List of top Geophysics Questions

The magnetic polarization results in a bound current Jb
(A) which is associated with magnetization of the material.
(B) which involves spin and orbital motion of electrons.
(C) which is the result of linear motion of charge when electric polarization changes.
(D) which is given by \( \nabla \times \vec{M} \) (where \( \vec{M} \) is magnetization).
Choose the correct answer from the options given below:

A long coaxial cable carries current 'I' (current flows down the surface of inner cylinder of radius 'r1' and back along the outer cylinder of radius 'r2'). The magnetic energy stored in a section of length 'L' is

Which of following Maxwell's equation shows non existence of magnetic monopoles?

	LIST I (Type of the Matrix)		LIST II (Property)
A.	Symmetric Matrix		I. aij = aji, for values of i and j
B.	Hermitian Matrix		II. aij = āji, for values of i and j
C.	Skew-Hermitian matrix		III. aij = -āji, for values of i and j
D.	Skew-Symmetric matrix		IV. aij = -aji, for values of i and j

Choose the correct answer from the options given below:

Let P and Q be two matrices such that P Q = 0 and P is non-singular, then
(a) Q is also non-singular
(b) Q = 0
(c) Q is singular
(d) P = Q
Choose the correct answer from the options given below:

If A is a skew-symmetric matrix of odd order, then the determinant of A is:

In the matrix equation: \[ \begin{bmatrix} 3 & -1 \\ 2 & 5 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 4 \\ -3 \end{bmatrix}, \] the values of \( x \) and \( y \) are:

In the system of linear equations AX = B, if A is a singular matrix and B is a null matrix, then which of the following is correct?

If \( (\sqrt{3} + 1)^n + (\sqrt{3} - 1)^n = 4 \), then the value of \( n \) is:

Statement (I): The determinant of a matrix A and its transpose A^T are equal.
Statement (II): The determinant of the product of two matrices A and B is the product of their determinants.
In light of the above statements, choose the most appropriate answer from the options given below:

The general value of \( \log(1 + i) + \log(1 - i) \) is:

The principal value of \( i^i \) is:

If \[ \theta = r e^{-x^2}, \] then for what value of \( n \), the following holds: \[ \frac{1}{2} \left( \frac{\partial^2 \theta}{\partial x^2} - \frac{\partial^2 \theta}{\partial r^2} \right) = \frac{\partial \theta}{\partial x}. \]

Given below are two statements:
Statement (I): The nth derivative of the function \( e^x \cos x \cos 2x \) is:
\[\frac{e^x}{2} \big[ (10^n) \cos(3x + n \tan^{-1} 3) + (2^n) \cos(x + \frac{n \pi}{4}) \big]\]
Statement (II): The nth derivative of the function \( x \cos 2x \cos 3x \) is:
\[\frac{1}{2} \big[ (2^n) \cos(2x + \frac{n \pi}{2}) + (4^n) \cos(4x + \frac{n \pi}{2}) + (6^n) \cos(6x + \frac{n \pi}{2}) \big]\]
In light of the above statements, choose the most appropriate answer from the options given below:

If the radius of curvature of the Folium \( x^3 + y^3 - 3xy = 0 \) at the point \( (3/2, 3/2) \) is 5, then the value of \( b^2 + 2a + 1 \) is:

The asymptote of the spiral \( r = \frac{\theta}{\sin \theta} \) is:

In a submarine telegraph cable, the speed of signaling varies as \( x^2 \log(1/x) \), where \( x \) is the ratio of the radius of the core to that of the covering. To attain the greatest speed, the value of this ratio is:

The volume of the solid standing on the area common to the curves \( x^2 = y, y = x \) and cut off by the surface \( z = y - x^2 \) is:

Let \( a \) be the magnitude of the directional derivative of the function: \[\phi(x, y) = \frac{x}{x^2 + y^2}\] along a line making an angle of \( 45^\circ \) with the positive x-axis at the point \( (0, 2) \). Then, the value of \( 1/a^2 \) is:

Given below are two statements:
Statement (I): If F is an irrotational vector field, then the angular velocity of the vector field is always greater than zero.
Statement (II): For a solenoidal vector function, the divergence is always zero.
Choose the most appropriate answer from the options given below:

The value of curl (\(\text{grad } f\)), where \( f = x^2 - 4y^2 + 5z^2 \), is:

The surface integral \[ \iint_S \mathbf{F} \cdot d\mathbf{S} \] where \( \mathbf{F} = x\hat{i} + y\hat{j} - z\hat{k} \) and \( S \) is the surface of the cylinder \( x^2 + y^2 = 4 \) bounded by the planes \( z = 0 \) and \( z = 4 \), equals:

The value of the integral $$ \oint_C \left[ (x^3 + xy) \, dx + (x^2 - y^3) \, dy \right] $$ where $C$ is the square formed by the lines $x = \pm 1$, $y = \pm 1$, is: