(a) Two ships M and N, moving with constant velocities, have position vectors (3i + 7j) and (4i + 5j) respectively. If the velocities of M and N are (5i + 6...

A uniform plank PQ of length 8m and mass 10kg is supported horizontally at the end P and at point R, 3 metres from Q. A boy of mass 20 kg walks along the pla...

Five students are to be selected from a large population. If 60% of them are boys and the rest are girls, find the probability that : (a) exactly 3 of them a...

The table shows the marks obtained by a group of students in a class test. Marks 40 - 44 45 - 49 50 - 54 55 - 59 60 - 64 65 - 69 No of students 4 9 18 23 10 ...

If the quadratic equation \((2x - 1) - p(x^{2} + 2) = 0\), where p is a constant, has real roots : (a) show that \(2p^{2} + p - 1 < 0\); (b) find the values ...

The equation of a curve is \(y = x(3 - x^{2})\). Find the equation of its normal of the point where x = 2.

If \(3x^{2} + 2y^{2} + xy + x - 7 = 0\), find \(\frac{\mathrm d y}{\mathrm d x}\) at the point (-2, 1).

The position vector of a particle of mass 3 kg moving along a space curve is given by \(r = (4t^{3} - t^{2})i - (2t^{2} - t)j\) at any time t seconds. Find t...

(a) Express \(\frac{2\sqrt{2}}{\sqrt{48} - \sqrt{8} - \sqrt{27}}\) in the form \(p + q\sqrt{r}\), where p, q and r are rational numbers. (b) If \(V = A\log_{...