The proposition $(\sim p) \vee (p \wedge \sim q)$ is equivalent to:

When the angle of inclination of an inclined plane is $\theta$, an object slides down with uniform velocity. If the same object is pushed up with an initial velocity $u$ on the same inclined plane, it goes up the plane and stops at a certain distance on the plane. Thereafter, the body:

$A$ point object is placed at the centre of a glass sphere of radius $6 \, cm$ and refractive index $1.5$. The distance of the virtual image from the surface of the sphere is.....$cm$.

When the engine is switched off,a vehicle of mass $M$ is moving on a rough horizontal road with momentum $p$. If the coefficient of friction between the road and the tyres of the vehicle is $\mu_k$,what is the distance travelled by the vehicle before it comes to rest?

Let $a, b, c$ be positive integers such that $\frac{a \sqrt{2}+b}{b \sqrt{2}+c}$ is a rational number,then which of the following is always an integer?

The fossil bone has a ${}^{14}C:{}^{12}C$ ratio,which is $\left( \frac{1}{16} \right)$ of that in a living animal bone. If the half-life of ${}^{14}C$ is $5730 \text{ years}$,then the age of the fossil bone is ......... $\text{years}$.