Physics
- The efficiency of an ideal heat engine working between the freezing point and boiling point of water, is Answer: 1. 26.8% Efficiency of an ideal (Carnot) engine is η=1-T₂/T₁ , with temperatures in kelvin. T₂=273 K (freezing point), T₁=373 K (boi... 1
- Consider a drop of rain water having mass 1 g falling from a height of 1 km. It hits the ground with a speed of 50 m/s. Take 'g' constant with a value 10 m/s^2. The work done by the (i) gravitational force and the (ii) resistive force of air is : Answer: 3. (i) 10 J (ii) - 8.75 J Key idea: use work-energy theorem: W_g+W_air=Δ KE . (i) W_g=mgh=0.001×10×1000=10 J. Δ KE=1/2(0.001)(50)²=1... 1
- The ratio of wavelengths of the last line of Balmer series and the last line of Lyman series is : Answer: 2. 4 Key idea: the last line of a series has n₂=∞ : dfrac1λ=RZ²(dfrac1n₁²-0) . Balmer ( n₁=2 ): dfrac1λ_B=R/4 . Lyman ( n₁=1 ): dfra... 1
- A potentiometer is an accurate and versatile device to make electrical measurements of E.M.F. because the method involves : Answer: 2. a condition of no current flow through the galvanometer Key idea: at the balance point no current flows through the galvanometer,... 1
- The photoelectric threshold wavelength of silver is 3250×10^-10 m. The velocity of the electron ejected from a silver surface by ultraviolet light of wavelength 2536×10^-10 m is :(Given h = 4.14×10^-15 eVs and c = 3×10^8 ms^-1) Answer: Dropped in the official answer key: full marks to every candidate Key idea: 1/2mv²=hc/λ-hc/λ₀ . hc=4.14×10⁻¹⁵×3×10⁸=1242 eV nm. Phot... 1
- Figure shows a circuit that contains three identical resistors with resistance R = 9.0 Ω each, two identical inductors with inductance L = 2.0 mH each, and an ideal battery with emf ε = 18 V. The current 'i' through the battery just after the switch… Answer: Dropped in the official answer key: full marks to every candidate Key idea: just after the switch closes, an inductor acts as an ope... 1
- Which one of the following represents forward bias diode ? Answer: 4. diode with 0 V on left, R, -2 V on right Key idea: a diode is forward biased when its p-side (the triangle base) is at higher pot... 1
- Suppose the charge of a proton and an electron differ slightly. One of them is -e, the other is (e+Δ e). If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (much greater than atomic size) apart… Answer: 2. 10⁻³⁷ C Key idea: each hydrogen atom then has a net charge Δ e , and the electric repulsion balances gravity. (Δ e)²/4πε₀d²=Gm_h²... 1
- The diagrams below show regions of equipotentials.A positive charge is moved from A to B in each diagram. Answer: 1. In all the four cases the work done is the same. Key idea: work done by an external agent moving a charge slowly is W=q(V_B-V_A)... 1
- A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of resulting system : Answer: 1. decreases by a factor of 2 Key idea: charge is conserved when the second capacitor is connected, but energy is not. Initially U=Q... 1
- The acceleration due to gravity at a height 1 km above the earth is the same as at a depth d below the surface of earth. Then : Answer: 3. d = 2 km Key idea: at height h (small): g'=g(1-2h/R) . At depth d : g'=g(1-d/R) . Equating: 2h/R=d/R⇒ d=2h=2 km. 1
- Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time t_1. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time t_2. The time… Answer: 2. t₁t₂/t₂+t₁ Key idea: add speeds. Let the stair length be L . Her walking speed is L/t₁ , escalator speed is L/t₂ . Combined speed... 1
- A gas mixture consists of 2 moles of O_2 and 4 moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is : Answer: 3. 11 RT Key idea: internal energy U=f/2nRT . O₂ is diatomic ( f=5 , vibration neglected): U=5/2×2RT=5RT . Ar is monatomic ( f=3 ):... 1
- One end of string of length l is connected to a particle of mass 'm' and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed 'v', the net force on the particle (directed towards center) w… Answer: 4. T Key idea: only the string tension acts in the horizontal plane. Weight and normal reaction cancel vertically. So the net force... 1
- Two blocks A and B of masses 3m and m respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of A and B immediately after the string is c… Answer: 1. g/3 , g Key idea: the spring force cannot change instantly, but the string tension vanishes at once. Before cutting, the spring h... 1
- If θ_1 and θ_2 be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dip θ is given by : Answer: 4. cot²θ=cot²θ₁+cot²θ₂ Key idea: in a vertical plane at angle α to the magnetic meridian, tanθ'=tanθ/cosα , i.e. cotθ'=cotθcosα . Fo... 1
- A 250 - Turn rectangular coil of length 2.1 cm and width 1.25 cm carries a current of 85 μA and subjected to a magnetic field of strength 0.85 T. Work done for rotating the coil by 180^° against the torque is : Answer: 4. 9.1 μ J Key idea: work done in rotating a coil from θ=0 to 180^° is W=MB(cos0-cos180)=2MB , with M=NIA . A=2.1×10⁻²×1.25×10⁻²=2.6... 1
- The ratio of resolving powers of an optical microscope for two wavelengths λ_1 = 4000 and λ_2 = 6000 is : Answer: 2. 3 : 2 Key idea: resolving power of a microscope is ∝dfrac1λ . R₁/R₂=λ₂/λ₁=6000/4000=3/2 , i.e. 3 : 2. 1
- Two Polaroids P_1 and P_2 are placed with their axis perpendicular to each other. Unpolarised light I_0 is incident on P_1. A third polaroid P_3 is kept in between P_1 and P_2 such that its axis makes an angle 45^° with that of P_1. The intensity of… Answer: 2. I₀/8 Key idea: the first polaroid halves unpolarised light; then use Malus's law I=Icos²θ . After P₁ : I₀/2 . After P₃ (45 ^° ):... 1
- A beam of light from a source L is incident normally on a plane mirror fixed at a certain distance x from the source. The beam is reflected back as a spot on a scale placed just above the source L. When the mirror is rotated through a small angle θ,… Answer: 4. y/2x Key idea: when a mirror rotates by θ , the reflected ray turns by 2θ . The spot moves by y=xtan2θ≈2θ x for small angles. So... 1
- A thin prism having refracting angle 10^° is made of glass of refractive index 1.42. This prism is combined with another thin prism of glass of refractive index 1.7. This combination produces dispersion without deviation. The refracting angle of seco… Answer: 1. 6 ^° Key idea: dispersion without deviation means the net deviation is zero: (μ₁-1)A₁=(μ₂-1)A₂ . (1.42-1)×10=(1.7-1)A₂⇒ 4.2=0.7A₂... 1
- A spring of force constant k is cut into lengths of ratio 1 : 2 : 3. They are connected in series and the new force constant is k'. Then they are connected in parallel and force constant is k''. Then k' : k'' is : Answer: 2. 1 : 11 Key idea: spring constant is inversely proportional to length. Pieces have lengths L/6,L/3,L/2 , so constants 6k,3k,2k . S... 1
- The two nearest harmonics of a tube closed at one end and open at other end are 220 Hz and 260 Hz. What is the fundamental frequency of the system ? Answer: 1. 20 Hz Key idea: a tube closed at one end has only odd harmonics: f₀,3f₀,5f₀,dots . Consecutive harmonics differ by 2f₀ . 260-220=... 1
- A physical quantity of the dimensions of length that can be formed out of c, G and e^2/4πε_0 is [c is velocity of light, G is universal constant of gravitation and e is charge] : Answer: 4. 1/c²[Ge²/4πε₀]^(1/2) Key idea: match dimensions. e²/4πε₀ is force × length ² : [ML³T⁻²] . G=[M⁻¹L³T⁻²] . Product Ge²/4πε₀=[L⁶T⁻⁴]... 1