$A$ convex lens is made up of three different materials as shown in the figure. For a point object placed on its axis,the number of images formed is:

$A$ fully charged capacitor has a capacitance $C$. It is discharged through a small coil of resistance wire,embedded in a block of specific heat $s$ and mass $m$ under thermally isolated conditions. If the temperature of the block is raised by $\Delta T$,the potential difference $V$ across the capacitor initially is

An increase in $CO_2$ concentration in the atmosphere will result in

$y=e^{a \sin ^{-1} x} \Rightarrow (1-x^2) y_{n+2}-(2 n+1) x y_{n+1}$ is equal to

$A$ positively charged $(+q)$ particle of mass $m$ has kinetic energy $K$ and enters a region with a horizontal magnetic field $\overrightarrow{B}$ in a vertically downward direction. The acceleration of the particle is:

Observe the following statements :
$A: \int \left(\frac{x^2-1}{x^2}\right) e^{\frac{x^2+1}{x}} d x = e^{\frac{x^2+1}{x}} + c$
$R: \int f^{\prime}(x) e^{f(x)} d x = f(x) + c$
Then which of the following is true?