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

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

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…

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

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

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

A polynomial P(x) leaves a remainder 2 when divided by (x - 1) and a remainder 1 when divided by (x - 2). The remainder when P(x) is divided by (x - 1)(x - 2) is

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

Let [x] denote the greatest integer not exceeding x and \(\{x\} = x - [x]\). If n is a natural number, then the sum of all values of x satisfying the equation \(2[x] = x + n\{x\}\) is