1 For an R-L-C circuit driven with a voltage amplitude vm and freqency $\omega_{0}=\frac{1}{\sqrt{LC}}$, the current exhibits resonance. The quality factor, Q is given A) $\frac{\omega_{0}L}{R}$ B) $\frac{\omega_{0}R}{L}$ C) $\frac{R}{\omega_{0}C}$ D) $\frac{CR}{\omega_{0}}$
2 The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the loop is B1. When the dipole moment is doubled by keeping the current costant, the magnetic field at the centre of the loop is B2. The ratio B1/B2 A) 2 B) $\sqrt{2}$ C) $\sqrt{3}$ D) $\frac{1}{\sqrt{2}}$
3 In an AC circuit, the instantaneous emf and current are given by $e=100\sin30t$ , $i=20\sin\left(30t-\frac{\pi}{4}\right)$ In one cycle of AC , the average power consumed by the circuit and the wattless current are, respectively A) 50 ,10 B) 50 ,0 C) 50/v2 ,0 D) 1000/v2 , 10
4 Two masses m1= 5 kg and m2 = 10 kg connected by an inextensible string over a frictionless pulley , are moving as shown in the figure. The coefficient of friction of horizontal surface is 0.15. The minimum weight m that should be put on top of m2 to stop the motion is A) 18.3 kg B) 10.3 kg C) 43.3 kg D) 27.3 kg
5 A particle is moving in a circular path of radius a under the action of an attractive potential $U=-\frac{k}{2r^{2}}$ , Its total energy is A) $-\frac{k}{4a^{2}}$ B) 0 C) $\frac{K}{2a^{2}}$ D) $-\frac{3k}{2a^{2}}$
6 From a unifrom circular disc of radius R and mass 9 M, a small disc of radius $\frac{R}{3}$ is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through centre of disc is A) $4MR^{2}$ B) $10MR^{2}$ C) $\frac{40}{9}MR^{2}$ D) $\frac{37}{9}MR^{2}$
7 A parallel plate capacitor of capacitance 90pF is connected to a battery of emf 20 V. If a dielectric material of dielectric constant K=$\frac{5}{3}$ is inserted between the plates ,the magnitude of the induced charge will be A) 1.2nC B) 0.3nc C) 2.4nC D) 0.9nC
8 An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii re,rp,rα is repectively, in a unifrom magnetic field B. The relation between re,rp, rα is>> A) $r_{e}\gt r_{p}= r_{\alpha}$ B) $r_{e}\lt r_{p}= r_{\alpha}$ C) $r_{e}\lt r_{p}\lt r_{\alpha}$ D) $r_{e}\lt r_{\alpha}\lt r_{p}$
9 If the series limit frequency of the Lyman series is vL, the the series limit frequency of the Pfund series is A) $25v_{L}$ B) $16v_{L}$ C) $\frac{v_{L}}{16}$ D) $\frac{v_{L}}{25}$
10 The reading of the ammeter for a silicon diode in the given circuit is A) 0 B) 15mA C) 11.5mA D) 13.5mA
11 Two batteries with emf 12V and 13V are connected in parallel across a load resistor of 10 Ω . The internal resistances of the two batteries are 1Ω and 2Ω, respectively. The voltage across the load lies between A) 11.6 V and 11.7 V B) 11.5 V and 11.6 V C) 11.4 V and 11.5 V D) 11.7 V and 11.8 V
12 A uniform capillary tube of inner radius r is dipped vertically in to a beaker filled with water. The water rises to a height h in the capillary tube above the water surface in the beaker. The surface tension of the water is $\sigma$ . The angle of contact between water and the wall of the capillary tube is θ . Ignore the mass of water in the meniscus. Which of the following statements is (are) true ? A) For a given material of the capillary tube, h decreases with increase in r B) For a given material of the capillary tube , h is independent of $\sigma$ C) If this experiment is performed in a lift going up with a constant acceleration, then h decreases D) h is proportional to contact angle$\theta$
13 In the figure below , the switches S1 and S2 are closed simultaneously at t=0 and a current starts to flow in the circuit. Both the batteries have the same magnitude of the electromotive force (emf) and the polarities are as indicated in the figure. Ignore mutual inductance between the inductors. The current I in the middle wires reaches its maximum magnitude Imax at time $t=\tau$ . which of the following statements is (are) true ? A) $I_{max}=\frac{V}{2R}$ B) $I_{max}=\frac{V}{4R}$ C) $\tau =\frac{L}{R} In 2$ D) $\tau =\frac{2L}{R} In 2$
14 The relation between $[\epsilon_{0}]$ and $[\mu_{0}]$ A) $[\mu_{0}]= [\epsilon_{0}][L]^{2}[T]^{-2}$ B) $[\mu_{0}]= [\epsilon_{0}][L]^{-2}[T]^{2}$ C) $[\mu_{0}]= [\epsilon_{0}^{}]^{-1}[L]^{2}[T]^{-2}$ D) $[\mu_{0}]= [\epsilon_{0}^{}]^{-1}[L]^{-2}[T]^{2}$
15 A ball is projected from the ground at an angle of 45° with the horizontal surface . It reaches a maximum height of 120m and returns to the ground. Upon hitting the ground for the first time, it loses half of its kinetic energy . Immediately after the bounce , the velocity of the ball makes an angle of 30° with the horizontal surface . The maximum height it reaches after the bounce, in metres, is......... A) 40 B) 25 C) 30 D) 15