JEE Advanced Mi...

Let A, B, C, D be real matrices (not necessarily square) such that A^T = BCD, BT = CDA, C^T = DAB and D^T = ABC, where A^T represents transpose of A. Then for the matrix S = ABCD

P is the foot of the perpendicular dropped from origin O on the line of intersection of the planes x – 2y + 3z = 5 and 2x + 3y + z + 4 = 0 then

k subsets of a set A (having n elements) are chosen at random with replacement. The probability that their intersection is

p and q are chosen randomly from the set {1, 2, 3, ...., 10} with replacement. The probability that the roots of the equation x² + px + q = 0 are

Statement-1 : If two balls are drawn without replacement from an urn containing 3 red and 2 blue balls, then the probability of the event that 'second ball drawn is blue' is 1/4.

Statement-2 : If two balls are drawn without replacement from an urn containing 3 red and 2 blue balls, then the probability of the event that 'first ball drawn is blue' is equal to the probability of the event that 'second ball drawn is blue'

If number of distinct terms in a quadratic form is 10, then number of variables in quadratic form is