GATE Questions

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In the given figure, ∠QRN = 40°, ∠PQR = 46° and MN is a tangent at R. What is the value (in deg) of x, y and z respectively?

What is the simplified value of (cotA + tan B)/(cot B + tan A)?

In the following questions a part of a sentence is given in bold, it is then followed by four sentences which try to explain the meaning of the idiom/phrase given in bold. Choose the alternative from the four given below each question which explains the meaning of the phrase correctly without altering the meaning of the sentence given as question. If none of the sentence explains the meaning of the highlighted phrase, choose option 5 i.e., “None of these” as your answer choice

I wouldn't be caught dead wearing an outfit like that – it's like something my grandmother would also not wear!

A container contains 165 litres of milk. Some quantity of milk is taken out and half of that quantity of milk, water is added in the container. Now ratio of milk to water in the container becomes 5:3. What is the quantity of water added in it?

Two boxes contain 4 and 16 balls respectively. Two balls in the first box and four in the second, are black. If a box is chosen randomly and two balls are drawn at random from it, what is the
probability that at least one ball is black if the ball is not replaced?

Train A, travelling at 84 kmph, overtook train B, traveling in the same direction, in 10 seconds. If train B had been traveling at twice its speed, then train A would have taken 22.5 seconds to overtake it. Find the length of train B, given that it is half the length of train A.

A solid sphere of radius 6 cm is melted and re-casted into a hollow cylinder of uniform thickness. If the external radius of the base of the cylinder is 5 cm and its height is 32 cm, find the uniform thickness of the cylinder ?