A 16.2 m long wooden log has a uniform diameter of 2 m. To what length the log should be cut to obtain a piece of 22 m³ volume?

• 3.5 m

• 7.0 m

• 14.0 m

• 22.0 m

What is the last digit of 7⁷³?

• 7

• 9

• 3

• 1

3.

A lucky man finds 6 pots of gold coins. He counts the coins in the first four pots to be 60, 30, 20 and 15, respectively. If there is a definite progression, what would be the numbers of coins in the next two pots?

• 10 and 5

• 4 and 2

• 15 and 15

• 12 and 10

A bee leaves its hive in the morning and after flying for 30 minutes due south reaches a garden and spends 5 minutes collecting honey. Then it flies for 40 minutes due west and collects honey in another garden for 10 minutes. Then it returns to the hive taking the shortest route. How long was the bee away from its hive? (Assume that the bee flies at constant speed)

• 85 min

• 155 min

• 135 min

• Less than 1 hour

A bird perched at the top of a 12 m high tree sees a centipede moving toward the base of the tree from a distance equal to twice the height of the tree. The bird flies along a straight line to catch the centipede. If both move at the same speed, at what distance from the base of the tree will the centipede be picked up by the bird?

• 16 m

• 9 m

• 12 m

• 14 m

An ant goes from A to C in the figure crawling only on the lines and taking the least length of path. The number of ways in which it can do so is

• 2

• 4

• 5

• 6

A point is chosen at random from a circular disc shown below. What is the probability that the point lies in the sector OAB?

• $\frac{2\mathrm{x}}{\mathrm{\pi }}$

• $\frac{\mathrm{x}}{\mathrm{\pi }}$

• $\frac{\mathrm{x}}{2\mathrm{\pi }}$

• $\frac{\mathrm{x}}{4\mathrm{\pi }}$

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°