$A$ block of mass $M$ is pulled along a horizontal frictionless surface by a rope of mass $m$. If a force $P$ is applied at the free end of the rope,the force exerted by the rope on the block is-

If $(a + \sqrt{2} b \cos x)(a - \sqrt{2} b \cos y) = a^2 - b^2$,where $a > b > 0$,then $\frac{dx}{dy}$ at $(\frac{\pi}{4}, \frac{\pi}{4})$ is

$\int_{-\pi / 2}^{\pi / 2} \sin |x| \, dx$ is equal to

The cubic equation whose roots are the squares of the roots of $x^3-2x^2+10x-8=0$ is

Which of the following is used in the industrial production of nitric acid by the Ostwald process?