#neet
- For a radioactive material, half-life is 10 minutes. If initially there are 600 number of nuclei, the time taken (in minutes) for the disintegration of 450 nuclei is Answer: 1. 20 If 450 of 600 nuclei disintegrate, 150 remain, which is 1/4 of the original. N/N₀=(1/2)ⁿ=1/4⇒ n=2 half-lives. Time =2×10=20 mi... 1
- The ratio of kinetic energy to the total energy of an electron in a Bohr orbit of the hydrogen atom, is Answer: 3. 1 : - 1 In a Bohr orbit, kinetic energy K=ke²/2r and potential energy U=-ke²/r . Total energy E=K+U=-ke²/2r=-K . K/E=K/-K=1:-1 1
- When the light of frequency 2_0 (where _0 is threshold frequency), is incident on a metal plate, the maximum velocity of electrons emitted is v_1. When the frequency of the incident radiation is increased to 5_0, the maximum velocity of electrons emi… Answer: 1. 1 : 2 Einstein's equation: K_max=hν-hν₀ . At 2ν₀ : K₁=hν₀ . At 5ν₀ : K₂=4hν₀ . Since K=1/2mv² , v∝sqrt K : v₁/v₂=√(1/4)=1/2 Ratio... 1
- An object is placed at a distance of 40 cm from a concave mirror of focal length 15 cm. If the object is displaced through a distance of 20 cm towards the mirror, the displacement of the image will be Answer: 3. 36 cm away from the mirror Use the mirror formula 1/v+1/u=1/f with f=-15 cm. Case 1: u=-40 : 1/v=-dfrac115+dfrac140=-5/120⇒ v=-24... 1
- The refractive index of the material of a prism is 2 and the angle of the prism is 30^°. One of the two refracting surfaces of the prism is made a mirror inwards, by silver coating. A beam of monochromatic light entering the prism from the other face… Answer: 3. 45^° The ray retraces its path only if it strikes the silvered face normally. The prism angle is A=30^° . For a ray hitting the s... 1
- An em wave is propagating in a medium with a velocity V=V i. The instantaneous oscillating electric field of this em wave is along +y axis. Then the direction of oscillating magnetic field of the em wave will be along Answer: 3. + z direction In an em wave, vec E , vec B and the direction of propagation are mutually perpendicular, and vec E×vec B points al... 1
- The magnetic potential energy stored in a certain inductor is 25 mJ, when the current in the inductor is 60 mA. This inductor is of inductance Answer: 4. 13.89 H Energy stored in an inductor: U=1/2LI² . L=2U/I²=frac2×25×10⁻³(60×10⁻³)²=frac0.053.6×10⁻³≈13.89\ H 1
- A battery consists of a variable number 'n' of identical cells (having internal resistance 'r' each) which are connected in series. The terminals of the battery are short-circuited and the current I is measured. Which of the graphs shows the correct… Answer: 1. (graph: I constant, horizontal line vs n) For n identical cells in series, total emf is nE and total internal resistance is nr .... 1
- A set of 'n' equal resistors, of value 'R' each, are connected in series to a battery of emf 'E' and internal resistance 'R'. The current drawn is I. Now, the 'n' resistors are connected in parallel to the same battery. Then the current drawn from ba… Answer: 1. 10 Series: total resistance nR+R , so I=E/(n+1)R . Parallel: total resistance R/n+R=(n+1)R/n , so I'=nE/(n+1)R . I'/I=n=10⇒ n=10 1
- A carbon resistor of (47±4.7) kΩ is to be marked with rings of different colours for its identification. The colour code sequence will be Answer: 3. Yellow - Violet - Orange - Silver Colour code digits: Yellow 4, Violet 7, Orange 3 (multiplier 10³ ), Silver ±10% , Gold ±5% . 47... 1
- A tuning fork is used to produce resonance in a glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperature of 27°C two successive resonances are produced at 20 cm and 73 cm of column length. If the… Answer: 3. 339 m/s In a resonance tube, two successive resonances are half a wavelength apart. dfracλ2=73-20=53 cm, so λ=106 cm =1.06 m. v=f... 1
- The electrostatic force between the metal plates of an isolated parallel plate capacitor C having a charge Q and area A, is Answer: 1. independent of the distance between the plates. The field of one plate is σ/2ε₀ , and this acts on the charge Q of the other plat... 1
- An electron falls from rest through a vertical distance h in a uniform and vertically upward directed electric field E. The direction of electric field is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest in it throu… Answer: 1. smaller The force magnitude is eE for both particles, so a=eE/m . Fall distance h=1/2at² gives t=√(2h/a) . The electron has a muc... 1
- A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is 20 m/s^2 at a distance of 5 m from the mean position. The time period o… Answer: 3. π s For SHM, a=ω²x . ω²=20/5=4⇒ω=2\ mathrmrad s⁻¹ . T=2π/ω=π\ s 1
- The power radiated by a black body is P and it radiates maximum energy at wavelength, λ_0. If the temperature of the black body is now changed so that it radiates maximum energy at wavelength 34λ_0, the power radiated by it becomes nP. The value of n… Answer: 2. 256/81 Wien's law: λ_mT= constant, so T∝dfrac1λ_m . Stefan's law: P∝ T⁴ . New wavelength is 3/4λ₀ , so T'=4/3T . n=(4/3)⁴=256/81 1
- Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3A. If the length of the first wire is increased by Δ l on applying a force F, how much force is… Answer: 1. 9 F Same volume: A l=3A l₂ , so the second wire has length l₂=l/3 . From Y=F l/A Δ l , F=YAΔ l/l . F₂=Y(3A)Δ l/l/3=9·YAΔ l/l=9F 1
- A small sphere of radius 'r' falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity, is proportional to Answer: 2. r⁵ At terminal velocity, heat is produced at the rate equal to the power of the viscous force: P=F v_t=6πη r v_t² . Terminal velo... 1
- A sample of 0.1 g of water at 100°C and normal pressure (1.013×10^5 Nm^-2) requires 54 cal of heat energy to convert to steam at 100°C. If the volume of the steam produced is 167.1 cc, the change in internal energy of the sample, is Answer: 3. 208.7 J First law: Δ U=Q-W , with W=PΔ V . Q=54×4.18≈225.7 J. Volume change: steam 167.1 cc minus water 0.1 cc, Δ V=167\ cm³=1.67... 1
- The moment of the force, F=4 i+5 j-6 k at (2, 0, -3), about the point (2, -2, -2), is given by Answer: 4. -7hat i-4hat j-8hat k Moment (torque) about a point: vecτ=vec r×vec F , where vec r goes from the point to the point of applicati... 1
- A student measured the diameter of a small steel ball using a screw gauge of least count 0.001 cm. The main scale reading is 5 mm and zero of circular scale division coincides with 25 divisions above the reference level. If screw gauge has a zero err… Answer: 4. 0.529 cm Observed reading =0.5+25×0.001=0.525 cm. Zero error is -0.004 cm, so the correction is +0.004 cm. d=0.525-(-0.004)=0.529... 1
- A particle executes linear simple harmonic motion with an amplitude of 3 cm. When the particle is at 2 cm from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is : Answer: 2. 4π/sqrt5 Key idea: in SHM v=ω√(A²-x²) and a=ω²x . At x=2 cm, A=3 cm: ω√(9-4)=ω²×2⇒ω=sqrt5/2 s ⁻¹ . T=2π/ω=4π/sqrt5 s. 1
- A U tube with both ends open to the atmosphere, is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of 10 mm above the water level on the other side. Meanwhile the water rises by… Answer: 3. 928 kg m ⁻³ Key idea: pressure at the same level in the same liquid is equal. Take points B (oil-water interface, left) and C (sa... 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 x and y coordinates of the particle at any time are x = 5t - 2t^2 and y = 10t respectively, where x and y are in meters and t in seconds. The acceleration of the particle at t = 2s is : Answer: 2. - 4 m/s ² Key idea: acceleration components are second derivatives of position. a_x=d²x/dt²=-4 m/s ² , a_y=d²y/dt²=0 . Accelerati... 1