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 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) $T\propto R^{\frac{(n+1)}{2}}$
5 A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross- section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere, ($\frac{\text{d}r}{\text{}r}$) is A) $\frac{Ka}{mg}$ B) $\frac{Ka}{3mg}$ C) $\frac{mg}{3Ka}$ D) $\frac{mg}{Ka}$
6 The mass of a hydrogen molecule is 3.32 x10-27 kg. If 1023hydrogen molecules strike per second, a fixed wall of area 2 cm2 at an angle of 45° to the normal and rebound elastically with a speed of 103 m/s, then the pressure on the wall is nearly A) $2.35\times 10^{3} N/m^{2}$ B) $4.70\times 10^{3} N/m^{2}$ C) $4.70\times 10^{2} N/m^{2}$ D) $2.35\times 10^{2} N/m^{2}$
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 The angular width of the central maximum in a single slit diffraction pattern is 60° .The width of the slit is 1μm. The slit illuminated by monochromatic plane waves. If another slit of same width is made near it, Young's fringes can be observed on a screen placed at a disance 50cm from the slits. If the observed fringe width is 1 cm, what is slit seperation distance? (i.e. distance between the centres of each slit). A) $50\mu m$ B) $25\mu m$ C) $100\mu m$ D) $75\mu m$
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 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) $2\times 10^{6}$
11 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
12 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) $150kWm^{-2}$
13 A moving coil galvnometer has 50 turns and each turn has an area 2 × 10-4 m2 .The magnetic field produced by the magnet inside the galvnometer is 0.02 T. The torsional constant of the suspension wire is 10-4 N-m rad -1 . When a current flows through the galvanometer, a full scale deflection occurs, if the coil rotates by 0.2 rad. The resistance of the coil of the galvanometer is 50 Ω . This galvanometer is to be converted into an ammeter capable of measuring current in the range 0 - 10A , For this purpose , a shunt resistance is to be added in parallel to the galvanometer . The value of this shunt resistance in ohms, is................ A) 6.25 B) 5.85 C) 5.55 D) 5
14 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
15 One mole of a monoatomic ideal gas undergoes four thermodynamic processes as shown schematically in the pV - diagram below. Among these four processes, one is isobaric, one is isochoric , one is isothermal and one is adiabatic. Match the processes mentioned in List -I with the corresponding statements in List -II A) $P\rightarrow4;Q\rightarrow3;R\rightarrow1;S\rightarrow2$ B) $P\rightarrow1;Q\rightarrow3;R\rightarrow2;S\rightarrow4$ C) $P\rightarrow3;Q\rightarrow4;R\rightarrow1;S\rightarrow2$ D) $P\rightarrow3;Q\rightarrow4;R\rightarrow2;S\rightarrow1$