data entry - Physics

The time period of a simple pendulum is $T$. When the length is increased by $10 \ cm$,its period is $T_1$. When the length is decreased by $10 \ cm$,its period is $T_2$. Then,the relation between $T, T_1$ and $T_2$ is

$\left\{x \in R: \frac{2x-1}{x^3+4x^2+3x} \in R\right\}$ equals

There are two holes,one each along the opposite sides of a wide rectangular tank. The cross-section of each hole is $0.01 ~m^2$ and the vertical distance between the holes is $1 ~m$. The tank is filled with water. The net force on the tank in newtons when the water flows out of the holes is (Density of water $= 1000 ~kg/m^3$,$g = 10 ~m/s^2$):

The de Broglie wavelength of a proton is twice the de Broglie wavelength of an alpha particle. The ratio of the kinetic energies of the proton and the alpha particle is

For a binomial variate $X$,if $n=4$ and $P(X=4)=6 P(X=2)$,then the value of $p$ is