The volume of one mole of the gas is changed from $V$ to $2 V$ at constant pressure $p$. If $\gamma$ is the ratio of specific heats of the gas, what is the change in internal energy of the gas?

If $a, b, c$ are unit vectors and the maximum value of $|a-b|^2+|b-c|^2+|c-a|^2$ is $k$,then $k(2|a|^2+3|b|^2-4|c|^2)=$

If $\alpha, \beta$ and $\gamma$ are the roots of the equation $x^3+p x^2+q x+r=0$,then the coefficient of $x$ in the cubic equation whose roots are $\alpha(\beta+\gamma), \beta(\gamma+\alpha)$ and $\gamma(\alpha+\beta)$ is

If the direction cosines of two lines are given by $l+m+n=0$ and $l^2-5m^2+n^2=0$,then the angle between them is

Dividing the interval $[0,6]$ into $6$ equal parts and by using the trapezoidal rule, the value of $\int_0^6 x^3 dx$ is approximately:

$A$ plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches $30^o$,the box starts to slip and slides $4.0\, m$ down the plank in $4.0\, s$. The coefficients of static and kinetic friction between the box and the plank will be,respectively: