If a proton and an alpha particle are accelerated through the same potential difference, then the ratio of their de Broglie wavelengths is

An infinite non-conducting sheet has a surface charge density of \(7 \times 10^{-7} \mathrm{C} \mathrm{m}^{-2}\) on one side. The distance between equipotential surfaces whose potentials differ by \(19.8 \mathrm{~V}\), will be
(Take \(\frac{1}{4 \pi \varepsilon_{\mathrm{o}}}=9 \times 10^9\) SI units)

Given figure shows the north and south poles of a permanent magnet in which a coil of \(n\) turns of cross-sectional area \(A\) is resting, such that when a current \(I\) is passed through the coil, the plane of the coil makes and angle \(\theta\) with respect to direction of magnetic field \(B\). If the plane of magnetic field and the coil are horizontal and vertical respectively, the torque on the coil will be

Match of the following.
\(\begin{array}{ll}
\hline \text{ Column I } & \text{ Column II } \\
\hline \begin{array}{ll}
\text{A. Ratio of } \frac{\Delta Q}{\Delta U} \text{ in an isobaric} \\
\text{process}
\end{array} & 1. \frac{T_1}{\left(T_1-T_2\right)} \\
\hline \begin{array}{ll}
\text{B. Ratio of } \frac{\Delta Q}{\Delta W} \text{ in an isobaric} \\
\text{process}
\end{array} & 2. \frac{T_2}{\left(T_1-T_2\right)} \\
\hline \begin{array}{l}
\text{C. Coefficient of performance} \\
\text{of a refrigerator}
\end{array} & 3. \frac{\gamma}{\gamma-1} \\
\hline \begin{array}{l}
\text{D. Coefficient of performance} \\
\text{of a heat pump}
\end{array} & 4. \gamma \\
\hline
\end{array}\)
Codes
\(\begin{array}{llll}A & B & C & D\end{array}\)

A material of \(0.25 \mathrm{~cm}^2\) cross-sectional area is placed in a magnetic field of strength \((\mathrm{H}) 1000 \mathrm{Am}^{-1}\). Then, the magnetic flux produced is
(Susceptibility of material is 313)
(Permeability of free space, \(\mu_0=4 \pi \times 10^{-7} \mathrm{Hm}^{-1}\) )

Two circular coils 1 and 2 are made from the same wire. The radius of the first coil is twice that of the second coil. What is the ratio of potential difference applied across them \(V_1 / V_2\), so that the magnetic field at their centre is the same?

The maximum wavelength of light which causes photoelectric emission from a photosensitive metal surface is \(\lambda_0\). Two light beams of wavelengths \(\frac{\lambda_0}{3}\) and \(\frac{\lambda_0}{9}\) incident on the metal surface. The ratio of the maximum velocities of the emitted photoelectrons is

In the figure, the value of \(Q\) so that the electrostatic potential energy of the system becomes zero is

Let the point L lying in the first quadrant be one end of a latus rectum of the ellipse \(\frac{x^2}{4}+\frac{y^2}{3}=1\). Let \(P\) and \(Q\) be the points where the normal drawn at \(\mathrm{L}\) to this given ellipse meets the major axis and the minor axis. Then the distance between \(\mathrm{P}\) and \(\mathrm{Q}\) is

For any natural number \(n,\left(15 \times 5^{2 n}\right)+\left(2 \times 2^{3 n}\right)\) is divisible by

If \(x^2+y^2+z^2 \neq 0, \quad x=c y+b z, \quad y=a z+c x\) and \(z=b x+a y\), then \(a^2+b^2+c^2+2 a b c\) is equal to

Let P be any point on the circle \(x^2+y^2=25\). Let L be the chord of contact of P with respect to the circle \(x^2+y^2=\) 9. The locus of the poles of the lines L with respect to the circle \(x^2+y^2=36\) is

In the structure of ${\mathrm{B}}_2{\mathrm{H}}_6$, the number of ${\mathrm{BH}}_2$ groups present in one plane, and the number of $\mathrm{B}-\mathrm{H}$ bonds, $\mathrm{B}-\mathrm{B}$ bonds, $\mathrm{B}-\mathrm{H}-\mathrm{B}$ bridge bonds are respectively