List of practice Questions

Let \( f(x) = \log x \). The number \( C \) strictly between \( e^2 \) and \( e^3 \) such that its reciprocal is equal to \( \frac{f(e^3) - f(e^2)}{e^3 - e^2} \) is
The value of the integral \( \int_C (2xy - x^2) \, dx + (x^2 + y^2) \, dy \) where \( C \) is the boundary of the region enclosed by \( y = x^2 \) and \( y^2 = x \), described in the positive sense, is
If \( P = \begin{pmatrix} 1 & 1 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 1 \end{pmatrix} \) is the modal matrix of \( A = \begin{pmatrix} 1 & 1 & 0 \\ 0 & 2 & 2 \\ 0 & 0 & 3 \end{pmatrix} \) then the sum of all the elements of \( P^{-1}AP \) is
If the system of equations \( kx + y + z = k - 1 \), \( x + ky + z = k - 1 \), and \( x + y + kz = k - 1 \) has infinite solutions, then \( k \) is
The polar moment of inertia of a plane figure about a point is indicative of:
The mass moment of inertia of an object is a measure of:
The study of the motion of bodies without considering the forces that cause the motion is known as:
D’Alembert’s Principle is used to:
In simple harmonic motion (SHM), the force acting on the particle is:
In steady state conduction, the temperature gradient within a solid material does not:
The mode of heat transfer that requires no medium is:
The primary mechanism of heat transfer in furnaces is:
Factors affecting furnace efficiency do not include:
A tool used to visualize energy flow and efficiency in a system is:
The principle of waste heat recovery that involves transferring heat from exhaust gases to the incoming air is:
The difference between recuperators and regenerators is primarily in their:
In recuperators, AMTD refers to:
Salt bath furnaces are used for:
Protective atmospheres in furnaces are used to:
The efficiency of a Carnot cycle is determined by:
The Gibbs-Helmholtz equation is used to determine:
The third law of thermodynamics states that:
In a reversible adiabatic expansion of an ideal gas:
Statistical entropy in thermodynamics is a measure that:
CMOS technology is widely used in fabricating: