All questions

• A potentiometer wire 4 m long of resistance 8 Ω is connected in series with a 12 Ω resistor and a 2 V cell of negligible internal resistance. The balancing length for a cell of emf 0.5 V is Answer: C. 2.5 m I=2/20=0.1 A; potential gradient =0.1×8/4=0.2 V/m; l=0.5/0.2=2.5 m. Current Electricity 1 answer
• A galvanometer of resistance 50 Ω gives full-scale deflection for 5 mA. The shunt needed to convert it into an ammeter of range 0–5 A is approximately Answer: D. 0.05 Ω S=I_gG/I-I_g=0.005×50/4.995≈0.05\ Ω . Current Electricity 1 answer
• A circular coil of 100 turns and radius 10 cm carries a current of 5 A. The magnetic field at its centre is (\(\mu_0=4\pi\times10^{-7}\) T m/A) Answer: D. π×10⁻³ T B=μ₀NI/2R=frac4π×10⁻⁷×100×50.2=π×10⁻³ T. Magnetic Fields due to Electric Current 1 answer
• A proton and an α-particle having the same kinetic energy enter a uniform magnetic field perpendicular to it. The ratio of the radii of their circular paths \(r_p:r_\alpha\) is Answer: A. 1 : 1 r=√(2mK)/qB . For α: mass 4m , charge 2e gives √(8mK)/2eB=√(2mK)/eB , same as proton. Magnetic Fields due to Electric Current 1 answer
• A rectangular coil of 50 turns and area 0.02 m2 carries 2 A in a uniform field of 0.5 T. The torque on it when its plane is parallel to the field is Answer: B. 1 N m Plane parallel to field means the normal is perpendicular to B : τ=NIAB=50×2×0.02×0.5=1 N m. Magnetic Fields due to Electric Current 1 answer
• The magnetic susceptibility of a paramagnetic salt is \(\chi\) at 300 K. Its susceptibility at 200 K will be Answer: D. 1.5chi Curie's law: chi∝1/T⇒chi'=chi×300/200=1.5chi . Magnetic Materials 1 answer
• A conducting rod of length 1 m moves at 5 m/s perpendicular to a uniform magnetic field of 0.4 T on frictionless rails connected through a 4 Ω resistor (other resistances negligible). The external force needed to keep it moving at constant speed is Answer: D. 0.2 N e=Blv=2 V, I=0.5 A, F=BIl=0.4×0.5×1=0.2 N. Electromagnetic induction 1 answer
• When the current in a coil falls uniformly from 2 A to zero in 0.05 s, an emf of 8 V is induced in it. The self-inductance of the coil is Answer: A. 0.2 H L=e/dI/dt=8/2/0.05=0.2 H. Electromagnetic induction 1 answer
• In a series LCR circuit, \(L=\frac{1}{\pi}\) H and \(C=\frac{1}{\pi}\) μF. The resonant frequency is Answer: A. 500 Hz f=1/2π√(LC)=frac12π·frac10⁻³π=500 Hz. AC Circuits 1 answer
• In a series RL circuit, R = 30 Ω and \(X_L\) = 40 Ω. The power factor of the circuit is Answer: D. 0.6 Z=√(30²+40²)=50\ Ω , cosφ=R/Z=0.6 . AC Circuits 1 answer
• Light of wavelength 310 nm falls on a metal of work function 2.5 eV. The stopping potential is (take \(hc=1240\) eV nm) Answer: C. 1.5 V E=1240/310=4 eV; eV₀=4-2.5=1.5 eV, so V₀=1.5 V. Dual Nature of Radiation and Matter 1 answer
• The de Broglie wavelength of an electron accelerated from rest through a potential difference of 100 V is about Answer: B. 1.227 Å λ=12.27/sqrt V Å =12.27/10=1.227 Å. Dual Nature of Radiation and Matter 1 answer
• The ratio of the wavelength of the first line of the Balmer series to that of the first line of the Lyman series in hydrogen is Answer: D. 27/5 frac1λ_B∝1/4-1/9=5/36 , frac1λ_L∝1-1/4=3/4 . λ_B/λ_L=3/4/5/36=27/5 . Structure of Atoms and Nuclei 1 answer
• \({}^{238}_{92}\mathrm{U}\) decays to \({}^{206}_{82}\mathrm{Pb}\). The numbers of α and β− particles emitted are Answer: D. 8 α and 6 β α count =238-206/4=8 , lowering Z by 16 to 76. To reach 82, 6 β⁻ are needed. Structure of Atoms and Nuclei 1 answer
• A 6 V Zener diode is used with a series resistance of 200 Ω across a 10 V supply. A load of 1 kΩ is connected across the Zener. The current through the Zener diode is Answer: C. 14 mA Series current =10-6/200=20 mA; load current =6/1000=6 mA; Zener current =14 mA. Semiconductor Devices 1 answer
• A projectile is fired so that its horizontal range equals its maximum height. The angle of projection with the horizontal is Answer: C. tan⁻¹(4) 2u²sinθcosθ/g=u²sin²θ/2g⇒tanθ=4 . Motion in a Plane 1 answer
• Blocks of mass 2 kg and 3 kg are in contact on a frictionless horizontal surface. A horizontal force of 10 N is applied to the 2 kg block. The contact force between the blocks is Answer: C. 6 N a=10/5=2 m/s²; force on 3 kg block =3×2=6 N. Laws of Motion 1 answer
• A ball of mass 0.15 kg moving at 20 m/s is hit straight back with the same speed. If the contact lasts 0.01 s, the average force on the ball is Answer: C. 600 N Δ p=0.15×40=6 N s; F=6/0.01=600 N. Laws of Motion 1 answer
• A planet has the same mean density as the earth but twice its radius. If the escape speed on earth is 11.2 km/s, the escape speed on the planet is Answer: A. 22.4 km/s v_e=√(2GM/R)=R√(8π Gρ/3)∝ R for equal density, so 2×11.2=22.4 km/s. Gravitation 1 answer
• At what height above the earth's surface does the acceleration due to gravity become one-fourth of its value on the surface? (R = 6400 km) Answer: A. 6400 km g/4=g/(1+h/R)²⇒1+h/R=2⇒ h=R . Gravitation 1 answer
• 100 g of water at 80 °C is mixed with 200 g of water at 20 °C. Neglecting heat losses, the final temperature is Answer: D. 40 °C 100(80-T)=200(T-20)⇒ T=40 °C. Thermal Properties of Matter 1 answer
• A source of frequency 900 Hz moves towards a stationary observer at 34 m/s. If the speed of sound is 340 m/s, the frequency heard is Answer: A. 1000 Hz n'=nv/v-v_s=900×340/306=1000 Hz. Sound 1 answer
• A convex lens of focal length 20 cm is placed in contact with a concave lens of focal length 40 cm. The combination behaves as a Answer: D. convex lens of focal length 40 cm 1/F=frac120-frac140=frac140 ; positive, so converging, F = 40 cm. Optics 1 answer
• The critical angle for light going from glass (\(\mu=1.5\)) to air is Answer: B. sin⁻¹(2/3) sin C=frac1μ=2/3 . Optics 1 answer