List of top Engineering Mathematics Questions

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
If \(\phi\) is a differentiable scalar function, then div grad \(\phi\) is
The solution of \( y'' - y' - 2y = 0 \) is
\(\lim_{x \to \infty} \frac{\sin x}{x} =\)
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
If \( A = \begin{bmatrix} 6 & -2 & 2 \\ -2 & 3 & -1 \\ 2 & -1 & 3 \end{bmatrix} \), then eigen value and its corresponding eigen vector
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

If $$ A = \begin{bmatrix} 2 & 3 & 4 \\0 & 4 & 2 \\0 & 0 & 3 \end{bmatrix} $$ then the eigenvalues of $ \text{adj}(A) $ are

If A is $$ A = \begin{bmatrix} 8 & 7 \\5 & 6 \end{bmatrix} $$ then the value of $ \text{det}(A^{121} - A^{120}) = ? $

The function $f(x,y) = x^2 + y^2 - xy - x - y + 5$ has

Find $x, y, z$ and $w$ given that $3 \begin{bmatrix} x & y \\z & w \end{bmatrix} = \begin{bmatrix} x & 5 \\-1 & 2w \end{bmatrix} +\begin{bmatrix} 6 & x+y \\z+w & 5 \end{bmatrix}$

Find the largest eigenvalue of the matrix $\begin{bmatrix} 5 & 4 \\1 & 2 \end{bmatrix}$

Evaluate the limit: $$ \lim_{x \to 0} \left( x - \sin x \right) \left( \frac{1}{x} \right) $$
The mean of a binomial distribution is 5, then its variance is
In the Taylor series expansion of $e^x$ about $x = 2$, the coefficient of $(x - 2)^4$ is

The Laurent series of $ f(z) = \frac{z}{(z^2+1)(z^2+4)} $ for $ |z|<1 $ is:

Let E and F be the events of a sample space S of an experiment, if $ P(S/F) = P(F/F) $, then $ P(S/F) $ is equal to: