JEE Main Test 1...

If A (3, 4, 5), B(4, 6, 3), C (-1, 2, 4) and D(1, 0, 5) are such that the angle between the lines DC and AB is θ, then cos θ is equal to

If the line passing through the points (5, 1, a) and (3, b, 1) crosses the YZ-plane at the point

In a college, 25% boys and 10% girls offer mathematics. There are 60% girls in the college. If a Mathematics student is chosen at random, then the probability that the student is a girl, will be

In a common emitter transistor amplifier, the output resistance is 500 kΩ and the current gain β = 49. If the power gain of the amplifier is 5 × 10⁶, the input resistance is

One Indian and four American men and their wives are to be seated randomly around a circular table. Then, the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife, is

A neutron is moving with velocity u. It collides head on and elastically with an atom of mass number A. If the initial kinetic energy of the neutron is E, then how much kinetic energy will be retained by the neutron after reflection?

A nucleus of mass M + ∆m is at rest and decays into two daughter nuclei of equal mass (M/2) each. Speed of light is c.

The speed of daughter nuclei is

Sodium ethoxide has reacted with ethanoyl chloride. The compound that is produced in the above reaction is

Sodium phenoxide when heated with CO₂ under pressure at 125°C yields a product which on acetylation produces C.

The compound that does not liberate CO₂ on treatment with aqueous sodium bicarbonate solution is