GANIT PRABHUTWA EXAMINATION-2018 Date: 09.12 ... - Rao ... RAO IIT ACADEMY / GANIT PRABHUTWA EXAMINATION-2018

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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

    10 of the task.

    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