Hot water cools from $60\,^{\circ}C$ to $50\,^{\circ}C$ in the first $10\,min$ and to $42\,^{\circ}C$ in the next $10\,min$. The temperature of the surrounding is ......... $^{\circ}C$.

$A$ tension of $20 ~N$ is applied to a copper wire of cross-sectional area $0.01 ~cm^2$. The Young's modulus of copper is $1.1 \times 10^{11} ~N/m^2$ and the Poisson's ratio is $0.32$. The decrease in the cross-sectional area of the wire is:

If $x=e^{y+e^{y+e^{y+\ldots}}}$,then $\frac{d y}{d x}=$

The value of $\lambda$ such that $\lambda x^2-10 x y+12 y^2+5 x-16 y-3=0$ represents a pair of straight lines is:

Among $Ni(CO)_4$,$[Ni(CN)_4]^{2-}$ and $[NiCl_4]^{2-}$,which of the following statements is correct regarding their magnetic properties?

In the circuit shown below,the $AC$ source has voltage $V = 20 \cos(\omega t)$ with $\omega = 2000 \, rad/sec$. The amplitude of the current will be nearest to.....$A$