List of top Geophysics Questions asked in Common University Entrance Test

The general solution of the differential equation \[ \frac{d^2y}{dx^2} - 5\frac{dy}{dx} + 6y = e^x \cos 2x \] is:

Given below are two statements:
{Statement (I):} Two families of curves such that every member of either family cuts each member of the other family at right angles are called orthogonal trajectories of each other.
{Statement (II):} The orthogonal trajectories of the curve \( xy = c \) is \( y = \frac{1}{x} \).
Choose the most appropriate answer from the options given below:

Statement (I): If a given component of the total applied force vanishes, the corresponding component of the linear momentum is not conserved.
Statement (II): If the component of applied torque along the axis of rotation vanishes, then the component of total angular momentum along the axis of rotation is conserved.
Choose the most appropriate answer:

The shortest distance between the lines
\[\frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{4}\]
and
\[\frac{x-2}{3} = \frac{y-4}{4} = \frac{z-5}{5}\]is:

The image of the point (1 3 4) in the plane 2x − y + z + 3 = 0 is

	LIST I		LIST II
A.	Intrinsic semiconductor		I. Used as a rectifier circuit
B.	N-Type Semiconductor		II. Pure form of Semiconductor
C.	P-Type Semiconductor		III. Doping of pentavalent impurity in semiconductor
D.	P-N Junction diode		IV. Doping of trivalent impurity in semiconductor

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	LIST I (Name of the surface)		LIST II
A.	Ellipsoid		I. x²/a² + y²/b² + z²/c² = 1
B.	Hyperboloid of one sheet		II. x²/a² - y²/b² - z²/c² = 1
C.	Hyperboloid of two sheets		III. -x²/a² + y²/b² + z²/c² = 1
D.	Central conicoid		IV. x²/a² + y²/b² + z = 1

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Displacement current is not a conventional current but it is:

The equation of motion for a compound pendulum is:

The Hamiltonian’s equation of motion is

Which of the following statements are true for ideal PN junction current voltage relationship?
(A) The abrupt depletion layer approximation applies.
(B) The Maxwell-Boltzmann approximation applies to carrier statistics.
(C) The concept of low injection applies.
(D) The total current is not constant throughout the entire pn structure.
Choose the correct answer from the options given below:

	LIST I		LIST II
A.	Intrinsic semiconductor		I. Used as a rectifier circuit
B.	N-Type Semiconductor		II. Pure form of Semiconductor
C.	P-Type Semiconductor		III. Doping of pentavalent impurity in semiconductor
D.	P-N Junction diode		IV. Doping of trivalent impurity in semiconductor

Choose the correct answer from the options given below:

Find the amplitude of the electric field in a parallel beam of light of intensity $2.0 \, \text{W/m}^2$:

	LIST I		LIST II
A.	∇ ⋅ E = ρ/ε₀		I. Gauss's Law in magnetostatics
B.	∇ ⋅ B = 0		II. Faraday's Law of electromagnetic Induction
C.	∇ × E = - ∂B/∂t		III. Gauss's Law in electrostatics
D.	∇ × B = μ₀J + μ₀ε₀ ∂E/∂t		IV. Modified Ampere's Law

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	LIST I		LIST II
A.	Bipolar npn transistor operate in the cut-off mode.		I. The base-emitter is reverse biased and
B.	Bipolar npn transistor operate in the saturation mode.		II. Both the base-emitter and base
C.	Bipolar npn transistor operate in the inverse active mode.		III. The base-emitter is forward biased
D.	Bipolar npn transistor operate in the forward active mode.		IV. Both the base-emitter and bas

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Consider phosphorus doping in silicon, for $T = 300 \, \text{K}$, at concentration $N_d = 10^{16} \, \text{cm}^{-3}$. The fraction of total electrons still in the donor states is:

Consider a silicon p-n junction at $T = 300 \, \text{K}$ with doping concentrations of acceptor $N_A = 10^{16} \, \text{cm}^{-3}$ and donor $N_D = 10^{15} \, \text{cm}^{-3}$. Assume that intrinsic concentration $n_i = 1.5 \times 10^{10} \, \text{cm}^{-3}$, relative permittivity $= 11.7$, and $V_{bi} = 0.635 \, \text{V}$. The width of the space charge region in the p-n junction is:

In Michelson Interferometer, the distance traversed by the mirror between two successive disappearances is $0.289 \, \text{mm}$. The difference between the wavelengths of two lines is (Assume the wavelength of one line is $5890 \, \text{\AA}$):

The position vector of a point in the frame S moving with constant velocity 10 cm/s along the X-axis is given by (11,9.8) cm. The position with respect to S if the two frames were coincident only 1/2 second earlier.

If the radius of Earth becomes half of its present value, with its mass remaining the same, the duration of one day will become:

For Newton’s Ring Experiment:
(A) The condition to get constructive interference is 2nt = (m + 1/2),m = 0,1,2,..., where n is the refractive index of the film and t is the thickness of the film.
(B) The condition to get destructive interference is 2nt = mx,m = 0,1,2,..., where n is the refractive index of the film and t is the thickness of the film.
(C) The condition to observe the colored ring, the source of light should be polychromatic.
(D) The condition to observe the colored ring, the source of light should be monochromatic.
Choose the correct answer from the options given below:

In an LCR circuit with L = 2 mH, C = 2 µF, and R = 0.2 , the quality factor will be

The four satellites are lying close to the earth at distances $h_1, h_2, h_3$, and $h_4$ meters respectively, away from the center of the earth. If the values of $h_i$'s are given in terms of $R$ (radius of the earth), write the time period of the satellite in increasing order:
$h_1 = R/3$
$h_2 = R/4$
$h_3 = R/5$
$h_4 = R/2$
Choose the correct answer from the options given below:

The function f(x) is said to be piecewise continuous, if it satisfies the following conditions (Dirichlet conditions):
(A) The function must have a finite number of maxima and minima.
(B) The function must have a finite number of infinite discontinuities, in a period of one oscillation.
(C) The function must have an infinite number of maxima and minima.
(D) The function must have a finite number of finite discontinuities, in a period of one oscillation
Choose the correct answer from the options given below