Which amendment to the Indian Constitution is known for imposing restrictions on the freedom of expression?

Let $f\left(x\right)$ be a polynomial of degree four and having its extreme values at $x=1$ and $x=2$. If $\underset{x\to 0 }{\lim }\left[1+\frac{\mathrm{f}\left(x\right)}{x^2}\right]=3$, then $f\left(2\right)$ is equal to 

A cylinder moves with linear velocity $v$ to the right and angular velocity ω in the anticlockwise direction. The cylinder was initially at rest. The cylinder does not perform pure rolling and stops after some time. What will be the radius of the cylinder?

A uniform sphere of radius $R$ is projected on a horizontal surface with a velocity $v_0$ and simultaneously given a spin ${\text{ω}}_0.$ Consequently, the sphere experiences a combined motion. Due to the friction between the sphere and the horizontal surface, both translational and rotational motion will stop simultaneously. Then, what must be the magnitude and direction of initial spin ${\text{ω}}_0$?

A rod of mass m and length l is hinged at one of its end A as shown in figure. A force F is applied at a distance x from A. The acceleration of centre of mass (a) varies with x as

In the figure given below, the end $\mathrm{B}$ of the rod $\mathrm{A}\mathrm{B}$ which makes angle $\mathrm{\theta }$ with the floor is pulled with a constant velocity ${\mathrm{v}}_0$ as shown. The length of rod is $\mathcal{l}\mathcal{ }$. At an instant when $\mathrm{\theta }=37°$