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

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

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?

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

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

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?

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

Which of the following straight lines are both tangent to the circle \(x^2 + y^2 - 6x + 4y - 12 = 0\)