Potential energy of a particle is given as \(u = \frac{A\sqrt{x}}{B+x}\). Find dimension of A and B :-

• (1) \(M^3 L^{3/2} T^{-2}\), \(L\)
• (2) \(M L^{5/2} T^{-1}\), \(L^2\)
• (3) \(ML^{5/2} T^{-2}\), \(L\)
• (4) \(ML^{7/2} T^{-3}\), \(L\)

In AC circuit supply voltage (\(V_{rms}\)) = 1000V, \(R = 80 \, \Omega\), \(X_L = 80 \, \Omega\) \& source frequency \(f = 50 \, Hz\). Find the power factor.

• (1) \(\frac{1}{\sqrt{2}}\)
• (2) \(\frac{1}{\sqrt{3}}\)
• (3) \(\frac{1}{\sqrt{5}}\)
• (4) \(\frac{1}{\sqrt{6}}\)

Electric field due to half Ring at center is 100 N/C. Find charge on Ring. Radius of Ring is 10cm.

• (1) \(\frac{\pi}{9}\times 10^{-9} \, C\)
• (2) \(\frac{\pi}{27}\times 10^{-9} \, C\)
• (3) \(\frac{\pi}{18}\times 10^{-9} \, C\)
• (4) \(\frac{\pi}{36}\times 10^{-9} \, C\)

A particle is released from point A of track as shown in figure find h so that normal reaction at highest point is 3 times the weight of block :-

• (1) \(h = 4 R\)
• (2) \(h = 3 R\)
• (3) \(h = 2.5 R\)
• (4) \(h = 6 R\)

Find tranverse magnification due to curved boundary between two mediums. \(n_1= 1\), \(n_2= 1.4\), and the object is at a distance \(4R\) from the pole.

• (1) \(–1.5\)
• (2) \(–1.67\)
• (3) \(+1.2\)
• (4) \(–0.8\)

Find heat dissipate in \(6\Omega\) resistance in 100 seconds.

• (1) \(31 \, J\)
• (2) \(35 \, J\)
• (3) \(40 \, J\)
• (4) \(28 \, J\)

In YDSE a glass slab of thickness \(8\mum\) is introduced in front of a slit. If central maxima shifts to the position of \(4^{th}\) minima, then find refractive index of glass slab (\(\lambda = 500 \, nm\)):-

• (1) \(\mu = 1.11\)
• (2) \(\mu = 1.22\)
• (3) \(\mu = 1.32\)
• (4) \(\mu = .22\)

A particle is performing SHM of amplitude A. Find the time required for particle to go from mean position to \(\frac{A}{\sqrt{2}}\). Time period of SHM is 5 secs :-

• (1) \(5/4 \, sec.\)
• (2) \(5/12 \, sec.\)
• (3) \(5/8 \, sec.\)
• (4) \(5/6 \, sec.\)

Find \(\mu\) so that blocks are at rest :

• (1) \(1/3\)
• (2) \(2/3\)
• (3) \(1/4\)
• (4) \(1/2\)

For the given circuit, find ratio of instantaneous voltage across inductor when current is 2mA \& when current is 4mA.

• (1) \(1.5\)
• (2) \(1\)
• (3) \(2\)
• (4) \(1.25\)

A sphere of mass 5 kg and radius 4 cm is rotating about fixed axis about diameter with 1200 r.p.m. To stop it in 10 sec, a torque is applied. Find magnitude of torque required and revolution made before it stops. Respectively :-

• (1) \(0.08 \, N-m and 50 Rev.\)
• (2) \(0.04 \, N-m and 100 Rev.\)
• (3) \(0.016 \, N-m and 200 Rev.\)
• (4) \(0.2 \, N-m and 100 Rev.\)

Intensity of two sources is same and path difference at point A and B are \(\frac{\lambda}{6}\) and \(\frac{\lambda}{3}\) respectively. Ratio of intensity at A \& B will be.

• (1) \(3\)
• (2) \(4\)
• (3) \(1/3\)
• (4) \(1/4\)

Find minimum \(R_S\) so that LED light does not get damaged (power rating of LED is 2 mW):-

• (1) \(1\Omega\)
• (2) \(2\Omega\)
• (3) \(3\Omega\)
• (4) \(4\Omega\)

The dimension of a solid cylinder is measured as given Mass = \(19.42 \pm 0.02 \, kg\), Diameter = \(20.20 \pm 0.02 \, cm\), Length = \(10.10 \pm 0.02 \, cm\). Find out % error in density.

• (1) \(0.5%\)
• (2) \(0.3%\)
• (3) \(0.4%\)
• (4) \(0.7%\)

Electric field in space is given by \(\vec{E} = 2x\hat{i} + 3y^2\hat{j} + 4\hat{k}\). A charge q = 3C is taken from \(r_i(0, -1, -3)\) to \(r_f(5, 1, 2)\). Find magnitude of \(\Delta U\)

Bulk's modulus of an ideal gas for isothermal process initially is B. Gas is compressed from volume \(V_0\) to \(\frac{V_0}{3}\) isothermally. Find the work done by gas.

• (1) \(BV_0\ell n3\)
• (2) \(\frac{BV_0}{3}\ell n3\)
• (3) \(BV_0\ell n(1/3)\)
• (4) \(3BV_0\ell n(1/2)\)

A cube of side 1mm is placed at centre of circular coil of radius 10cm. current flowing in coil is 2A. Find magnetic field energy stored in cube. (\(\pi = 3.14\))

• (1) \(1.57 \times 10^{-14} \, J\)
• (2) \(6.28 \times 10^{-14} \, J\)
• (3) \(12.56 \times 10^{-14} \, J\)
• (4) \(9.42 \times 10^{-14} \, J\)

Unpolarised light with intensity \(I_0\), incident on polariser. Find angle between axis of polarises and analyser so that intensity of emergent light becomes \(\frac{3I_0}{8}\) :-

• (1) \(60^\circ\)
• (2) \(30^\circ\)
• (3) \(90^\circ\)
• (4) \(0^\circ\)

Shortest wavelength of Lyman is x, then difference of wavelengths of \(1^{st}\) Balmer and \(2^{nd}\) Balmer line is terms of x will be :-

• (1) \((28/15)x\)
• (2) \((26/15)x\)
• (3) \((13/15)x\)
• (4) \((11/15)x\)

A small drop of mass 1 gm starts falling from rest from a height of 1 km. When it reaches the ground with speed of 5 m/s, magnitude of work done by resistance force is \(x \times 10^{-3} \, J\). Find x :-

• (1) \(845\)
• (2) \(247.5\)
• (3) \(987.5\)
• (4) \(None\)

If P is the midpoint of median. Find distance of COM from P.

• (1) \(6.18\)
• (2) \(5.18\)
• (3) \(6.88\)
• (4) \(1.32\)

Two wires are joint together and is elongated with force as shown in figure. If \(\frac{Y_1}{Y_2} = \frac{20}{11}\). Find out \(\frac{\ell_1}{\ell_2}\) so that they have same elongation.

• (1) \(11/20\)
• (2) \(20/11\)
• (3) \(11/10\)
• (4) \(10/11\)

Find the ratio of momentum of photons of \(1^{st}\) \& \(2^{nd}\) line of Balmer series of hydrogen atom.

• (1) \(10/20\)
• (2) \(11/27\)
• (3) \(15/20\)
• (4) \(20/27\)

A point source is kept at center of sphere. The intensity of light at point A is I, then intensity at point B is :

• (1) \(I/2\)
• (2) \(2I\)
• (3) \(I\)
• (4) \(I/3m\)