In an acute angled triangle,$\cot B \cot C + \cot A \cot C + \cot A \cot B$ is equal to

Assertion $(A):$ Above Curie temperature, a ferromagnetic material becomes paramagnetic.

Reason $(R):$ When a magnetic material is heated to very high temperature, it loses its magnetic properties.

The enthalpy change $(\Delta H)$ for the reaction $N_{2(g)} + 3H_{2(g)} \to 2NH_{3(g)}$ is $-92.38 \ kJ$ at $298 \ K$. The internal energy change $\Delta U$ at $298 \ K$ is $...... \ kJ$.

The equation of the plane passing through the point $(1, 2, -3)$ and perpendicular to the planes $3x + y - 2z = 5$ and $2x - 5y - z = 7$ is:

Water in a river $20 \ m$ deep is flowing at a speed of $10 \ ms^{-1}$. The shearing stress between the horizontal layers of water in the river in $Nm^{-2}$ is (Coefficient of viscosity of water $= 10^{-3} \ SI$ units).

$\int_0^{2 \pi} \sin^6 x \cos^5 x \, dx$ is equal to