If $x$ and $y$ are acute angles such that $\cos x + \cos y = \frac{3}{2}$ and $\sin x + \sin y = \frac{3}{4}$,then $\sin(x+y)$ is equal to

If the function $y = \sin^{-1} x$, then $(1 - x^2) \frac{d^2 y}{d x^2}$ is equal to

$A$ stone tied to a string of length $L$ is whirled in a vertical circle,with the other end of the string at the center. At a certain instant of time,the stone is at its lowest position and has a speed $u$. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is

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 $g=10 \ m/s^2$)

$A$ circle with center at $(2,4)$ is such that the line $x+y+2=0$ cuts a chord of length $6$. The radius of the circle is

$A$ parallel beam of white light falls on a convex lens. Images of blue,red,and green light are formed on the other side of the lens at distances $x, y,$ and $z$ respectively from the pole of the lens. Then: