Physics
- Let a wire be suspended from the ceiling (rigid support) and stretched by a weight W attached at its free end. The longitudinal stress at any point of cross-sectional area A of the wire is : Answer: 3. W/A The wire is in equilibrium under the weight W at the free end (the wire's own weight is neglected). The tension at every cros... 1
- A nucleus of mass number 189 splits into two nuclei having mass number 125 and 64. The ratio of radius of two daughter nuclei respectively is : Answer: 4. 5 : 4 Nuclear radius is R=R₀A^(1/3) . R₁/R₂=(125/64)^(1/3)=5/4 The ratio is 5:4 . Option (4). 1
- A wheatstone bridge is used to determine the value of unknown resistance X by adjusting the variable resistance Y as shown in the figure. For the most precise measurement of X, the resistances P and Q : Answer: 3. should be approximately equal and are small A Wheatstone bridge is most sensitive when all four arms have comparable resistance,... 1
- A big circular coil of 1000 turns and average radius 10 m is rotating about its horizontal diameter at 2 rad s^-1. If the vertical component of earth's magnetic field at that place is 2 × 10^-5 T and electrical resistance of the coil is 12.56 Ω, then… Answer: 4. 1 A Maximum emf in a rotating coil is ε_max=NBAω , with the field component perpendicular to the axis (vertical component here).... 1
- A series LCR circuit with inductance 10 H, capacitance 10 μF, resistance 50 Ω is connected to an ac source of voltage, V = 200 (100 t) volt. If the resonant frequency of the LCR circuit is _0 and the frequency of the ac source is , then : Answer: 3. ν₀ = ν = 50/π Hz Compare the source frequency with the resonant frequency. Source: ω=100\ rad/s⇒ν=100/2π=50/π Hz. Resonance: ω₀=1... 1
- The truth table for the given logic circuit is : Answer: 4. Truth table (A B C): 0 0 1; 0 1 0; 1 0 1; 1 1 0 Trace the circuit. The upper NAND gets A and B: Y₁=A· B . The lower NAND gets bar... 1
- Two point charges -q and +q are placed at a distance of L, as shown in the figure.The magnitude of electric field intensity at a distance R (R>>L) varies as : Answer: 3. 1/R³ The two charges form an electric dipole with dipole moment p=qL . Their fields nearly cancel at a large distance. For Rgg L... 1
- A capacitor of capacitance C = 900 pF is charged fully by 100 V battery B as shown in figure (a). Then it is disconnected from the battery and connected to another uncharged capacitor of capacitance C = 900 pF as shown in figure (b). The electrostati… Answer: 4. 2.25 × 10⁻⁶ J Initial charge: Q=CV=900×10⁻¹²×100=9×10⁻⁸\ C . After connecting to an identical uncharged capacitor, charge is cons... 1
- A ball is projected with a velocity, 10\ ms^-1, at an angle of 60° with the vertical direction. Its speed at the highest point of its trajectory will be : Answer: 3. 5√(3)\ ms⁻¹ The angle is measured from the vertical, so the angle with the horizontal is 30^° . At the highest point only the hor... 1
- The volume occupied by the molecules contained in 4.5 kg water at STP, if the intermolecular forces vanish away is : Answer: 1. 5.6 m ³ With intermolecular forces gone, the water molecules behave like an ideal gas, and one mole occupies 22.4 L at STP. Moles... 1
- From Ampere's circuital law for a long straight wire of circular cross-section carrying a steady current, the variation of magnetic field in the inside and outside region of the wire is : Answer: 4. a linearly increasing function of distance r upto the boundary of the wire and then decreasing one with 1/r dependence for the ou... 1
- Two transparent media A and B are separated by a plane boundary. The speed of light in those media are 1.5 × 10^8 m/s and 2.0 × 10^8 m/s, respectively. The critical angle for a ray of light for these two media is : Answer: 3. sin⁻¹(0.750) Refractive index n=c/v : n_A=3×10⁸/1.5×10⁸=2 and n_B=3×10⁸/2×10⁸=1.5 . Total internal reflection is possible when li... 1
- Match List - I with List - II :List - I: (a) Gravitational constant (G) (b) Gravitational potential energy (c) Gravitational potential (d) Gravitational intensityList - II: (i) [L^2T^-2] (ii) [M^-1L^3T^-2] (iii) [LT^-2] (iv) [ML^2T^-2]Choose the corr… Answer: 3. (a) - (ii), (b) - (iv), (c) - (i), (d) - (iii) Find each dimension from its formula. (a) G=Fr²/m² : [M⁻¹L³T⁻²] , so (ii) (b) Pote... 1
- The area of a rectangular field (in m^2) of length 55.3 m and breadth 25 m after rounding off the value for correct significant digits is : Answer: 1. 14 × 10² Area =55.3×25=1382.5\ m² . In multiplication the answer keeps as many significant figures as the least precise number. 2... 1
- Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R).Assertion (A) : The stretching of a spring is determined by the shear modulus of the material of the spring.Reason (R) : A coil spring of copper… Answer: 4. (A) is true but (R) is false Assertion: when a spring is stretched, the wire of the coil is mainly twisted, which is a shear defo... 1
- Let T_1 and T_2 be the energy of an electron in the first and second excited states of hydrogen atom, respectively. According to the Bohr's model of an atom, the ratio T_1 : T_2 is : Answer: 1. 9 : 4 In Bohr's model the energy magnitude is E_n∝ 1/n² . First excited state is n=2 and second excited state is n=3 . T₁/T₂=1/4/... 1
- In the given nuclear reaction, the element X is :^22_11Na → X + e^+ + Answer: 4. ²²₁₀Ne The emission of a positron is beta-plus decay: a proton turns into a neutron, so the mass number stays the same and the at... 1
- A copper wire of length 10 m and radius (10^-2/√(π)) m has electrical resistance of 10 Ω. The current density in the wire for an electric field strength of 10 (V/m) is : Answer: 1. 10⁵ A/m ² Current density is J=σ E=E/ρ , so first find resistivity from R=ρ L/A . A=π r²=π·dfrac10⁻⁴π=10⁻⁴\ m² ρ=RA/L=dfrac10×10⁻... 1
- The peak voltage of the ac source is equal to : Answer: 4. √(2) times the rms value of the ac source For a sinusoidal ac, V_rms=V₀/sqrt2 , so the peak value is V₀=sqrt2 V_rms . Option (4)... 1
- A square loop of side 1 m and resistance 1 Ω is placed in a magnetic field of 0.5 T. If the plane of loop is perpendicular to the direction of magnetic field, the magnetic flux through the loop is : Answer: 3. 0.5 weber Flux is φ=BAcosθ . The plane of the loop is perpendicular to the field, so the normal is parallel to B and θ=0 . φ=0.5×... 1
- When light propagates through a material medium of relative permittivity ε_r and relative permeability μ_r, the velocity of light, v is given by : (c - velocity of light in vacuum) Answer: 1. v = c/√(ε_r μ_r) In a medium, v=1/√(με) with μ=μ₀μ_r and ε=ε₀ε_r . Since c=dfrac1√(μ₀ε₀) , we get v=c/√(ε_rμ_r) . Option (1) is c... 1
- The energy that will be ideally radiated by a 100 kW transmitter in 1 hour is : Answer: 2. 36 × 10⁷ J Energy radiated equals power times time. E=Pt=100×10³\ W×3600\ s=3.6×10⁸\ J=36×10⁷\ J Option (2) is correct. 1
- In half wave rectification, if the input frequency is 60 Hz, then the output frequency would be : Answer: 4. 60 Hz A half-wave rectifier conducts only in one half of each ac cycle, so there is one output pulse per input cycle. Output freq... 1
- In the given circuits (a), (b) and (c), the potential drop across the two p-n junctions are equal in : Answer: 1. Both circuits (a) and (c) Two diodes in series with a battery see the same current, so their voltage drops are equal when both ar... 1