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2) If three metallic spheres of radii 6 cms, 8 cms and 10 cms are melted to from a single sphere, the diameter of the new sphere will be:

3) Sixty men can build a wall in 40 days, but though they begin the work together, 5 men quit every ten days. The time needed to build the wall is:

4) Shyam is travelling on his cycle and has calculated to reach point 'A' at 2 PM If he travels at 10 kmph. he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach point 'A' at 1 PM:

5) An aeroplane travelling at 700 km. p. h. in level flight drops a bomb from a height of 1000 metres on a target. The time taken from releasing the bomb to hitting the target is nearest to the figure:

6) In a History examination, the average for the entire class was 80 marks. If 10% of the students scored 95 marks and 20% scored 90 marks. What was the average marks of the remaining students of the class

Solution

Let h be the height.

Volume 3312 pi = 12*12 pi h + 2/3*pi* 12*12*12

Dividing this by 12*12 pi

23 = h + 2/3*12

23- 8 = h

ie., h = 15

Is it not the correct answer? whether this answer has been given ?

**Ques No.2**

Let the radii of the 3 spheres be r1, r2 and r3

r1 =6, r2 = 8 and r3= 10

let the radius of the new sphere formed after melting the above 3 spheres be r. the volume of the new sphere will be the total volume of the 3 spheres with radius r1, r2 and r3

ie., 4/3 pi r cube = 4/3 pi ( r1 cube+r2 cube+r3 cube)

dividing by 4/3 pi

r cube = r1 cube+r2 cube+ r3 cube = 6*6*6 + 8*8*8 + 10*10*10 = 216+512+1000 =1728

Since 12* 12*12= 1728

r = 12

^{3}+4/3*22/7*b

^{3}+4/3*22/7*c

^{3}=4/3*22/7*R

^{3}

4/3*22/7*(a

^{3}+b

^{3}+c

^{3})=4/3*22/7*R

^{3}

6

^{3}+8

^{3}+10

^{3}=R

^{3}

R

^{3}=1738

R=12

total marks of all students = 80 *100 = 8000 no. of students

10% students scored= 95 marks

total marks of 10% students = 95 * (10/100*100) = 950

similarly,

total marks of 20% students = 90*20 = 1800

marks of remaining students = 8000-1800-950 = 5250 which are the total marks of remaining students

remaining students = 70

Av. of remaining= 5250/70

= 75 ANS.

area of an equilateral triangle, A = √3a^2/4 where a is the length of a side

Area as a function of x, A(x) = √3a^2/4

A'(x) = √3a/2

when a=12, A'(x) = √3 * 12/2 = 6√3

Required rate = 6√3 cm

^{2}/min

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