If $\theta$ is the angle between the tangents from $(-1,0)$ to the circle $x^2+y^2-5x+4y-2=0$,then $\theta$ is equal to

An ink mark is made on a piece of paper on which a glass slab of thickness $t$ is placed. The ink mark appears to be raised up through a distance $x$ when viewed at nearly normal incidence. If the refractive index of the material of the glass slab is $\mu$,then the thickness of the glass slab is given by:

The standard entropies of $X_2$,$Y_2$,and $XY_3$ are $60$,$40$,and $50 \ J \ K^{-1} \ mol^{-1}$ respectively. For the reaction $\frac{1}{2}X_2 + \frac{3}{2}Y_2 \to XY_3$,$\Delta H = -30 \ kJ$. What will be the temperature in $K$ at equilibrium?

$D$-glucose and $D$-fructose can be differentiated by

According to the kinetic theory of gases,when two molecules of gas collide with each other,then:

$\sec h^{-1}\left(\frac{1}{2}\right)-\operatorname{cosec} h^{-1}\left(\frac{3}{4}\right)$ is equal to