List of practice Questions

Given the second-order ordinary differential equation: \( y'' + 3y' - 4y = 0 \) with the initial conditions \( y(0) = 3 \), and \( y'(0) = -7 \), the value of \( y(1) \) is \(\underline{\hspace{2cm}}\) (round off to two decimal places).
The directional derivative of \( f(x, y, z) = x^2 + 3y^2 + z^2 \), at point \( (2, 1, 0) \) along the unit vector in \( x \)-direction, \( \hat{i} \), is \(\underline{\hspace{2cm}}\).
A productivity test conducted on a crude oil well indicates a stabilized flow rate of 150 STB/day (water-free oil production) at a bottom-hole flowing pressure of 935 psig. After shutting the well for 24 hours, the bottom-hole pressure reached a static value of 1250 psig. The Absolute Open Flow (AOF) potential of the well is \(\underline{\hspace{2cm}}\) STB/day.
Select the INCORRECT statement related to Enhanced Oil Recovery (EOR) techniques from the following options.
An Ideal Pressure Buildup Test yields a single straight line for all times, when shut-in Bottom-Hole Pressure (\(P_{ws}\)) is plotted against \(\log_{10} \left( \frac{t_p + \Delta t}{\Delta t} \right)\). Here \( t_p \) is the well production time and \(\Delta t\) is the time elapsed since shut-in. However, in an actual Pressure Buildup Test, a non-linear curve is obtained which can be logically divided into distinct regions. Choose the INCOMPLETE option from the following.
When two immiscible fluid phases are placed in contact with a solid surface, one phase usually is attracted to solid more strongly than the other phase. The more strongly attracted phase is called the 'wetting phase'. The inter-molecular interaction of the non-wetting phase with the solid is \(\underline{\hspace{2cm}}\)I\(\underline{\hspace{2cm}}\) than its intra-molecular interaction. Due to this, the non-wetting phase tends to occupy the \(\underline{\hspace{2cm}}\)II\(\underline{\hspace{2cm}}\) of the reservoir.
Coal bed methane is methane gas adsorbed in coal seams. To desorb the methane from the coal seam it should be exposed to CO\(_2\) and/or N\(_2\). Which ONE of the following is an appropriate reason to enhance the desorption process?
Select the CORRECT statements from the following.
Well testing operations on a typical crude oil reservoir
If the specific heat ratio of natural gas is 1.28, the critical pressure ratio (ratio of outlet pressure to upstream pressure) through a choke is \(\underline{\hspace{2cm}}\) (round off to two decimal places).
Identify the CORRECT statements for a $n \times n$ matrix.
During a drilling operation, kick occurs if
The value of \( \lim_{x \to 0} \frac{4x^3 - 2x^2 + x}{3x^2 + 2x} \) is \(\underline{\hspace{2cm}}\) (correct up to one decimal place).
Given two complex numbers, \( z_1 = 4 + 3i \) and \( z_2 = 2 - 5i \), the real part of \( z_1z_2 \) is \(\underline{\hspace{2cm}}\).
The number of 'three-digit numbers' that can be formed using the digits from 1 to 9 without the repetition of each digit is \(\underline{\hspace{2cm}}\).
A saturated oil reservoir has an average reservoir pressure of 3000 psia, tested for flowing bottom-hole pressure (BHP) of 2000 psia and production rate of 500 STB/day. The maximum reservoir deliverability based on Vogel's equation for two-phase flow is \(\underline{\hspace{2cm}}\) STB/day.
A measure of the potential of crude oil to form surfactants for Enhanced Oil Recovery (EOR) is given by the Total Acid Number (TAN). TAN is the mass of \(\underline{\hspace{2cm}}\) (in milligrams) that is required to neutralize one gram of crude oil.
In Water-Alternating-Gas (WAG) injection, the purpose of the injection is to \(\underline{I}\) \(\underline{\hspace{2cm}}\) the "relative permeability" of gas and to \(\underline{II}\) \(\underline{\hspace{2cm}}\) the "mobility" of the gas.
Solids that may possibly form in the offshore pipelines during the production of oil and gas from deep-water reservoirs are
Oil and gas pipelines, which are at an elevated pressure (about 3 MPa) and sub-ambient temperature (below 298 K), may get blocked by the formation of solid hydrates. One of the strategies adopted to inhibit the formation of hydrates is the injection of Thermodynamic Hydrate Inhibitors (THIs) into the reservoir fluid.
Identify all suitable chemicals that are commonly used as THIs.
Six circular biscuits of diameter 10 cm are arranged on a circular plate as shown below. What is the circumference of the plate in centimetres?
A necklace made of white and black cube beads, arranged in a particular sequence, is shown in the figure. Find out the number of black beads. Blue mark indicates the start of the necklace and red mark indicates the end of the necklace.
The front view of a solid object is shown in the image. If the views from all six sides are the same, how many surfaces does it have?
What is the value of the ratio $\frac{\text{Area of the hexagon}}{\text{Area of the grey triangle}}$?

A solid object under a spotlight forms a shadow as shown in the image. Which of the options can be produced by rotating the object? 

The shown figure is first cloned and flipped on the axis PP, and the resulting image is cloned and flipped on the axis QQ. How many triangles does the resulting image have?