List of top Geophysics Questions

In levelling between two points A and B on the opposite banks of a river, the readings are taken by setting the instrument both at A and B, as shown in the table. If the RL of A is 150.000 m, the RL of B (in m) is ....... (rounded off to 3 decimal places).

The maximum value of the function $ h(x) = -x^3 + 2x^2 $ in the interval $[-1, 1.5]$ is equal to ......... (rounded off to 1 decimal place).

Organic fraction of municipal solid waste (OFMSW) with bulk density of 315 kg/m$^3$ and water content of 30% is mixed with municipal sludge of bulk density 700 kg/m$^3$ and water content of 70%, such that the water content of the mixture is 40%. The amount (in kg) of sludge to be mixed per kg of OFMSW (rounded off to 2 decimal places) and the density of the mixture (in kg/m$^3$) (rounded off to the nearest integer) are calculated. Which of the following options is/are true:

If the horizontal distance between a staff point and the point of observation is $ d $, the error due to the curvature of the earth is proportional to

If the Fore Bearing of the lines AB and BC are 60° and 122°, respectively, then the interior angle $ \angle ABC $ (in degrees) is .......... (round off to the nearest integer).

Match the following in Column I with Column II.

The figure shows a propped cantilever with uniform flexural rigidity $ EI $ (in N.m$^2$) and subjected to a moment $ M $ (in N.m). Consider forces and displacements in the upward direction as positive.
Find the upward reaction at the propped support B (in N) when this support settles by $ \Delta $ (in metres).

A circular tube of thickness 10 mm and diameter 250 mm is welded to a flat plate using 5 mm fillet weld along the circumference. Assume Fe410 steel and shop welding.
As per IS 800:2007, the torque that can be resisted by the weld (in kN.m) is __________ (round off to one decimal place).

Free residual chlorine concentration in water was measured to be 2 mg/l (as Cl$_2$). The pH of water is 8.5. By using the chemical equation given below, the HOCl concentration (in $\mu$moles/l) in water is ___________ (round off to one decimal place).
\[ {HOCl} \rightleftharpoons {H}^+ + {OCl}^-, \quad pK = 7.50 \] Atomic weight: Cl = 35.5

Pick one or more CORRECT statement(s) from the choices given below, in the context of upstream and downstream cut-offs provided below the concrete apron of weirs/barrages constructed across alluvial rivers.

In the context of construction materials, which of the following statements is/are CORRECT?

The bacteria mainly responsible for crown corrosion in a sewer is ___________.

Given the following staff readings at two levels, determine the Reduced Level (RL) of B.

Given: - RL of A = 150 m - Find RL of B

Given the bearing N30°W, determine the corresponding Whole Circle Bearing (WCB). \

Given: - Bearing = N30°W - Find WCB

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:

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:

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:

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:

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

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:

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

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:

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

Choose the correct answer from the options given below:

The shape of air film formed between the plano-convex lens and the glass slab in Newton’s ring experiment is

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