QUIZ 2 math

QUIZ 2

 

  1. One tap can fill a water tank in 40 mins and another tap can make the filled tank empty in 60 mins. If both the taps are open together, already half filled tank would be full in-
  1. 60 min
  2. 75 min

    (C) 125 min

     (D) 120 min

 

  1. Three solid spheres have their radii 3cm, 4cm and 5cm. The spheres are melted to

form a solid sphere of bigger radius. Then the radius of the new sphere is-

  1. 3 cm
  2. 5 cm

    (C) 6 cm

    (D) 8 cm

 

  1. Two shopkeepers announce the same price of rs 1000 for a sewing machine. The first offers successive discounts of 20% and 10 % while the second offers successive discounts of 15% and 15 %. The difference in their selling price is-
  1. Rs  2.5
  2. rs 20

    (C) rs  22

    (D) rs 36

 

  1. The amount of extension in a spring is proportional to the weight hung on it. If the weight of 10 kgs produces an extension of 0.6 cm, what weight would produce an extension of 6 cm?
  1. 50 kgs
  2. 100 kgs

    (C) 80 kgs

    (D) 120 kgs

 

  1. 16 copies of a book were sold for Rs 2400 thereby gaining cost price of 4 copies. The cost price of a copy of the book is-
  1. Rs 120
  2. rs150

     (C) rs 1200

     (D) rs 1500

 

  1. In a marriage party, 45 % are women, 43 % are men and there are 156 children. How

many men are there in the marriage party?

  1. 756
  2. 448

     (C) 559

     (D) 324

 

  1. A train is running at a speed of 112 kms/ hr. The distance covered by the train in

meters in 36 secs is-

  1. 280
  2. 1120

     (C) 1080 m

     (D) 1180

 

  1. If a + b = 5, then the value of (a – 3)7 + (b – 2)7 is-
  1. 27
  2. 37

     (C) 1

     (D) 0

 

  1. If x2 – 3x + 1 = 0, then the value of x4+1/x4 is-
  1. 51
  2. 49

     (C) 47

     (D) 50

 

  1. The length of a median of an equilateral triangle is 163 cms. Then the area of the triangle is-
  1. 256 cm²
  2. 2563cm²

     (C) 5123 cm²

     (D) 768 cm²

 

  1. O is the circumcentre of a triangle ABC. The point A and the chord BC are on the opposite side of O. If BOC = 130°. Then angle BAC is-
  1. 65°
  2. 60°

     (C) 70°

     (D) 75°

 

  1. In an acute – angled triangle ABC if cos (B + C – A) = 32 and sin(C + A – B) = 1, then C is-
  1. 45°
  2. 75°

    (C) 60°

    (D) 72.5°

 

13.If P2+ 1P3 = 1 (P > 0), then the value of P3+ 1P3 is-

  1. 1
  2. 2

    (C)  3

     (D) 0

 

  1. The average salary of all workers in a workshop is RS 14000. The average salary of

7 technicians is Rs 18000 and the average salary of the rest is Rs10000. The total number of workers in the workshop is

  1. 12
  2. 13

    (C) 14

    (D) 15

 

  1. If 3a = 4b = 6c and a + b + c = 2729 , then a2+b2+c2 is equal to
  1. 87
  2. 3 29

     (C) 82

     (D) 83

 

ANS KEY

 

  1. A
2. C 3. A 4. B 5. A
6. C 7. B 8. D 9. C 10. B
11. A 12. C 13. D 14. C 15. A

 

Solutions

 

  1. (A) LCM OF 40 and 60 = 120 liter total capacity of tank

                        In one min tank fill = 3-2 = 1 liter

            Total time to fill the half tank = 60/1 = 60 min (ans)

 

  1. (c) total volume of small spheres = 4/3 * 22/7 (27+64+125)/3=22/7*288 = volume of           

           big spheres

          R3= 216

          R = 6 (ans)

       

  1. (A)  first successive discount = (20 + 10 – 20*10/100) % = 28 %

          Second successive discount = (15 + 15 – 15*15/100) % = 27.25%

            Difference in discount = .25%

            Selling price  difference = 1000* .25/100 = 2.5 (ans)

 

  1. (B)   .6 ———–10 KG

            6———–100 kg  (ans)

 

  1. (a)    Let C.P. of one book = Rs 100

         C.P. of 16 Book = 1600

          Profit =  Rs 400

          S.P.  1600 + 400 =  Rs 2000

           C.P. of 1 Book =  Rs120 (ans)

       

6 . (c) men                     women                children

          43%                     45%                      12%

          ?                                                           156

 

         12% —————-156

          43%—————42*13 = 559     (ans)

 

  1. (b) 112*5/18*36 = 1120 (ans)        

  

  1. (d)   a + b = 5

          B = 5 – a

        Put this in equation

       (a-3)7 + (5-a-2)7= (a-3)7 – (a -3)7 = 0 (ans)

 

  1. (c) x2– 3x +1 = 0

        Divide by x

        X – 3 + 1/x = 0

       X + 1/x = 3

       x^2 + 1/x^2 = 3^2 – 2 = 7

       x^4 + 1/x^4 = 7^2 – 2 = 49 – 2 = 47 (ans)

 

  1. (b) area of equilateral triangle = (163)2/3 = 2563(ans)

 

  1. (a) angle BOC = 130 degree ( o is the center of circle )

          Angle make by a chord on center is double, angle make on circumference by the same chord .

 

Angle BOC = half of angle BAC

                   = 130/2 = 65 degree (ans)

 

  1. (c) cos (B + C – A) = 32

 

B + C – A = 30° …(i)

 

sin (C + A – B) = 1

 

(C + A – B) = 90° …(ii)

 

Adding equ. (i) and (ii),

 

2C = 120o

 

C = 600 (ans)

 

  1. (c) P2+ 1P3 = 1

     Square root on both sides

P + 1/p = 3

cube on both sides

 

P3+ 1P3 = 33 –  33 = 0 (ans)

 

  1. (c) let total employ be x.

          14000*x = 7*18000 + (x-7)*10000

             14000x = 126000 + 10000x – 70000

                      X = 56000/4000 = 14 (ans)

 

  1. (a) 3a = 4b = 6c

        a : b : c

        4 : 3 : 2

       a + b + c = 2729 (Given)

     X = 329

   a2+b2+c2 = 87 (ans)

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