A helicopter flies along the sides of a square field of side length 100 kms. The first side is covered at a speed of 100 kmph, and for each subsequent side the speed is increased by 100 kmph till it covers all the sides. The average speed of the helicopter is

If \(\log_{\cos x}(\sin x) + \log_{\sin x}(\cos x) = 2\), then the value of x is

In a triangle ABC, let D be the mid-point of BC, and AM be the altitude on BC. If the lengths of AB, BC and CA are in the ratio of 2:4:3, then the ratio of the lengths of BM and AD would be

If \(\frac{a+b}{b+c} = \frac{c+d}{d+a}\), which of the following statements is always true?

In a chess tournament there are 5 contestants. Each player plays against all the others exactly once. No game results in a draw. The winner in a game gets one point and the loser gets zero point. Which of the following sequences cannot represent the scores of the five players?

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

A rabbit is sitting at the base of a staircase which has 10 steps. It proceeds to the top of the staircase by climbing either one step at a time or two steps at a time. The number of ways it can reach the top 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

Let \(a_1, a_2, a_3\) be three distinct real numbers in geometric progression. If the equations \(a_1x^2 + 2a_2x + a_3 = 0\) and \(b_1x^2 + 2b_2x + b_3 = 0\) have a common root, then which of the following is necessarily true?