A ray of light, after getting reflected twice from a hemispherical mirror of radius R(see the above fig), emerges parallel to the incident ray. The separation of the original incident ray and the final reflected ray is

• R

• R$\sqrt{2}$

• 2R

• R$\sqrt{3}$

A king ordered that a golden crown be made for him for 8 kg of gold and 2 kg of silver. The goldsmith took away some amount of gold and replaced it by an equal amount of silver and the crown when made, weighed 10 kg. Archimedes knew that underwater gold lost 1/20^th of its weight, when silver lost 1/10^th. When the crown was weighed underwater, it was 9.25 kg. how much gold was stolen by the goldsmith?

• 0.5 kg

• 1 kg

• 2 kg

• 3 kg

What is the angle between the minute and hour hands of the clock at 7:35?

• 0°

• 17.5°

• 19.5°

• 20°

A stream of ants go from point A to point B and return to point A along the same path all the ants move at a constant speed and from any given point 2 ants pass per second one way. It takes 1 minute for an ant to go from A to B. How many returning ants will an ant meet in its journey from A to B?

• 120

• 60

• 240

• 180

The capacity of the conical vessel shown above is V. it is filled with water up to half its height. The volume of water in the vessel is

• $\frac{\mathrm{v}}{2}$

• $\frac{\mathrm{v}}{4}$

• $\frac{\mathrm{v}}{8}$

• $\frac{\mathrm{v}}{16}$

A large tank filled with water is to be emptied by removing half of the water present in it every day. After how many days will there be closet to 10% water left in the tank?

• One

• Two 

• Three

• Four

N is a natural number. If n⁵ is odd, which of the following is true?

(A) n is odd

(B) n³ is odd

(C) n⁴ is even

• A only

• B only

• C only

• A and B only

Suppose you expand the product (x₁ + y₁)(x₂ + y₂)…..(x₂₀ + y₂₀). How many terms will have only one x and rest y’s?

• 1

• 5

• 10

• 20

In the figure below the number of the circle in the blank rows must be.

• 12 and 20

• 13 and 20

• 13 and 21

• 10 and 11

If we plot the weight (w) versus age (t) of a child in a graph, the one that will never be obtained from amongst the four graphs given below is