$A$ baby has been born with a small tail. It is a case exhibiting:

$\sum_{k=1}^{2n+1} (-1)^{k-1} k^2$ is equal to

If a hydrogen electrode is dipped in two solutions of $pH = 3$ and $pH = 6$ and a salt bridge is connected,the $emf$ of the resulting cell is .......... $V$.

The $pK_a$ values of four carboxylic acids are given below. Identify the weakest carboxylic acid.

As shown in the figure,a metal rod makes contact and completes the circuit. The circuit is perpendicular to the magnetic field with $B = 0.15 \, T$. If the resistance is $3 \, \Omega$,the force needed to move the rod as indicated with a constant speed of $2 \, m/s$ is:

$\int(x+1)^2 e^x d x$ is equal to