Mathematics Past Questions and Answers

If \(2\sin^{2} \theta = 1 + \cos \theta, \leq \theta \leq find the value of \(\theta\).

If \(\begin{vmatrix} 1+2x & -1 \\ 6 & 3-x \end{vmatrix} = -3 \), find the values of x.

Find \(\int \frac{x^{3} + 5x + 1}{x^{3}} \mathrm {d} x\)

Find the coordinates of the point which divides the line joining P(-2, 3) and Q(4, 6) internally in the ratio 2 : 3.

A particle starts from rest and moves in a straight line such that its acceleration after t seconds is given by \(a = (3t - 2) ms^{-2}\). Find the other time when the velocity would be zero.