GATE Questions

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circumference of A = 2πr = 8 => so r = 4π
volume = π×4π2×10 = 160π
circumference of B = 2πr   = 10 => so r = 5π
volume = π×5π2×8 =  200π
so ratio of capacities = 160/200 = 0.8
so capacity of A will be 80% of the capacity of B.

In the figure, there are 21 columns containing 2 cubes each and 4 columns containing 1 cube each. 

∴Total number of cubes = (21 x 2) + (4 x 1) = 42 + 4 = 46.

3/15 + 4/16 + x/24 = 1

⇒x=1315

Given word is SCOOTY

ATQ,

Except S & Y number of letters are 4(C 2O's T)

Hence, required number of arrangements = 4!/2! x 2! = 4!

= 4 x 3 x 2

= 24 ways.

We have 12 months.

In every month we get 28 or more days. 

So that implies we get 28 days in each and every month.

First line will cut all other 14, similarly second will cut 13, and so on
Total = 14+13+12+11+10+9+8+7+6+5+4+3+2+1 = 105.

It takes four of those little squares -- each one 1/2 inch on a side -- to cover one square inch. That's because each one is 1/2 x 1/2, or 1/4 of a square inch.
In a rectangle that is 48 inches by 48 inches, there are 2304 square inches.(1 ft = 12 inches)
Since it takes 4 little squares to cover 1 sq inch, then it would need 2304 x 4 squares (1/2 inch on a side each) to cover a rectangle 4 feet by 4 feet.

That is 9,216 of those squares.

Let the side of the square be 's' cm

length of rectangle = (s+5) cm

breadth of rectangle = (s-3)cm

(s+5) (s-3) = 

s2 - 5s - 3s - 15 = s2 

2s = 15

Perimeter of rectangle = 2(L+B) = 2(s+5 + s–3) = 2(2s + 2)

= 2(15 + 2) = 34 cm