JEE Main Test 144

The general solution of the differential equation

If sound travelling at 340 ms^-1 enters water where its speed becomes 1480 ms^-1, then critical angle for total internal reflection is

The vectors a and b are not perpendicular and c and d are two vectors satisfying b × c = b × d and a ∙ d = 0. Then, the vector d is equal to

The line joining points (1, 1, 2) and (3, -2, 1) meets the plane 3x + 2y + z = 6 at the point

The current gain of a transistor in common-base mode is 0.995. The current gain of the same transistor in common emitter mode is

Box A contains 2 black and 3 red balls, while box B contains 3 black and 4 red balls. Out of these two boxes one is selected at random and the probability of choosing box A is double that of box B. If a red ball is drawn from the selected box, then the probability that it has come from box B, is

Two cards are drawn successively with replacement from a well shuffled deck of 52 cards, then the mean of the number of aces is

In a radioactive disintegration, the ratio of initial number of atoms to the number of atoms present at an instant of time equal to its mean life is

Two protons are kept at a separation of 40Å. F_n is the nuclear force and F_e is the electrostatic force between them. Then,