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?

A man buys 10 kg of wheat at a rate of ₹26/kg. The wheat is mixed with 6 kg of other good quality of wheat to get a mixture at a price of ₹35/kg. The price of good quality wheat per kg (in ₹) is:

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?