$\int \left(1+x-\frac{1}{x}\right) e^{x+\frac{1}{x}} ~d x$ is equal to

The electric resistance of a certain wire of iron is $R$. If its length and radius are both doubled,then

The velocity of a particle which starts from rest is given by the following table. The total distance travelled (in metre) by the particle in $10 \ s$,using the Trapezoidal rule is given by:

$t$ (in second)	$0$	$2$	$4$	$6$	$8$	$10$
$v$ (in m/s)	$0$	$12$	$16$	$20$	$35$	$60$

The equation of the tangent at $(-4, -4)$ on the curve $x^2 = -4y$ is

When a certain conductivity cell was filled with $0.1 \ M$ $KCl$,it had a resistance of $85 \ \Omega$ at $25 \ ^oC$. When the same cell was filled with an aqueous solution of $0.052 \ M$ unknown electrolyte,the resistance was $96 \ \Omega$. Calculate the molar conductivity of the unknown electrolyte at this concentration ............ $\Omega ^{-1} cm ^{2} mol ^{-1}$ (Given : Specific conductivity of $0.1 \ M$ $KCl = 1.29 \times 10^{-2} \ \Omega ^{-1} cm ^{-1}$)

$A$ mass $M$ hangs on a massless rod of length $l$ which rotates at a constant angular frequency. The mass $M$ moves with steady speed in a circular path of constant radius. Assume that the system is in steady circular motion with constant angular velocity $\omega$. The angular momentum of $M$ about point $A$ is $L_A$ which lies in the positive $z$ direction and the angular momentum of $M$ about $B$ is $L_B$. The correct statement for this system is