Physics
- The energy required to break one bond in DNA is 10^-20 J. This value in eV is nearly : Answer: 3. 0.06 Convert joules to eV using 1\ eV=1.6×10⁻¹⁹ J. E=frac10⁻²⁰1.6×10⁻¹⁹=0.0625≈0.06\ eV Answer: option 3. 1
- A wire of length L, area of cross section A is hanging from a fixed support. The length of the wire changes to L_1 when mass M is suspended from its free end. The expression for Young's modulus is : Answer: 4. MgL/A(L₁ - L) Young's modulus Y=stress/strain . Stress =Mg/A Strain =L₁-L/L , since the extension is L₁-L and the original length... 1
- The quantities of heat required to raise the temperature of two solid copper spheres of radii r_1 and r_2 (r_1 = 1.5 r_2) through 1 K are in the ratio : Answer: 1. 27/8 Heat needed for a 1 K rise is Q=mcΔ T . Both spheres are copper, so c is the same and Q∝ m∝ r³ . Q₁/Q₂=(r₁/r₂)³=(1.5)³=27/8... 1
- A capillary tube of radius r is immersed in water and water rises in it to a height h. The mass of the water in the capillary is 5 g. Another capillary tube of radius 2r is immersed in water. The mass of water that will rise in this tube is : Answer: 3. 10.0 g Capillary rise: h=2Tcosθ/rρ g , so h∝1/r . Mass of water in the tube m=ρπ r²h∝ r²·1/r=r . Radius doubled gives mass double... 1
- For which one of the following, Bohr model is not valid ? Answer: 4. Singly ionised neon atom (Ne ^+ ) The Bohr model works only for one-electron (hydrogen-like) systems, where the electron feels ju... 1
- The energy equivalent of 0.5 g of a substance is : Answer: 2. 4.5×10¹³ J Use Einstein's mass-energy relation E=mc² . E=0.5×10⁻³×(3×10⁸)²=4.5×10¹³\ J Answer: option 2. Remember to convert gram... 1
- The solids which have the negative temperature coefficient of resistance are : Answer: 4. insulators and semiconductors Metals have a positive temperature coefficient of resistance: resistance rises with temperature as... 1
- Light of frequency 1.5 times the threshold frequency is incident on a photosensitive material. What will be the photoelectric current if the frequency is halved and intensity is doubled ? Answer: 4. zero Photoelectric emission needs frequency ν≥ν₀ , whatever the intensity. Initially ν=1.5ν₀ . Halved, it becomes 0.75ν₀<ν₀ , bel... 1
- A 40 μF capacitor is connected to a 200 V, 50 Hz ac supply. The rms value of the current in the circuit is, nearly : Answer: 3. 2.5 A Capacitive reactance X_C=1/2π fC . X_C=frac12π×50×40×10⁻⁶≈79.6\ Ω I_rms=fracV_rmsX_C=200/79.6≈2.5\ A Answer: option 3. 1
- The ratio of contributions made by the electric field and magnetic field components to the intensity of an electromagnetic wave is : (c = speed of electromagnetic waves) Answer: 2. 1 : 1 In an electromagnetic wave the energy is shared equally between the electric and magnetic fields. Electric energy density =... 1
- Light with an average flux of 20 W/cm^2 falls on a non-reflecting surface at normal incidence having surface area 20 cm^2. The energy received by the surface during time span of 1 minute is : Answer: 3. 24×10³ J Energy received = flux × area × time. E=20\ W/cm²×20\ cm²×60\ s=24000\ J=24×10³\ J Answer: option 3. 1
- The increase in the width of the depletion region in a p-n junction diode is due to : Answer: 2. reverse bias only In reverse bias, the applied voltage adds to the barrier. Majority carriers are pulled away from the junction,... 1
- For transistor action, which of the following statements is correct ? Answer: 4. The base region must be very thin and lightly doped. For transistor action the base must be very thin and lightly doped, so most... 1
- A spherical conductor of radius 10 cm has a charge of 3.2×10^-7 C distributed uniformly. What is the magnitude of electric field at a point 15 cm from the centre of the sphere ?≤ft(1/4πε_0 = 9×10^9\ N m^2/C^2) Answer: 2. 1.28×10⁵ N/C Outside a uniformly charged sphere, the field is the same as that of a point charge at the centre. E=1/4πε₀Q/r²=frac... 1
- In a certain region of space with volume 0.2 m^3, the electric potential is found to be 5 V throughout. The magnitude of electric field in this region is : Answer: 1. zero Electric field is the negative gradient of potential: E=-dV/dx . The potential is constant (5 V) throughout the region, so i... 1
- A screw gauge has least count of 0.01 mm and there are 50 divisions in its circular scale.The pitch of the screw gauge is : Answer: 3. 0.5 mm Least count =pitch/number of circular divisions . pitch=0.01\ mm×50=0.5\ mm Answer: option 3. 1
- A body weighs 72 N on the surface of the earth. What is the gravitational force on it, at a height equal to half the radius of the earth ? Answer: 2. 32 N Gravitational force varies as g , and g at height h is g(R/R+h)² . With h=R/2 : (R/1.5R)²=4/9 . F=72×4/9=32\ N Answer: optio... 1
- A cylinder contains hydrogen gas at pressure of 249 kPa and temperature 27^°C.Its density is : (R = 8.3 J mol^-1 K^-1) Answer: 2. 0.2 kg/m ³ Use the ideal gas equation in density form: P=ρ RT/M . M=2×10⁻³ kg/mol, T=300 K, P=2.49×10⁵ Pa. ρ=PM/RT=frac2.49×10⁵×2... 1
- The mean free path for a gas, with molecular diameter d and number density n can be expressed as : Answer: 2. 1/√(2) nπ d² The standard result for the mean free path of a gas is λ=1/sqrt2 nπ d² It falls with number density n (more molecule... 1
- The Brewsters angle i_b for an interface should be : Answer: 3. 45^° < i_b < 90^° Brewster's law: tan i_b=μ , where μ is the relative refractive index of the interface. Since μ>1 for an ordinar... 1
- A ray is incident at an angle of incidence i on one surface of a small angle prism (with angle of prism A) and emerges normally from the opposite surface. If the refractive index of the material of the prism is μ, then the angle of incidence is nearl… Answer: 3. μ A For a small-angle prism, with emergent ray normal to the second face, the angle of refraction at the second face is 0. Since... 1
- In a guitar, two strings A and B made of same material are slightly out of tune and produce beats of frequency 6 Hz. When tension in B is slightly decreased, the beat frequency increases to 7 Hz. If the frequency of A is 530 Hz, the original frequenc… Answer: 2. 524 Hz Frequency of a string f∝√(T) . Decreasing tension of B lowers its frequency. Beat frequency was 6 Hz and rose to 7 Hz afte... 1
- The phase difference between displacement and acceleration of a particle in a simple harmonic motion is : Answer: 1. π rad For SHM, x=Asinω t , and acceleration a=-ω²x . The negative sign means acceleration is always opposite in direction to disp... 1
- Two particles of mass 5 kg and 10 kg respectively are attached to the two ends of a rigid rod of length 1 m with negligible mass.The centre of mass of the system from the 5 kg particle is nearly at a distance of : Answer: 3. 67 cm Take the 5 kg mass as the origin. Centre of mass: x_cm=5(0)+10(100)/5+10=1000/15≈67\ cm It lies closer to the heavier mass,... 1