Mathematics Tes...

Three persons \({P}, {Q}\) and \({R}\) independently try to hit a target. If the probabilities of their hitting the target are \(\frac{3}{4}, \frac{1}{2}\) and \(\frac{5}{8}\) respectively, then the probability that the target is hit by \({P}\) or \({Q}\) but not by \({R}\) is:

The derivative of \(\ln (x+\sin x)\) with respect to \((x+\cos x)\) is:

If A is a 2 × 3 matrix and AB is a 2 × 5 matrix, then B must be a

If the roots of \(a(b-c) x^2+b(c-a) x+c(a-b)=0\) are equal, then \(a, b, c\) are:

The ratio of the coefficient of \(\mathrm{x}^{15}\) to the term independent of \(\mathrm{x}\) in the expansion of \(\left(\mathrm{x}^{2}+\frac{2}{\mathrm{x}}\right)^{15}\) is:

Evaluate \(\int_{0}^{\frac{\pi}{2}} \log \sin x d x\).