For a situation shown in figure, find the refrective index of glass so that it will suffer total internal reflection at the vertical surface.

$A$ body weighs $72 \ N$ on the surface of the earth. What is the gravitational force (in $N$) on it,at a height equal to half the radius of the earth?

The order of catenation property for $C$,$Si$,and $Ge$ is $Ge < Si < C$. Which of the following represents the bond energy $\left( kJ \ mol^{-1} \right)$ for $C-C$,$Si-Si$,and $Ge-Ge$ bonds respectively?

The length of an elastic string is $a \, m$ when the longitudinal tension is $4 \, N$ and $b \, m$ when the longitudinal tension is $5 \, N$. The length of the string in metres when the longitudinal tension is $9 \, N$ is

Match List-$I$ with List-$II$ :

List-$I$ (Defects)	List-$II$ (Shown by)
$a$. Frenkel defect	$i$. Non-ionic solids and density of the solid decreases
$b$. Schottky defect	$ii$. Non-ionic solids and density of the solid increases
$c$. Vacancy defect	$iii$. Ionic solids and density of the solid decreases
$d$. Interstitial defect	$iv$. Ionic solids and density of the solid remains constant

Choose the correct answer from the options given below :

The value of the integral $\int_0^4 \frac{dx}{1+x^2}$ obtained by using the Trapezoidal rule with $h=1$ is