Find the value of α* + β*
Let M = \(\begin{array}{l}\begin{bmatrix} sin^4 \theta & -1-sin^2 \theta\\ 1 + cos^2 \theta & cos^4 \theta \end{bmatrix} = \alpha I... View Article
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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
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 = \(\begin{array}{l}\sqrt{\frac{\frac{B}{2\rho }}{\frac{B}{\rho }}}= \frac{1}{\sqrt{2}}\end{array} \) Vpipe = Vair/√2 fn = Vpipe(n+1)/2l f1-f0 = Vpipe/... 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 \(\begin{array}{l}\vec{V_{A}}\end{array} \) = (−6t + 8)\(\begin{array}{l}\hat{i}\end{array} \) = 2 \(\begin{array}{l}\hat{i}\end{array} \) y =... 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... 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,... 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... 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) ρ0 b. (2/3) ρ0 c. ρ0/5 d. ρ0/3 Solution: Let the mass of the sphere be m and... View Article
Choose the correct Boolean expression for the given circuit diagram
Choose the correct Boolean expression for the given circuit diagram: a. A.B b. A + B c. \(\begin{array}{l}\bar{A}+ \bar{B}\end{array} \)... 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... 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... 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... 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−1 b. h2c1/3G3/2A−1 c. h0 G -1 c 5 A−1 d. h−2/3 c−1/3 G4/3 A−1 Solution:... 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 qenc 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 \(\begin{array}{l}\left | \vec{E} \right |\end{array} \) =... 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... 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... 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 cm b. 20 cm c. 30 cm d. 40 cm Solution: m = f0/fe = 5 f0 =... 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... 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/7L b. 4v/7L c. 3v/7√2L d. 3v/7L Solution: There is no external torque on the system about the hinge... 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 μF b. 3.2 μF c. 4.2 μF d. 8.4 μF Solution: Given that, C1 + C2 = 10... View Article
