Let a, b, c be real numbers greater than 1, and n be a positive real number not equal to 1. If \(\log_n(\log_2 a) = 1\), \(\log_n(\log_2 b) = 2\) and \(\log_n(\log_2 c) = 3\), then which of the following is true?

A goldsmith bought a large solid golden ball at INR 1,000,000 and melted it to make a certain number of solid spherical beads such that the radius of each bead was one-fifth of the radius of the original ball. Assume that the cost of making golden beads is negligible. If the gold…

If the harmonic mean of the roots of the equation \((5 + \sqrt{2})x^2 - bx + 8 + 2\sqrt{5} = 0\) is 4 then the value of b is

If a three-digit number is chosen at random, what is the probability that it is divisible neither by 3 nor by 4?

Consider an 8 x 8 chessboard. The number of ways 8 rooks can be placed on the board such that no two rooks are in the same row and no two are in the same column is

The length of the line segment joining the two intersection points of the curves \(y = 4970 - |x|\) and \(y = x^2\) is ______.

The set of all real values of x satisfying the inequality \(\frac{x^2(x+1)}{(x-1)(2x+1)^3} > 0\) is

In a chess tournament, there are four groups, each containing an equal number of players. Each player plays - against every other player belonging to one's own group exactly once; - against each player belonging to one of the remaining three groups exactly twice; - against each p…

If \(A = \begin{bmatrix}1 & 2\\ 3 & a\end{bmatrix}\) where a is a real number and \(\det(A^3 - 3A^2 - 5A) = 0\) then one of the values of a can be