In the reaction,$C_2H_5OC_2H_5 + CO \xrightarrow[150^{\circ}C, 500 \text{ atm pressure}]{BF_3} X$. What is $X$?

Let $P = \{\theta : \sin \theta - \cos \theta = \sqrt{2} \cos \theta\}$ and $Q = \{\theta : \sin \theta + \cos \theta = \sqrt{2} \sin \theta\}$ be two sets,then:

If $f(x) = \sqrt{\frac{x - \sin x}{x + \cos^2 x}}$,then $\lim_{x \to \infty} f(x)$ is

$A$ bar magnet of magnetic moment $M$ and moment of inertia $I$ is freely suspended such that the magnetic axial line is in the direction of the magnetic meridian. If the magnet is displaced by a very small angle $\theta$,the angular acceleration is (Magnetic induction of earth's horizontal field $= B_H$)

If $\theta$ lies in the first quadrant and $5 \tan \theta = 4$,then $\frac{5 \sin \theta - 3 \cos \theta}{\sin \theta + 2 \cos \theta}$ is equal to

Two identical balls $A$ and $B$ are released from the positions shown in figure. They collide elastically on the horizontal portion $MN$. The ratio of the maximum height attained by $A$ and $B$ after the collision will be: (neglect friction)