List of practice Questions

Given an input line of numbers and words, a machine rearranges them following a particular rule in each step. Using the illustrated pattern, find the position of $58$ in the \emph{fourth step for:} Input: \texttt{cb kb eb 58 49 23 38 jb nb gb 69 82}
During a half-moon phase, the Earth-Moon-Sun form a right triangle. If the Moon-Earth-Sun angle at this half-moon phase is measured to be $89.85^\circ$, the ratio of the Earth-Sun and Earth-Moon distances is closest to
In a locality, the houses are numbered in the following way: The house-numbers on one side of a road are consecutive odd integers starting from 301, while the house-numbers on the other side of the road are consecutive even numbers starting from 302. The total number of houses is the same on both sides of the road. If the difference of the sum of the house-numbers between the two sides of the road is 27, then the number of houses on each side of the road is
Which one of the given options is a possible value of $x$ in the following sequence? \[ 3,\; 7,\; 15,\; x,\; 63,\; 127,\; 255 \]
The number of half-lives \((t_{1/2})\) required for a radioactive isotope to decrease to \(2\%\) of its original abundance is _________ (rounded off to two decimal places).
A monochromatic cosine wave with frequency \(0.24\ \text{Hz}\) and wavelength \(16\ \text{km}\) interferes with another monochromatic cosine wave with frequency \(0.3\ \text{Hz}\) and wavelength \(10\ \text{km}\). The group velocity of the resulting wave in km/s is _________ (rounded off to one decimal place).
A magnetic field (B) of strength 50000 nT induces a magnetization (M) of magnitude 5 A/m in a rock. Given the magnetic permeability of free space \(\mu_0 = 4\pi \times 10^{-7}\,\text{H/m}\), the susceptibility of the rock is __________ (rounded off to three decimal places).
A plane P-wave is incident at an angle of \(60^\circ\) with respect to the normal to a horizontal reflector. If the incident medium is a homogeneous Poisson solid (\(\nu=0.25\)), the angle of the reflected, mode-converted S-wave with respect to the normal (in degrees) is _______ (rounded off to one decimal place).
A marine seismic survey was performed in a region with a flat, horizontal sea bed at a depth of 100 m from the sea surface. The datum of the stacked seismic section was fixed at the sea surface. If the P-wave velocity in water is \(1600\ \text{m/s}\), the radius of the first Fresnel zone at the sea bed at a frequency of \(50\ \text{Hz}\) corresponding to the stacked seismic section is _________ (rounded off to one decimal place).
Choose the CORRECT statement(s) on the phenomenon of spatial aliasing of seismic data.
The speed of a ship is given as \(V_1\) (km/h) and \(V_2\) (knots). The latitude of observation and the direction of the ship with respect to the North are \(\theta_1\) and \(\theta_2\), respectively. The CORRECT expression(s) for the Eötvös correction in mGal is/are:
Which of the following statements pertaining to the interpretation of Neutron log is/are CORRECT ?
If $\vec{B$ is the magnetic field in a region free of currents, then which of the following statements is/are correct? }
Which of the following operations performed in the time-domain with any two causal seismic signals result(s) in the \textbf{subtraction of their corresponding phase spectra in the frequency domain? }
A geophysical forward problem is expressed as \( d = 7m_1^2 m_2 + 6m_2 \), where \( m_1 \) and \( m_2 \) represent the model parameters and \( d \) represents the data. Then, the relationship between data and model parameters is
Assuming that the polar flattening of the Earth \( f = 3.353 \times 10^{-3} \), the difference between the geodetic and geocentric latitudes is maximum at
Which of the following statements related to an equipotential surface is/are CORRECT?
A Wenner resistivity survey was performed with a spacing of 15 m between the current electrodes. Potential difference values of \(-25\ \text{mV}\) and \(225\ \text{mV}\) were measured before and after injecting \(100\ \text{mA}\) current into the ground. The apparent resistivity in \(\Omega\cdot\text{m}\) after correcting for the self-potential effect is:
Nine equally spaced electrodes are placed along a profile to perform Dipole–Dipole multi-electrode resistivity imaging. The maximum number of data points that can be obtained at measurement level \(n=2\) is:
Match the electromagnetic methods in Group–I with their corresponding frequency range in Group–II. Group–I:
P. Very Low Frequency
Q. Radio Magnetotelluric
R. Ground Penetrating Radar
S. Control Source Magnetotelluric
Group–II:
1. 10 MHz – 1 GHz
2. 1 Hz – 20 kHz
3. 100 kHz – 1 MHz
4. 15 kHz – 30 kHz
The magnitude of horizontal and vertical components of the total magnetic field at a particular location are 40500 nT and 36450 nT, respectively. The magnetic inclination at the same location in degrees is ________ (rounded off to one decimal place).
A stress tensor $\sigma$, with elements in MPa, is as given. The maximum value of the principal stress in MPa is \[ \sigma = \begin{bmatrix} 1 & 0 & \sqrt{2}
0 & 1 & 0
\sqrt{2} & 0 & 0 \end{bmatrix} \]
An overdetermined linear inverse problem is expressed as \( Gm = d \), where \( G \) is the data kernel, \( m \) is the vector of model parameters and \( d \) is the vector of observed data. If damping is applied to the inverse problem and the resultant generalized inverse is represented by \( G^{-g} \), the \textbf{model resolution matrix can be expressed as:}
The ratio of the largest to the smallest amplitude of waveforms that can be accurately recorded by a digital seismometer is reported as \(10^7\). Then, the dynamic range of the seismometer in dB is _______ (in integer).
A petroleum company estimates that a reservoir holds oil with a prior probability of 60\%. It then acquires petrophysical data that suggests the presence of oil. If the petrophysical analysis is accurate with a probability of 70\%, the posterior probability of the presence of oil in \% is ________ (rounded off to two decimal places).