The expression $\tan 9^{\circ}-\tan 27^{\circ}-\tan 63^{\circ}+\tan 81^{\circ}$ is equal to

Assertion $(A)$: The aqueous solution of $CH_3COONa$ is alkaline in nature. Reason $(R)$: Acetate ion undergoes anionic hydrolysis. The correct answer is

$A$ uniform metal rod of $2\,mm^2$ cross-section fixed between two walls is heated from $0\,^{\circ}C$ to $20\,^{\circ}C$. The coefficient of linear expansion of the rod is $12 \times 10^{-6}\,/^{\circ}C$. Its Young's modulus of elasticity is $10^{11}\,N/m^2$. The energy stored per unit volume of the rod will be ....... $J/m^3$.

Three moles of an ideal monoatomic gas undergo a cyclic process as shown in the figure. The temperatures of the gas in different states marked as $1, 2, 3$ and $4$ are $400 \ K, 700 \ K, 2500 \ K$ and $1100 \ K$ respectively. The work done by the gas during the process $1-2-3-4-1$ is (universal gas constant is $R$): (in $R$)

If the radius of a nucleus with mass number $125$ is $1.5 \text{ fermi}$,then the radius of a nucleus with mass number $64$ is: (in $\text{ fermi}$)

The diameter of the objective of a telescope is $1 \ m$. Its resolving limit for light of wavelength $4538 \ \mathring{A}$ will be: