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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.  50.1 ......

(A) 0.1 (B) 1 (C) 0.001 (D) 0.00001

Sol: (D)

   55 1 5 10.1 10 10 0.00001100000     

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 2c a b  2 2 220 21c  

400 441 

C

a=20

b=21

841 2 841c 

841 29c  

Topic:Geometry / Sub-topic:Triangles / L-Easy / Ganit Prabhutwa Examination

3. Find the value of 2 2a b if 12a b  and 10ab  (A) 124 (B) 104 (C) 164 (D) 144

Sol: (A)

12a b  ; 10ab 

JEE | MEDICAL-UG | BOARDS | KVPY | NTSE | OLYMPIADS

GANIT PRABHUTWA EXAMINATION-2018 Time: 3 hrs.

Date: 09.12.2018 Std. VIII Max.Marks : 100

• RAO IIT ACADEMY / GANIT PRABHUTWA EXAMINATION-2018 / STD - VIII / QP + SOLUTIONS

2 2

 2 2 2 2a b a b ab   

 2 2 212 2 10a b   2 2144 20 a b  

2 2 124a b  

Topic:Algebra / Sub-topic:_/ L-Easy / Ganit Prabhutwa Examination

4. Which member of the set  2,3,5,7,9,11,13 is not a prime number ? (A) 2 (B) 11 (C) 9 (D) 5

Sol: (C)

9 is not a prime number.

 9 3 3  Topic:Number System / Sub-topic:Prime Numbers / L-Easy / Ganit Prabhutwa Examination

5. Which of the following is the product of 8,937 and 125 ?

(A) 93700 (B) 937000 (C) 7496500 (D) 4685000

Sol: (B)

The given three numbers are 8; 937; 125

8 937 125 

937 125 8 

937 1000

937000 Topic:Integers, Decimals & Fractions / Sub-topic: Integers/ L-Easy / Ganit Prabhutwa Examination

6. Find : :x y z if 2 3 4x y z 

(A) 6 : 4 : 3 (B) 2 :3: 4 (C) 4: 3:8 (D) 3: 2 :3 Sol: (A)

2 3 4x y z k  

2 kx  ; 3

ky  ; 4 kz 

: : : : 2 3 4 k k kx y z 

1 1 1: : 2 3 4

6 : 4 : 3 Topic: Ratios and Proportions / Sub-topic:Proportions / L-Easy / Ganit Prabhutwa Examination

• RAO IIT ACADEMY / GANIT PRABHUTWA EXAMINATION-2018 / STD - VIII / QP + SOLUTIONS

3 3

7. Find the difference between the simple interest and the compound interest on Rs. 1600 at the rate 5 p.c.p.a. for 2 years.

(A) Rs. 160 (B) Rs. 80 (C) Rs. 4 (D) Rs. 5

Sol: (C)

S.I. 1600 2 5 160

100 100 PTR  

  

. . 1 100

trC I P P      

251600 1 1600 100

      

4411600 1 400

    

411600 164 400

 

. . . . 164 160C I S I  

Rs. 4

Topic:Simple Interest and Compound Interest/ Sub-topic:_/ L-Medium / Ganit Prabhutwa Examination

8. Find the middle term (geometric mean) of 0.25 and 400.

(A) 10 (B) 1 (C) 100 (D) 0.1

Sol: (A) 2b ac , ,a b c  geometric progression

2 400 0.25b   2 4 25b  

4 25b  

100 10b  

Topic:Sequence and Series/ Sub-topic: Geometric Progressions/ L-Easy / Ganit Prabhutwa Examina- tion

9. Mohanlal got a profit 1 4

th

of the cost price when he sold an article for Rs. 400. Find the profit percent.

(A) 40 (B) 10 (C) 25 (D) 20

Sol: (C)

Let cost price be x

• RAO IIT ACADEMY / GANIT PRABHUTWA EXAMINATION-2018 / STD - VIII / QP + SOLUTIONS

4 4

profit 4 x

 Selling price 400

Profit percentage P ro fi t 1 0 0

.C P  

/ 4 100x x

 

25%

Topic:Profit and Loss/ Sub-topic:_/ L-Medium / Ganit Prabhutwa Examination

10. Whole numbers m,n are such that 121nm  . Find the value of   11 nm 

(A) 1024 (B) 10000 (C) 1 (D) 1000

Sol: (D) 2121 11 121nm   

11, 2m n 

   1 2 1 31 11 1 10 1000nm      

Topic:Number System / Sub-topic:Exponents / L-Medium / Ganit Prabhutwa Examination

(B) Write only answer of each of the following subquestions. [10 M]

1. The sides of a rectangle are 24 cm and 18 cm. Find the perimeter of the square drawn on its diagonal.

Sol. In :BCD 2 2 2BD BC CD 

   2 224 18 

A B

CD E

F

24 cm

18 cm

576 324  2 900BD cm

30 , perimeter 4 30 120BD cm cm   

Topic:Mensuration/ Sub-topic:Rectangles_/ L-Medium / Ganit Prabhutwa Examination

2. Find the values of x and a, from the information given in the adjoining figure.

105o65o

Sol. 180ACP ACB   

105 180a   

• RAO IIT ACADEMY / GANIT PRABHUTWA EXAMINATION-2018 / STD - VIII / QP + SOLUTIONS

5 5

180 105o oa  

75a  

Also, ABC ACB x   {external angle of a triangle}

A x

a B C P

105o65o 65o a x 

65 75o ox  

140x  

140 , 75ox a   

Topic:Lines and Angles / Sub-topic:_/ L-Medium / Ganit Prabhutwa Examination

3. Rakhi completes a task in 10 days, while Rama takes 5 days to finish the same task. If they work

together, in how many days will they finish the task ?

Sol. Rakhi completes a task in 10 days.

In one day, Rakhi completes 1

Similarly, in one day, Rama completes 1 5 of the task.

If Rakhi and Rama completes the task in ‘x’ days working together.

In one day, they will do 1 x of the task.

1 1 1 10 5 x

  

1 1 2 10x 

10 days 3

x 

 They will finish the task in 10 3 or 3.33 days.

Topic:Time and Work / Sub-topic:_/ L-Easy / Ganit Prabhutwa Examination

4. If 183 = 5832, then find the value of 23 5.832 5 .

Sol. 318 5832

32 3 2 13 5.832 5 5832 10 5 18 10 25 45        

Topic:Integers, Decimals & Fractions / Sub-topic:Decimals_/ L-Easy / Ganit Prabhutwa Examination

• RAO IIT ACADEMY / GANIT PRABHUTWA EXAMINATION-2018 / STD - VIII / QP + SOLUTIONS

6 6

5. The bisectors of and B C  of ABC meet at incentre I. 54m A   , find the measure of BIC .

Sol.

A

B C

I

In , 180ABC A B C     

54 180B C   

126B C    ...(i)

In , 180BIC IBC ICB BIC      ...(ii)

1But 2

IBC B   ...(iii) { the angles are bisected}

1and 2

ICB C   ...(iv)

from (ii), (iii), (iv)

1 1 180 2 2

B C BIC     

 1 180 2

B C BIC    

1 126 180 2

O BIC   

180 63BIC   

117BIC   Topic:Geometry / Sub-topic:Triangles/ L-Medium / Ganit Prabhutwa Examination

Q.2 Solve the following : [15 M]

1. PQRS is a rhombus : 40m MQR   . Find the measures of ; , ,QSR PQR QPS   .

• RAO IIT ACADEMY / GANIT PRABHUTWA EXAMINATION-2018 / STD - VIII / QP + SOLUTIONS

7 7

Sol. Given : 40oMQR 

2PQR MQR   { QM is angle bisector of PQR }

40°

2 40 80o o   180oQRS PQR  

 180 80o oQRS  

100oQRS  In :QRS

180oQRS QSR SQR   

100 40 180o o oQSR   { SQR MQR   }

40oQSR   Also, QPS QRS  

100oQPS 

40 , 80 and 100o o oQSR PQR QPS       Topic:Quadrilaterals and Polygons/ Sub-topic:Quadrilaterals/ L-Medium / Ganit Prabhutwa Examina-

tion

2. Exactly at what time between 2 and 3 will the hour hand overlap the minute hand ?

Sol. At 2 o’ clock, hour hand will be at 2 and minute hand will be at 12.

In one hour, hour hand covers 360 30 12

o o  per hour..

 In one minute, hour hand cover 030 1

60 min 2

o       

per minute.

Also, in one minute, minute hand covers 360 6 per minute 60

o o 

12 1 2

3

4 567

8 9 10

11

 Let they meet after x minutes :

 16 60 2

ox x 

 6 602 oxx  

11 60 2

ox 

120 minutes 11

x 

 They will after 120 11 or 10.909 minutes or

10 minutes 10 60 seconds 11

 

• RAO IIT ACADEMY / GANIT PRABHUTWA EXAMINATION-2018 / STD - VIII / QP + SOLUTIONS

8 8

 10 minutes + 55 seconds  They will overlap at 2 hours 10 minutes and 55 seconds

Topic:Geometry/ Sub-topic:_/ L-Medium / Ganit Prabhutwa Examination

3. Find the average of the first 20 consecutive odd numbers.

Sol. First 20 consecutive odd numbers a

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