List of top Engineering Mathematics Questions

The Laplace transform of the function f(t) = t sin t is
By eliminating a & b from z = ax + by + (a/b) then, P.D.E formed is _____
Let X be a continuous random variable denoting the temperature measured. The range of temperature is [0, 100] degree Celsius and let the probability density function of X be f(x) = 0.01 for \(0 \le X \le 100\). The mean is
If \( \vec{a}, \vec{b}, \vec{c} \) are unit vectors, then \( |\vec{a}-\vec{b}|^2 + |\vec{b}-\vec{c}|^2 + |\vec{c}-\vec{a}|^2 \) does not exceed
Find the greatest value of the directional derivative of the function \( f = x^2 y z^3 \) at (2,1,-1)
Probability that a leap year has 53 Sundays is
If \(\lambda\) is an eigenvalue of a non-singular matrix A . Then the eigenvalue of (adjA) is
If any function is even, in Fourier series it contains
Let A and B be two real symmetric matrices of order n. Then which of the following is true?

\(P(A) = \frac{1}{3}\), \(P(B) = \frac{3}{4}, P(A \cap B) = \frac{1}{6}\), then probability of \( A \) alone is

If the trapezoidal rule with a single interval [0, 1] is exact for the approximate value of \( \int_0^1 (x^3 - cx^2) \, dx \). Then the value of \( c \).
The system of equations \( AX = B \), has a unique solution if ____ .

The Particular integral of \((D^3 - 6D^2 + 11D - 6)y = e^{-2x}\) is:

If \( A \) and \( B \) are two events such that \(P(A \cap B) = \frac{1}{3}\), \(P(A \cup B) = \frac{5}{6}\), and \(P(B) = \frac{1}{2}\), then the events are:

Solution of the differential equation $(D^2 + 9)y = \sin 2x$ is:
A fair coin is tossed 4 times. The probability that at least one head occurs is
The solution of \( y'' - y' - 2y = 0 \) is
If \(\phi\) is a differentiable scalar function, then div grad \(\phi\) is
The line integral of the vector field \( \vec{F} = (zx, xy, yz) \) along the boundary of the triangle with vertices (1,0,0), (0,1,0), (0,0,1) anticlockwise, when viewed from the point (2,2,2) is
\(\lim_{x \to \infty} \frac{\sin x}{x} =\)
The eigen vectors of the matrix \(\begin{bmatrix} 1 & 2 \\ 0 & 4 \end{bmatrix}\) are in the form \(\begin{bmatrix} 1 \\ a \end{bmatrix}\) and \(\begin{bmatrix} 1 \\ b \end{bmatrix}\), then \( a + b =\)
A feasible solution to a linear programming problem
The solution to a transportation problem with \( m \)-rows (supplies) and \( n \)-columns (destinations) is feasible if number of positive allocations are

The standard deviation for the following frequency is 

From the given data value of $\int_{1}^{2} \frac{1}{x} dx$ using Simpson’s 1/3rd rule is