If the eccentricity of a hyperbola is $\frac{5}{3}$,then the eccentricity of its conjugate hyperbola is

If $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}$ and $|\overrightarrow{a}|=3, |\overrightarrow{b}|=4$ and $|\overrightarrow{c}|=\sqrt{37}$,then the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is:

In a step-up transformer, the turn ratio is $1:2$. A Leclanche cell $(e.m.f. 1.5\,V)$ is connected across the primary. The voltage developed in the secondary would be.......$V$

The excess pressure inside a spherical soap bubble of radius $1 ~cm$ is balanced by a column of oil (specific gravity $= 0.8$), $2 ~mm$ high. The surface tension of the bubble is: (in $~N/m$)

In the expansion of $(1+x)^n$,the coefficients of $p$-th and $(p+1)$-th terms are respectively $p$ and $q$. Then $p+q=$

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