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

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

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

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 the difference between compound interest and simple interest for a certain amount of money invested for 3 years at an annual interest rate of 10% is INR 527, then the amount invested in INR is

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?

In a group of 120 students, 80 students are from the Science stream and the rest are from the Commerce stream. It is known that 70 students support Mumbai Indians in the Indian Premier League; all the other students support Chennai Super Kings. The number of Science students who…

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…

The minimum number of times a fair coin must be tossed so that the probability of getting at least one head exceeds 0.8 is