RAO IIT ACADEMY / GANIT PRABHUTWA EXAMINATION-2018 / STD - VIII / QP + SOLUTIONS 1 1 N.B. For Q. No. 2 to 5 proper procedure and explanation is necessary. Q.1 Choose the correct alternative answer in each of the following. [10 M] 1. 5 0.1 ...... (A) 0.1 (B) 1 (C) 0.001 (D) 0.00001 Sol: (D) 5 5 1 5 1 0.1 10 10 0.00001 100000 Topic:Integers, Decimals & Fractions / Sub-topic:Decimals/ L-Easy / Ganit Prabhutwa Examination 2. Find the hypotenuse of a right angled triangle having sides 20 and 21 (A) 29 (B) 28 (C) 41 (D) 25 Sol: (A) 2 2 2 c a b 2 2 2 20 21 c 400 441 C a=20 b=21 841 2 841 c 841 29 c Topic:Geometry / Sub-topic:Triangles / L-Easy / Ganit Prabhutwa Examination 3. Find the value of 2 2 a b if 12 a b and 10 ab (A) 124 (B) 104 (C) 164 (D) 144 Sol: (A) 12 a b ; 10 ab JEE | MEDICAL-UG | BOARDS | KVPY | NTSE | OLYMPIADS GANIT PRABHUTWA EXAMINATION-2018 Time: 3 hrs. Date: 09.12.2018 Std. VIII Max.Marks : 100
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RAO IIT ACADEMY / GANIT PRABHUTWA EXAMINATION-2018 / STD - VIII / QP + SOLUTIONS
1 1
N.B. For Q. No. 2 to 5 proper procedure and explanation is necessary.
Q.1 Choose the correct alternative answer in each of the following. [10 M]
1. The points A, B, C, D, E, F lie on a circle. Find m BAF m FED m DCB .
Sol.
A
B
C D
E
F
Join F and C
Now, FEDC is a cyclic quadrilateral
also, FABC is a cyclic quadrilateral
Now, 0180 .......FED FCD i (opposite angles of a cyclic quadrilateral)
also 0180 .......BAF FCB ii (opposite angles of a cyclic quadrilateral)
Now adding (i) and (ii)0 0180 180FED FCD BAF FCB
RAO IIT ACADEMY / GANIT PRABHUTWA EXAMINATION-2018 / STD - VIII / QP + SOLUTIONS
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0360
0360BAF FED DCB DCB FCB FCD
Topic:Quadrilaterals and Polygons/ Sub-topic:Polygons/ L-Medium / Ganit Prabhutwa Examination2. GCD of two numbers is 23 and their product is 19044. Find all possible pairs of such numbers.
Sol. Let the numbers be x, y
GCD of , 23x y
19044xy
19044 828
23LCM
of , 23GCD x y , 828 23 36LCM 2 2of , 23 2LCM x y
Numbers can be 2 223,828 , 23 2 , 23 3
23,828 and 92,207
Topic:Number System/ Sub-topic:HCF and LCM_/ L-Difficult / Ganit Prabhutwa Examination
5) In the adjoining figure, line || line m. From the information given in the figure find the measure of .ABC
Sol.
A
BD C
0110ABC
Topic:Lines and Angles/ Sub-topic:_/ L-Easy / Ganit Prabhutwa ExaminationQ.4) Solve the following subquestions. [20 M]
1. Divide 4 24 by 2 2 .x x x Find quotient and remainder. Write answer as
dividend = divisor × quotient + remainderSol.
2 2 2x x
2 2 2x x 4 4x 4 3 22 2x x x ( )
( )
3 22 2 4x x 3 22 4 4xx x
( )
22 4 4x x 22 4 4x x
0
2Quotient 2 2x x
Remainder = 0
RAO IIT ACADEMY / GANIT PRABHUTWA EXAMINATION-2018 / STD - VIII / QP + SOLUTIONS
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4 2 24 2 2 2 2 0x x x x x
Topic:Algebra/ Sub-topic:_/ L-Medium / Ganit Prabhutwa Examination2. The speed of a boat in still water is 25 km/hr. The time required for the boat to travel 120 km against the
stream is 32 times the time required to travel the same distance along the same stream. Find the speed of the
stream.
Sol. Let speed of stream /x km hr
Speed against stream 25 /x km hr
Speed along stream 25 /x km hr
distanceTime =speed
Time against stream 32
(Time along stream)
120 3 12025 2 25x x
2 25 3 25x x
5 25x 5 /x km hr
Topic:Time, Speed and Distance/ Sub-topic:_/ L-Medium / Ganit Prabhutwa Examination
3. Solve : 2 326 0.63
xo
Sol. 2 326 0.63
xo
2 32 613 10
x
2 35 33 5
x
1 3 225 5
3 3
x
13 22
x
RAO IIT ACADEMY / GANIT PRABHUTWA EXAMINATION-2018 / STD - VIII / QP + SOLUTIONS
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13 22
x
56
x
Topic:Algebra/ Sub-topic:Exponents_/ L-Easy / Ganit Prabhutwa Examination4. If a polygon has 90 diagonals, then find the number of sides of the polygon.
Sol. Number of diagonals 3
2n n
2 3 902
n n
2 3 180n n 2 3 180 0n n
12 15 0n n
12 Rejectedn
15n
Topic:Geometry/ Sub-topic:Polygons/ L-Medium / Ganit Prabhutwa ExaminationQ.5) Solve the following subquestions. [25 M]
1. Factorise : 2 28 8 5 14x x x x
Sol. 2 28 8 5 14x x x x
2Let 8x x y
5 14y y
2 5 14y y
2 7y y
2 28 2 8 7x x x x ( 2 8x x y )
2 8 2 1 7x x x x
Consider : 2 8 2x x
2 4Roots2
b b aca
8 64 82
RAO IIT ACADEMY / GANIT PRABHUTWA EXAMINATION-2018 / STD - VIII / QP + SOLUTIONS
4. In the adjoining figure ABC and PQR are congruent. All small triangles are congruent, each side ofsmall triangle is 4 find the area of the figure.
P
Q R
A B
C
4
4
4 4 4
4
44
Sol.
4 44 4
44
4 4
44 4
4
4 4
44
4A B
RQ
C
P
Area of the figure = Area of PQR (equilateral with side length = 12)
+ 3 (area of smaller equilateral triangles with side length = 4)
RAO IIT ACADEMY / GANIT PRABHUTWA EXAMINATION-2018 / STD - VIII / QP + SOLUTIONS
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2 23 312 3 44 4
36 3 12 3 48 3 sq.units
Topic:Geometry/ Sub-topic:Triangles and Polygons_/ L-Medium / Ganit Prabhutwa Examination5. Some kg of tea at the rate of Rs. 320 per kg is mixed with 5 kg of tea at the rate of Rs. 280 per kg. Now
the rate of the mixture so formed is Rs. 300 per kg. How much tea of the rate of Rs. 320 per kg was taken?Sol. Let the amount of tea of Rs. 320 per kg taken be x kg.
Mixture contains x kg. of Rs. 320 per kg tea. + 5 kg. of Rs. 280 per kg tea.