Gas is being pumped into a spherical balloon at the rate of $30 \ ft^3 / min$. The rate at which the radius increases when it reaches the value $15 \ ft$, is:

To the free end of a spring hanging from a rigid support,a block of mass $m$ is hung and slowly allowed to come to its equilibrium position. Then the stretching in the spring is $d$. If the same block is attached to the same spring and allowed to fall suddenly,the amount of stretching is: (force constant,$k$)

The potential energy of a particle of mass $m$ is given by $U(x) = \begin{cases} E_0; & 0 \le x \le 1 \\ 0; & x > 1 \end{cases}$. $\lambda_1$ and $\lambda_2$ are the de-Broglie wavelengths for $0 \le x \le 1$ and $x > 1$ respectively. If the total energy of the particle is $2E_0$,the ratio $\frac{\lambda_1}{\lambda_2}$ will be

The speed of an electron having a wavelength of $10^{-10} \ m$ is ........... $\times 10^6 \ m/s$.

In an unbiased $p-n$ junction,holes diffuse from the $p-$region to $n-$region because

If the difference between the roots of $x^2+ax+b=0$ and $x^2+bx+a=0$ is the same,and $a \neq b$,then: