Let $f$ be a differentiable function such that $f(1)=2$ and $f^{\prime}(x)=f(x)$,for all $x \in \mathbb{R}$. If $h(x)=f(f(x))$,then $h^{\prime}(1)$ is equal to

$A$ car is fitted with a convex side-view mirror of focal length $20\ cm$. $A$ second car $2.8\ m$ behind the first car is overtaking the first car at a relative speed of $15\ m/s$. The speed of the image of the second car as seen in the mirror of the first one is

Which one of the following orders is correct for the bond dissociation energies of halogen molecules?

Two concentric coils each of radius equal to $2\pi \, cm$ are placed at right angles to each other. $3\, A$ and $4\, A$ are the currents flowing in each coil respectively. The magnetic induction in $Wb/m^2$ at the centre of the coils will be $(\mu_0 = 4\pi \times 10^{-7} \, Wb/A \cdot m)$.

$A$ circular disc of radius $R$ is removed from a bigger circular disc of radius $2R$ such that the circumferences of the discs touch. The centre of mass of the new disc is at a distance $\alpha R$ from the centre of the bigger disc. The value of $\alpha$ is

The point $(3,2)$ undergoes the following three transformations in the order given:
$(i)$ Reflection about the line $y=x$.
(ii) Translation by the distance $1$ unit in the positive direction of $x$-axis.
(iii) Rotation by an angle $\frac{\pi}{4}$ about the origin in the anti-clockwise direction.
Then,the final position of the point is: