A stationary tuning fork is in resonance with an air column in a pipe. If the tuning fork is moved with a speed of $2 \mathrm{m} {\mathrm{s}}^{-1}$ in front of the open end of the pipe and parallel to it, the length of the pipe should be changed for the resonance to occur with the moving tuning fork. If the speed of sound in air is $320 \mathrm{m} {\mathrm{s}}^{-1},$ the smallest value of the percentage change required in the length of the pipe is ________.

A bubble has surface tension $S$. The ideal gas inside the bubble has ratio of specific heats $\gamma =\frac{5}{3}$. The bubble is exposed to the atmosphere and it always retains its spherical shape. When the atmospheric pressure is $P_{a1}$, the radius of the bubble is found to be $r_1$ and the temperature of the enclosed gas is $T_1$. When the atmospheric pressure is $P_{\mathrm{a}2}$, the radius of the bubble and the temperature of the enclosed gas are $r_2$ and $T_2$, respectively. Which of the following statement(s) is(are) correct?

A thin uniform annular disc (see figure) of mass \(M\) has outer radius \(4 R\) and inner radius \(3 R\). The work required to take a unit mass from point \(P\) on its axis to infinity is

The left and right compartments of a thermally isolated container of length \(L\) are separated by a thermally conducting, movable piston of area \(A\). The left and right compartments are filled with \(\frac{3}{2}\) and 1 moles of an ideal gas, respectively. In the left compartment the piston is attached by a spring with spring constant k and natural length \(\frac{2 L}{5}\). In thermodynamic equilibrium, the piston is at a distance \(\frac{L}{2}\) from the left and right edges of the container as shown in the figure. Under the above conditions, if the pressure in the right compartment is \(P=\frac{\mathrm{k} L}{\mathrm{~A}} \alpha\), then the value of \(\alpha\) is \(\qquad\)

A charge is kept at the central point \(\mathrm{P}\) of a cylindrical region. The two edges subtend a half-angle \(\theta\) at \(\mathrm{P}\), as shown in the figure. When \(\theta=30^{\circ}\), then the electric flux through the curved surface of the cylinder is \(\Phi\). If \(\theta=60^{\circ}\), then the electric flux through the curved surface becomes \(\Phi / \sqrt{n}\), where the value of \(n\) is _______ .

A wheel of radius R and mass M is placed at the bottom of a fixed step of height R as shown in the figure. A constant force is continuously applied on the surface of the wheel so that it just climbs the step without slipping. Consider the torque $\tau$ about an axis normal to the plane of the paper passing through the point Q. Which of the following options is/are correct?

A block of mass \(5 \mathrm{~kg}\) moves along the \(x\)-direction subject to the force \(F=(-20 x+10) \mathrm{N}\), with the value of \(x\) in metre. At time \(t=0 \mathrm{~s}\), it is at rest at position \(x=1 \mathrm{~m}\). The position and momentum of the block at \(t=(\pi / 4) \mathrm{s}\) are

Paragraph:
The coordination number of \(\mathrm{Ni}^{2+}\) is 4 .
\(\mathrm{NiCl}_2+\mathrm{KCN}\) (excess) \(\rightarrow A\) (cyano complex)
\(\mathrm{NiCl}_2+\) conc. \(\mathrm{HCl}\) (excess) \(\rightarrow B\) (chloro complex)
Question:
The hybridization of \(A\) and \(B\) are

A Hydrogen-like atom has atomic number $Z$. Photons emitted in the electronic transitions from level $n=4$ to level $n=3$ in these atoms are used to perform photoelectric effect experiment on a target metal. The maximum kinetic energy of the photoelectrons generated is $1.95 \mathrm{eV}$. If the photoelectric threshold wavelength for the target metal is $310 \mathrm{nm}$, the value of $Z$ is _____.
[Given $hc=1240 \mathrm{eV}-\mathrm{nm}$ and $Rhc=13.6 \mathrm{eV}$, where $R$ is the Rydberg constant, $h$ is the Planck’s constant and $c$ is the speed of light in vacuum]

The correct statements (s) about intermolecular forces is(are)

Which one of the following options represents the magnetic field $\overrightarrow{B}$at $O$ due to the current flowing in the given wire segments lying on the $xy$plane?

Let $m$ be the minimum possible value of ${\log }_3\left(3^{y_1}+3^{y_2}+3^{y_3}\right)$ , where $y_1, y_2, y_3$ are real numbers for which $y_1+y_2+y_3=9$. Let $M$ be the maximum possible value of $\left({\log }_3{x}_1+{\text{log}}_3 x_2+{\text{log}}_3 x_3\right)$, where $x_1, x_2, x_3$ are positive real numbers for which $x_1+x_2+x_3=9$. Then the value of ${\text{log}}_2 \left(m^3\right)+{\text{log}}_3\left(M^2\right)$ is

The compound(s) which react(s) with ${\mathrm{NH}}_3$ to give boron nitride $\left(\mathrm{BN}\right)$ is(are)