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Find the value of α* + β*

Let M = M2 = αM + βIa11 = sin θ – 1 – sin2 θ – cos2 θ – cos2 θ sin2 θ = β + α sin4 θ sin8 θ – 2 – cos2 θsin2 θ= β + α sin4 θa21 = sin4 θ + cos2... View Article

Four resistors of resistance 15 Ω, 12 Ω, 4Ω and 10Ω respectively in cyclic order to form a wheatstone’s network. The resistance that is to be connected in parallel with the resistance of 10 to balance the network is

[(10R)/(10+R) ]×12 = 15 ×4 R = 10Ω... View Article

A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP is 300 m/s, the frequency difference between the fundamental and second harmonic of this pipe is __Hz.

V = √(B/ρ) Vpipe/ Vair = Vpipe = Vair/√2 fn = Vpipe(n+1)/2l f1-f0 = Vpipe/ 2l = 300/2√2 = 106.06 Hz ( if √2 = 1.414) ≈ 106 Hz... View Article

A particle is moving along the x-axis with its coordinate with time t given by x(t) = -3t² + 8t + 10 . Another particle is moving along the y-axis with its coordinate as a function of time given by y = 5 – 8t³ m. At t = 1 s, the speed of the second particle as measured in the frame of the first particle is given as √v . Then v (m/s) is

x = −3t2 + 8t + 10 = 2 y = 5 − 8t3 v = √(242 + 22) v = 580 m/s... View Article

A point object in air is in front of the curved surface of a plano-convex lens. The radius of curvature of the curved surface is 30 cm and the refractive index of lens material is 1.5, then the focal length of the lens (in cm) is

Applying Lens makers’ formula, 1/f = (μ - 1)[(1/R1) - (1/R2)] R1 =∞ R2 = -30 cm μ = 1.5 1/f = (1.5 - 1)[(1/∞) - (1/-30)] 1/f = 0.5/30 f = 60 cm... View Article

A body of mass =0.10 has an initial velocity of [latex]3hat{i}[/latex] / . It collides elastically with another body, B of the mass which has an initial velocity of [latex]5hat{j}[/latex] / . After collision, A moves with a velocity [latex]v= 4(hat{i}+hat{j})[/latex] / . The energy of B after collision is written as ( /10) , the value of is

Mass of each object, 1= 2 = 0.1 Initial velocity of 1st object, 1=5 / Initial velocity of 2nd object, 2 =3 / Final velocity of 1st... View Article

The critical angle of a medium for a specific wavelength, if the medium has relative permittivity 3 and relative permeability 4/3 for this wavelength, will be

a. 15°b. 30°c. 45°d. 60°Solution:If the speed of light in the given medium is V then,V = 1/√(μƐ)We know that, n = c/vn = √(μr Ɛr) = 2sin θc = ½θc = 300... View Article

Consider a solid sphere of density ρ(r) = ρ₀ (1- r²/R²), 0< r ≤ R. The minimum density of a liquid in which it float is just

a. (2/5) ρ0b. (2/3) ρ0 c. ρ0/5d. ρ0/3Solution:Let the mass of the sphere be m and the density of the liquid be ρL ρ = ρ0 ( 1 - r2/R2), 0< r ≤... View Article

Choose the correct Boolean expression for the given circuit diagram

Choose the correct Boolean expression for the given circuit diagram:a. A.Bb. A + Bc.... View Article

At time t = 0 magnetic field of 1000 Gauss is passing perpendicularly through the area defined by the closed loop shown in the figure.

At time t = 0 magnetic field of 1000 Gauss is passing perpendicularly through the area defined by the closed loop shown in the figure. If the... View Article

The graph which depicts the result of Rutherford gold foil experiment with α- particle is

The graph which depicts the result of Rutherford gold foil experiment with α- particle is: : Scattering angle ∶ Number of scattered −... View Article

A leak proof cylinder of length 1 m, made of metal which has very low coefficient of expansion is floating in water at

A leak proof cylinder of length 1 m, made of metal which has very low coefficient of expansion is floating in water at 0o C such that its height... View Article

The dimension of stopping potential ₀ in photoelectric effect in units of Planck’s constant (h), speed of light (c), and gravitational constant (G) and Ampere (A) is

a. h2/3 c5/3 G1/3 A−1b. h2c1/3G3/2A−1c. h0 G -1 c 5 A−1d. h−2/3 c−1/3 G4/3 A−1Solution:V = K(h)a(I)b(G)c(c)d Unit of stopping potential is (V0)... View Article

If finding the electric field around a surface is given by [latex]left | vec{E} right | = frac{q_{enclosed}}{varepsilon_{0} left | A right |}[/latex] is applicable. In the formula Ɛ₀ is permittivity of free space, A is area of Gaussian and q_enc is charge enclosed by the Gaussian surface. This equation can be used in which of the following equation?

a. Only when the Gaussian surface is an equipotential surface.b. Only when is constant on the surfaced. for any choice of Gaussian... View Article

Proton with kinetic energy of 1 MeV moves from south to north…

Proton with kinetic energy of 1 MeV moves from south to north. It gets an acceleration of 1012 m/s2 by an applied magnetic field (west to east).... View Article

Consider two solid spheres of radii ₁= 1 m, ₂ = 2 m and masses M₁ & M₂, respectively.

Consider two solid spheres of radii 1= 1 m, 2 = 2 m and masses M1 & M2, respectively. The gravitational field due to two spheres 1 and 2... View Article

The magnifying power of a telescope with tube length 60 cm is 5. What is the focal length of its eyepiece?

a. 10 cmb. 20 cmc. 30 cmd. 40 cmSolution:m = f0/fe = 5f0 = 5fe f0 + fe = 5fe + fe = 6fe = length of the tube6fe = 60 cmfe = 10 cm... View Article

When photons of energy 4 eV strikes the surface of a metal A, the ejected photoelectrons have maximum kinetic energy

When photons of energy 4 eV strikes the surface of a metal A, the ejected photoelectrons have maximum kinetic energy eV and de-Broglie wavelength... View Article

Consider a uniform rod of mass 4 and length pivoted about its centre. A mass is moving with a velocity making angle θ=π/4 to the rod’s long axis collides with one end of the rod and stick to it. The angular speed of the rod-mass system just after collision is

a. 3√2v/7Lb. 4v/7Lc. 3v/7√2Ld. 3v/7LSolution: There is no external torque on the system about the hinge point. So, = 6v/7√2L = 3√2 v/7L... View Article

Effective capacitance of parallel combination of two capacitors ₁ and ₂ is 10 μF. When these capacitor are individually connects to a voltage source of 1 , the energy stored in the capacitor ₂ is 4 times of that in ₁. If these capacitors are connected in series, their effective capacitance will be:

a. 1.6 μFb. 3.2 μFc. 4.2 μFd. 8.4 μFSolution: Given that,C1 + C2 = 10 μF …(i)4( ½ C1V2) = ½ C2V2 4C1 = C2 …(ii)From equations (i) and (ii)C1... View Article

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