The number of nuclei of a radioactive substance at time $t = 0$ is $1000$,and at time $t = 2 \ s$,it is $900$. Then,the number of nuclei at time $t = 4 \ s$ will be:

$\int(x+1)^2 e^x d x$ is equal to

An electron beam travels with a velocity of $1.6 \times 10^7 \ m/s$ perpendicularly to a magnetic field of intensity $0.1 \ T$. Calculate the radius of the path of the electron beam. (Given: $m_e = 9 \times 10^{-31} \ kg$,$e = 1.6 \times 10^{-19} \ C$)

The number of photo-electrons emitted per second from a metal surface increases when

$A$ proton and an $\alpha$-particle are accelerated through a potential difference of $100 \ V$. The ratio of the wavelength associated with the proton to that associated with an $\alpha$-particle is

In a resonance tube experiment,a tuning fork resonates with an air column of length $12 ~cm$ and again resonates when the air column is $38 ~cm$ long. The end correction will be: (in $~cm$)