If $5 \cos x + 12 \cos y = 13$,then the maximum value of $5 \sin x + 12 \sin y$ is:

If $a>0$,then $\int_{-\pi}^\pi \frac{\sin ^2 x}{1+a^x} d x$ is equal to

Using the Trapezoidal rule,find the approximate value of $\int_1^4 y \, dx$ based on the following table:

$x$	$1$	$2$	$3$	$4$
$y$	$0.7111$	$0.7222$	$0.7333$	$0.7444$

(in $.1833$)

One end of a uniform glass capillary tube of radius $r=0.025 \ cm$ is immersed vertically in water to a depth $h=1 \ cm$. The excess pressure in $N/m^2$ required to blow an air bubble out of the tube is: (Surface tension of water $T=7 \times 10^{-2} \ N/m$,Density of water $\rho=10^3 \ kg/m^3$,Acceleration due to gravity $g=10 \ m/s^2$)

If $200 \text{ MeV}$ of energy is released in the fission of one nucleus of ${}_{92}^{236}U$,the number of nuclei that must undergo fission to release an energy of $1000 \text{ J}$ is

The major product of the following reaction is