Two goods trains 132 m and 108 m in length are running towards each other on parallel tracks. The first train is running at a speed of 32 km/h and the second at a speed of 40 km/h. How much time will they take to cross each other after meeting?

Ghanshyam is thrice as old as Akash. 10 years ago, Ghanshyam was four times as old as Akash. What is the difference between their current ages (in years)?

On dividing a number by 55, we get 28 as the remainder. On dividing the same number by 11, what is the remainder?

The cost of a machine is Rs. 20,000 and its estimated useful life is 10 years. The scrap value of the machine, when its value depriciates at 10% p.a, is:

use (0.9)¹⁰ = 0.35

Let C be the circle of radius π/4, centered at z = \(\frac{1}{4}\) in the complex z-plane that is traversed counter-clockwise. The value of the contour integral ∮_c\(\frac{{{{\rm{z}}^{\rm{2}}}}}{{{\rm{si}}{{\rm{n}}^{\rm{2}}}{\rm{4z}}}}\)dz is

Let X be a real-valued random variable such that E[e^X] < ∞ and E[e^X] = e^E[X]. Then which of the following is correct?

There are three urns U₁, U₂, U₃, each with balls of two colours. U₁ contains 2 white balls and 3 black balls, U₂ contains 3 white balls and 2 black balls and U₃ contains 5 white balls and 5 black balls. An urn is chosen at random and a ball is drawn from that urn at random. What is the probability that U₂ was chosen given that the ball picked is black in colour?