$\int_{-\pi / 2}^{\pi / 2} \sin ^4 x \cos ^6 x \, dx$ is equal to

The length of an elastic string is $a$ metres when the longitudinal tension is $4 \ N$ and $b$ metres when the longitudinal tension is $5 \ N$. The length of the string in metres when the longitudinal tension is $9 \ N$ is

Rutherford's experiment on scattering of $\alpha-$particles showed for the first time that the atom has

If the pair of lines $ax^2-7xy-3y^2=0$ and $2x^2+xy-6y^2=0$ have exactly one line in common and $a$ is an integer,then the equation of the pair of bisectors of the angles between the lines $ax^2-7xy-3y^2=0$ is

In the visible region, the dispersive powers and the mean angular deviations for crown and flint glass prisms are $\omega, \omega^{\prime}$ and $d, d^{\prime}$ respectively. The condition for obtaining dispersion without deviation, when the two prisms are combined, is:

The output characteristics of an $n-p-n$ transistor represent,($I_C=$ collector current,$V_{C E}=$ potential difference between collector and emitter,$I_B=$ base current,$V_{B B}=$ voltage given to base,$V_{B E}=$ the potential difference between base and emitter)