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 are boys;

(b) at least 3 of them are girls.

The table shows the marks obtained by a group of students in a class test.

(a) Draw a histogram for the distribution ;

(b) Use your histogram to estimate the median of the distribution.

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 the force acting on it at t = 2 seconds.

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 plank starting from P. If the plank is in equilibrium, calculate the 

(a) reactions at P and R when he walked 1.5 metres;

(b) distance he had walked when the two reactions are equal;

(c) distance he walked before the plank tips over.

(a) The nth term of a sequence is given by \(T_{n} = 4T_{n - 1} - 3\). If twice the third term is five times the second term, find the first three terms of the sequence.

(b) Given that \(\begin{pmatrix} 2 & 0 & 1 \\ 5 & -3 & 1 \\ 0 & 4 & 6 \end{pmatrix} \begin{pmatrix} 1 \\ m \\ r \end{pmatrix} = \begin{pmatrix} k \\ 2 \\ 26 \end{pmatrix}\), find the values of the constants k, m and r.