$A$ person moves $30\, m$ north and then $20\, m$ towards east and finally $30\sqrt{2}\, m$ in south-west direction. The displacement of the person from the origin will be

Efficiency of a heat engine whose sink is at a temperature of $300 ~K$ is $40 \%$. To increase the efficiency to $60 \%$,keeping the sink temperature constant,the source temperature must be increased by (in $~K$)

The square root of $134 + \sqrt{6292}$ is:

The resistance of an ammeter is $13 \Omega$ and its scale is graduated for a current up to $100 \text{ A}$. After an additional shunt has been connected to this ammeter,it becomes possible to measure currents up to $750 \text{ A}$ by this meter. The value of the shunt resistance is

If $(2+\sin x) \frac{dy}{dx} + (y+1) \cos x = 0$ and $y(0) = 1$,then $y\left(\frac{\pi}{2}\right)$ is

The slope of the normal to the curve $x = \sqrt{t}$ and $y = t - \frac{1}{\sqrt{t}}$ at $t = 4$ is ...