$\lim _{x \rightarrow 0} \frac{\sin \left(\pi \cos ^2 x\right)}{x^2}$ is equal to

Two planoconvex lenses each of focal length $10 \, cm$ and refractive index $3/2$ are placed as shown. In the space left, water $(R.I = 4/3)$ is filled. The whole arrangement is in air. The optical power of the system is (in diopters):

Water is flowing through a tube of non-uniform cross-section. The ratio of the radius at the entry and exit ends of the pipe is $3:2$. Then the ratio of velocities at the entry and exit of the liquid is

The monomer $( X )$ involved in the synthesis of Nylon $6,6$ gives positive carbylamine test. If $10$ moles of $X$ are analyzed using Dumas method, the amount $($in grams$)$ of nitrogen gas evolved is $....$
Use: Atomic mass of $N ($in amu$) = 14$

The number of radial nodes of $3s$ and $2p$ orbitals respectively are

$A$ musical instrument $P$ produces sound waves of frequency $n$ and amplitude $A_P$. Another musical instrument $Q$ produces sound waves of frequency $\frac{n}{4}$. The waves produced by $P$ and $Q$ have equal energies. If the amplitude of waves produced by $P$ is $A_P$,the amplitude of waves produced by $Q$ will be: (in $A_P$)