1 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
2 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
3 The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1% , the maximum error in determining the density is A) 3.5% B) 4.5% C) 2.5% D) 6%
4 In a collinear collision, a particle with an initial speed v0 strikes a stationary particle of the same mass. If the final total kinetic energy is 50% is greater than the orginal kinetic energy, the magnitude of the relative velocity between the two particles after collision ,is A) $\frac{v_{0}}{2}$ B) $\frac{v_{0}}{4}$ C) $\frac{v_{0}}{\sqrt{2}}$ D) $\sqrt{2} v_{0}$
5 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) $\frac{37}{9}MR^{2}$
6 Two moles of an ideal monoatomic gas occupies a volume V at 27° C. The gas expands adiabatically to a Volume 2 V. Calculate(i) the final temperature of the gas and (ii) change in its internal energy. A) (i)189 K (ii) 2.7 KJ B) (i) 195 K (ii) -2.7 KJ C) (i) 189 K (ii) -2.7 KJ D) (i) 195 K (ii) 2.7 KJ
7 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) $\frac{v_{L}}{25}$
8 On interchanging the resistances, the balance point of a meter bridge shifts to the left by 10cm. The resistance of their series combination is 1kΩ. How much was the resistance on the left slot before interchanging the resistances? A) 990Ω B) 505Ω C) 550Ω D) 910Ω
9 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) $\tau =\frac{2L}{R} In 2$
10 Two vectors A and B are defined as $A= a\hat{i}$ and $B= a (\cos wt\hat{i}+\sin w\hat{j})$, where a is a constant and $w=\frac{\pi}{6}rad $$s^{-1}$ . If $\mid A+B\mid =\sqrt{3}\mid A-B\mid$ at time $t= \tau$ for the first time, the value of $\tau$ in seconds, is A) 3.00 s B) 2.00 s C) 5.00 s D) 7.00 s
11 Two infinitely long straight wires lie in the xy-plane along the lines x=± R. The wire located at x=± R carries a constant current I1 and the wire located at x= -R carries a constant cureent I2. A circular loop of radius R is suspended with its centre at (0,0,√3R) and in a plane parallel to the xy-plane . This loop carries a constant current I in the clockwise direction as seen from above the loop.The current in the wire taken to be postive , if it is in the +$\hat{j}$- direction . Which of the following statements regarding the magnetic field B is (are) true ? A) If $l_{1}=l_{2}$, then B cannot be equal to zero at the origin (0,0,0) B) If $l_{1}\gt0$ and $l_{2}\lt0$ , then B can be equal to zero at the origin (0,0,0) C) If $l_{1}\lt0$ and $l_{2}\lt0$, then B can be equal to zero at the origin (0,0,0) D) If $l_{1}=l_{2}$ , then the z-component of the magnetic field at the centre of the loop is $(-\frac{\mu_{0}l}{2R})$
12 A spring block system is resting on a frictionless floor as shown in the figure. The spring constant is 2.0 Nm-1 and the mass of the block is 2.0 kg. Ignore the mass of the spring. Initially ,the spring is in an unstretched condition. Another block of mass 1.0kg moving with a speed of 2.0 ms-1 collides elastically with the first block. The collision is such that the 2.0kg block does not hit the wall. The distance , in metres, between the two blocks when the spring returns to its unstretched position for the first time after the collision is... A) 2.09m B) 2.5m C) 3.0m D) 1.6 m
13 A particle of mass m is initially at rest at the origin . It is subjected to a force and starts moving along the X-axis . Its kinectic energy K changes with time as $\frac{\text{d}K}{\text{d}t}=\gamma t$ , where $\gamma $ is a positive constant of appropriate dimensions. Which of the following statements is (are) true? A) The force applied on the particle is constant B) The speed of the particle is proportional to time C) The distance of the particle from the origin increases linearly with time. D) The force is conservative.
14 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
15 Consider a hydrogen -like ionised atom with atomic number Z , with a single electron. In the emission spectrum of atom, the photon emitted in the n= 2 to n=1 transition has energy 74.8 eV higher than the photon emitted in the n=3 to n=2 transition.The ionisation energy of the hydrogen atom is 13.6 eV. The value of Z is.......... A) 3 B) 6 C) 4 D) 2
