One mole of an ideal diatomic gas undergoes a transition from $A$ to $B$ along a path $AB$ as shown in the figure. The change in internal energy of the gas during the transition is:

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

Which of the following compounds is planar and non-polar?

Let $\overrightarrow{a}=\hat{i}-2 \hat{j}+3 \hat{k}$,$\overrightarrow{b}=2 \hat{i}+3 \hat{j}-\hat{k}$ and $\overrightarrow{c}=\lambda \hat{i}+\hat{j}+(2 \lambda-1) \hat{k}$. If $\overrightarrow{c}$ is parallel to the plane containing $\overrightarrow{a}$ and $\overrightarrow{b}$,then $\lambda$ is equal to

If the normal to the curve $y=f(x)$ at the point $(3,4)$ makes an angle $3\pi/4$ with the positive $x$-axis, then $f'(3)$ is

The atomic numbers of Vanadium $(V)$,Chromium $(Cr)$,Manganese $(Mn)$,and Iron $(Fe)$ are $23, 24, 25$,and $26$ respectively. Which of these elements will have the highest second ionization enthalpy?