The temperature of $5$ moles of a gas at constant volume is changed from $100^{\circ} C$ to $120^{\circ} C$. The change in internal energy is $80 \ J$. The total heat capacity of the gas at constant volume in $J/K$ is:

Two coaxial solenoids of different radii carry current $I$ in the same direction. Let $\vec{F}_1$ be the magnetic force on the inner solenoid due to the outer one and $\vec{F}_2$ be the magnetic force on the outer solenoid due to the inner one. Then:

$A$ magnet of magnetic moment $50\,\hat{i}\,\text{A}\,\text{m}^2$ is placed along the $x$-axis in a magnetic field $\vec{B} = (0.5\,\hat{i} + 3.0\hat{j})\,\text{T}$. The torque acting on the magnet is:

Which of the following is an aldohexose?

What is the optimal soil $pH$ for plant growth?

If $I_n = \int_0^{\pi / 4} \tan^n \theta \, d\theta$ for $n = 1, 2, 3, \ldots$, then $I_{n-1} + I_{n+1}$ is equal to