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 A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the n th power of R. If the period of rotation of the particle is T, then A) $T\propto R^{\frac{3}{2}}$ For any n B) $T\propto R^{\frac{n}{2}}$ C) $T\propto R^{\frac{n}{2}+1}$ D) $T\propto R^{\frac{(n+1)}{2}}$
3 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) $\sqrt{2} v_{0}$
4 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) $r_{e}\lt r_{\alpha}\lt r_{p}$
5 The reading of the ammeter for a silicon diode in the given circuit is A) 0 B) 15mA C) 11.5mA D) 13.5mA
6 A telephonic communication service is working at carrier freequency of 10 GHz. Only 10% of it is utilised for transmission. How many telephonic channels can be transmitted simultaneously, if each channel requires a bandwidth of 5kHz? A) $2\times 10^{4}$ B) $2\times 10^{3}$ C) $2\times 10^{5}$ D) $2\times 10^{6}$
7 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
8 A ring and a disc are initially at rest , side by side , at the top of an inclined plane which makes an angle 60° with the horizontal . They start to roll without slipping at the same instant of time along the shortest path. If the time difference between their reaching the ground is $\frac{(2-\sqrt{3})}{\sqrt{10}}$ s, then the height of the top of the inclined plane, in meters is ... [Take, g=10 m s-2 ] A) 0.50 m B) 0.95m C) 0.75m D) 1.00m
9 In the XY-plane , the region y >0 has a uniform magnetic field $B_{1}\hat{K}$ and the region y<0 has another uniform magnetic field $B_{2}\hat{K}$ . A positively charged particle is projected from origin along the positive Y-axis with speed $v_{0}=\pi$ms-1 at t=0, as shown in figure. Neglect gravity in this problem. Let t=T be the time when the particle crosses the X-axis from below for the first time . If B2 =4B1, the average speed of the particle , in ms-1 , along the X-axis in the time interval T is........ A) 2 m/s B) 5 m/s C) 6 m/s D) 1 m/s
10 Sunlight of intensity 1.3kWm-2 is incident normally on a thin convex lens of focal length 20 cm. Ignore the energy loss of light due to the lens and assume that the lens aperture size is much smaller than its focal length. The average intensity of light , in kW m-2, at a distance 22 cm from the lens on the other side is ..... A) $130kWm^{-2}$ B) $140kWm^{-2}$ C) $120kWm^{-2}$ D) $150kWm^{-2}$
11 Two conducting cyclinders of equal length but different radii are connected in series between two heat baths kept at temperatures T1= 300K and T2=100K, as shown in the figure. The radius of the bigger cyclinder is twice that of the smaller one and the thermal conductivites of the materials of the smaller and the larger cyclinders are K1 and K2 , respectively . If the temperature at the junction of the cyclinders in the steady state is 200K, then K1/K2= ......... A) 3 B) 4 C) 2 D) 5
12 The realtion between [E] and [B] is A) $[E]=[B][L][T]$ B) $[E]=[B][L]^{-1}[T]$ C) $[E]=[B][L]^{}[T]^{-1}$ D) $[E]=[B][L]^{-1}[T]^{-1}$
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 An infinitely long thin non-conducting wire is parallel to the Z-axis and carries a uniform line charge density λ . It pierces a thin non-conducting spherical shell of radius R in such a way that the arc PQ subtends an angle 120° at the centre O of the spherical shell, as shown in the figure. The permittivity of free space is ε0 . Which of the following statements is (are) true? A) The electric flux through the shell is $\sqrt{3}R\lambda /\epsilon_{0}$ B) The z-component of the electric field is zero at all the points on the surface of the shell. C) The electric flux through the shell is $\sqrt{2}R\lambda /\epsilon_{0}$ D) The electric field is normal to the surface of the shell at all points.
15 In a radioactive decay chain, $_{90}^{232}Th$ nucleus decays to $_{82}^{212}Pb$ nucleus. Let $N_{\alpha}$ and $N_{\beta}$ be the number of $\alpha$ and $\beta$- particles repectively, emitted in this decay process. Which of the following statements is(are) true? A) $N_{\alpha}=5$ B) $N_{\alpha}=6$ C) $N_{\beta}=2$ D) $N_{\beta}=4$