List of practice Questions

The line integral of the vector field \( \vec{F} = x\hat{i} - 2y\hat{j} + z\hat{k} \) along the straight line path from the point \((-1,2,3)\) to \((2,3,5)\), is ..........
The Laplace transform of \( e^{-2t} \cos(\sqrt{2} t) \) is .......
Consider the improper integral \( I = \int_{2025}^{2030} \frac{1}{(x - 2025)^k} \, dx \), where \( k > 0 \). Which of the following is true for \( I \)?
The eigenvalues of the matrix \( \begin{bmatrix} 2 & 1 - 2i \\ 1 + 2i & -2 \end{bmatrix} \) are ..........
If \( \begin{bmatrix} 2k+7 & 2k^2 - 5k + 3 \\ 3k - 3 & 15 \end{bmatrix} \) is a \(2 \times 2\) symmetric matrix, then the value of \(k\) is .........
In LD process, silicon removal takes place before carbon removal since:

Match the following processes with their physical principles:

\(C_p\), the heat capacity at constant pressure is given by:
"Power sharing increases trust between different groups." Support the statement.
Consider the ordinary differential equation \( x^2 \frac{d^2y}{dx^2} - 2x \frac{dy}{dx} + 2y = 0 \) with \( y(x) \) as a general solution. Given the values \( y(1) = 1 \), \( y(2) = 5 \), the value of \( y(3) \) is equal to ..........
Evaluation of the integral \(\int_{2}^{4} x^2 \, dx\) using the trapezoidal rule (with two equal segments) gives a value of .......
Let \( f(x) = x^3 - x - 3 \). In finding a positive real root of \( f(x) = 0 \) using Newton-Raphson method, if the starting guess \( x_0 = 2 \), then the numerical value of the root \( x_1 \) after the first iteration is .........
Which of the following is a common defect in wire drawing processes, particularly when excessive friction is present at the die-workpiece interface?
Back Scattered electrons are used in:
Which of the following types of penetrant is most commonly used for detecting very fine surface cracks in non-porous materials?
Permanent mould casting is best suited for which of the following production areas?
What is the relationship between the frequency of the sound waves and the ability to detect smaller defects in Ultrasonic testing?
The wax pattern in investment casting is removed by:
In shell moulding, the binder used to hold the sand grains together is:
How brazing is differ from welding?
Which of the following is NOT a part of a typical gating system in sand casting?
What is the main problem when welding stainless steels, particularly in the HAZ (Heat-Affected Zone)?
What is the effect of increasing the riser-to-casting volume ratio?
Which of the following is the major drawback of using X-rays compared to gamma rays for inspecting thick materials in Radiography Test?
The following technique is most probably recommended for consolidation of nanostructured and amorphous powders: