A = {1,2 } and B = { x,y } Write A X B.
8. If A×B ={(a,x),(a,y),(b,x),(b,y)} find the set A.
9. Let A= {1,2} and B= {3,4}. Find the no. of relations from A to B.
For 4 marks
1. Find the domain and range of the real function √"� − 9
2. Find the domain and range √9 − "�
3. Find the domain and range of the function √49 − "�
4. Let A={1,2,3,4,8}. Let R be the relation on set A defined by {(a,b): a, b ЄA, b is exactly
divisible by a} a) write R in roster form b)Find the range of R.
5. Let f=((1,1),(2,3),(0,-1),(-1,-3)} be a linear function from Z into Z. Find f(x).
6. If A = {1, 2, 3, . . .,18}. Let R be the relation on A defined by R={(a,b): a,b ЄA, 3a-
b=0} then (a) Write R in roster form (b) Find the domain of R (c) Find the range of
R.
7. If A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by {(a,b): a,b ЄA, b is exactly
divisible by a} then (a) Write R in roster form (b) Find the domain of R (c) Find the
range of R.
8. The Cartesian product A X A has 9 elements among which are found (-1,0) and (0,1). Find
the set A and the remaining elements of A X A .
Class XI (Mathematics) www.mathsNmethods.in
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Ch3 Trigonometry For 1 mark
1. Evaluate tan ��)�
2. Evaluate tan �)�
3. Evaluate cos�−17100�
4. Evaluate cos�− )� �
5. 1��� �ℎ� 3456� �� �789��:�!;<= ��:
6. 1��� cosec ?��@ �� A��" = ���
�� 4�� " 5��� �� 3�� D64��4��. 7. Find cot ?− ��F
� @. 8. Find the value of cosec�− ��)
� �
9. If cot " = − ��� , x lies in 2
nd quadrant then find sin " .
10. Find the principal solution(s) of tan " =��√�
11. Evaluate sin 500
- sin 700+ sin 10
0
For 4 marks
1. Prove that HIJ ��!HIJ ��!HIJ ��JK= ��!JK= ��!JK= �� = cot 3"
3. The sum of 2 numbers is 6 times their geometric means, show that the numbers are in the ratio
(3 + 2√2): (3 - 2√2).
4. If the sum of m terms of an AP is equal to the sum of either the next n terms or the
next p terms, then prove that �w + �� ? �k − �
�@ = �w + �� ? �k − �
9@. 5.
Class XI (Mathematics) www.mathsNmethods.in
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Ch 10 Straight Lines
For 1 mark
1. Reduce the equation x-y =4 in normal form.
2. Find y intercept for the equation 2" + 3p − 5 = 0. 3. Find y intercept for the equation 12" + 3p − 5 = 0. 4. Find the slope of the line which makes an angle of 135
0 with x axis in clockwise direction.
5. Find the distance between the lines 5x+3y-7=0 and 15x+9y+14=0. 6. Find the angle between the lines 2x-y+3=0 and x+2y+3=0. 7. Find the value of λ for which the lines 3x+4y=5, 5x+4y=4 and λx+4y=6 meet at a point.
8. Find the equation of the line with slope ��� and which is concurrent with the lines 4x+3y-7=0 and
8x+5y-1=0. 9. Find the value of q if the lines x+q=0,y-2=0 and 3x+2y+5=0 are concurrent.
For 4 marks
1. Find the equation of the line whose perpendicular distance from the origin is 4 and the
angle which the normal makes with the positive direction of x axis is 150.
2. Find the equation of the right bisector of the line segment joining the points (3,4) and (-1,2).
3. Find the equation of the line passing through the point of intersection of the lines 4x + 7y -3
=0 and 2x -3y +1 =0 that has equal intercepts on the axes.
4. Find the equation of the line passing through the intersection of the lines x+y+3=0 and x-
y+2=0 and having y-intercept equal to 4.
5. Find the coordinates of the foot of perpendicular from the point (3,8) to the line x+3y=7. 6. Find the coordinates of the foot of perpendicular from the point (-1,3) to the line 3x-4y=16.
For 6 marks 1. Find the equation of the straight line which passes through the
point (3,4) and the sum of its intercepts on the axes is 14.
2. A line is such that its segment between the lines 5x-y +4 =0 and 3x+4y-4 =0 is bisected
at the point (1,5). Obtain its equation.
3. Find the image of the point (3,8) with respect to the line x+3y=7 assuming the line to
be plane mirror.
Class XI (Mathematics) www.mathsNmethods.in
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Ch11 Conic Section
For 1 mark
1. Find the equation of the parabola whose focus(6,0); directrix x=-6.
2. Find the eccentricity of the hyperbola 16x2 -9y
2 =576.
3. Find the equation of the parabola whose focus(0,6); directrix y= -6.
4. Find the length of latus rectum of the hyperbola 16x2 -9y
2 =576.
5. Find the eccentricity of the hyperbola 9x2 -16y
2 =144.
6. Find the length of latus rectum of the hyperbola 16x2 -9y
2 =576.
7. Find the equation of the parabola which is symmetric about the y- axis , and passes through the
points (2,-3).
Class XI (Mathematics) www.mathsNmethods.in
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For 4 marks
1. Find the equation of the circle passing through the points (2,-2) and (3,4) and whose centre
is on the line x + y =2.
2. Find the equation of the circle passing through the points (2,-3) and (-1,1) and whose centre
is on the line x - 3y =11.
3. Find the equation of the circle passing through the points (4,1) and (6,5) and whose centre is
on the line 4x + y =16.
4. Find the equation of the hyperbola whose foci are (0,∓12) and the length of the latus
rectum is 36.
5. Find the equation of the hyperbola whose foci are (∓4,0) and the length of the latus rectum
is 12.
6. Find the vertices, foci, eccentricity and the length of the latus rectum of the ellipse
5x2+12y
2=20.
7. Find the vertices, foci, eccentricity and the length of the latus rectum of the ellipse
5x2+15y
2=40.
For 6 marks
1. Find the equation of the circle which passes through (-1,1) and centre of the circle x
2+y
2-4x-6y-
5=0 and whose centre lies on the line x-3y-11=0.
2. Find the equation for the ellipse whose major axis on the x-axis and passes through the points
(4,3) and (6,2).
3. Find the equation for the ellipse whose major axis on the x-axis and passes through the points
(4,3) and (-1,4).
Class XI (Mathematics) www.mathsNmethods.in
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Ch12 3-D
For 1 mark
1. Write the octant of the point (2,-3,5)
2. Find the point on the x- axis which is at a distance of 4 from the point (1,2,3)
For 4 marks
1. 4 students in traditional dresses represent 4 states of India, standing at the points represented by
O(0,0,0), A(a,0,0), B(0,b,0) and C(0,0,c). Find the place, in terms of coordinates, where a girl representing
‘BHARATMATA’ be placed so that ‘BHARATMATA’ is equidistant from the 4 students. What message
does it convey?
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For 6 marks
1. Using section formulae prove that points (-2,3,5), (1,2,3) and (7,0,-1) are collinear. Also find the ratio in which
3rd
point divide line segment joining the first 2.
2. Using section formulae prove that points (3,2,-4), (5,4,-6) and (9,8,-10) are collinear. Also find the ratio in
which 3rd point divide line segment joining the first 2 .