List of top Engineering Mathematics Questions

If $p = \frac{1}{8}; n = 640; q = \frac{7}{8}$, then variance Binomial Distribution

Integrating factor of the linear differential equation $\frac{dy}{dx} + \frac{2y}{x} = x \log x$ is
General solution of $(D^2 - 5D + 6)y = 0$ is $y(x) =$
The probability of getting 4 heads in 6 tosses of a fair coin is.
Let $ u(x,t) $ satisfy the initial boundary value problem $$ \frac{\partial u}{\partial t} = \frac{\partial^2 u}{\partial x^2}, \quad x \in (0,1), t>0 $$ given that $$ u(x, 0) = \sin(\pi x), \quad x \in [0,1], \quad u(0,t) = u(1,t) = 0, \quad t>0. $$ Then $ u \left( x, \frac{1}{\pi^2} \right) $ for $ x \in (0,1) $ is
Evaluate the limit $$ \lim_{x \to \infty} \frac{\sin x}{x} $$
Consider the differential equation $$ \frac{dy}{dx} + a y = e^{-bt} \quad \text{with} \quad y(0) = 0. $$ Then the Laplace transform of $ y(t) $ is
The integrating factor of equation $$ \sec^2 y \frac{dy}{dx} + x \tan y = x^3 $$ is
The function $ (1 + \cos x) \sin x $ is maximum at
The following system has non-trivial solution $ px + qy + rz = 0, qx + ry + pz = 0, rx + py + qz = 0 $ then which one of the following is TRUE?
Let A be square matrix of order m, then nullity of A is
The coefficient of correlation is independent of
If \( x^2 - x - 4 = 0 \) by bisection method, first two approximations \( x_1 \) and \( x_2 \) are 1 and 2, then \( x_3 \) is
Probability Density function $f(x)$ of a continuous random variable is given by $f(x) = ce^{-|x|}, -\infty<x<\infty$. If the total probability $\int_{-\infty}^{\infty} f(x) dx = 1$ then $c =$
A problem of statistics is given to three students A, B and C whose chances of solving are $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$ respectively. What is the probability that the problem will be solved?
The probability that at least one of the events A and B occurs is 0.6. If A and B occur simultaneously with the probability 0.2 then $P(A) + P(B) = $?
$\lim_{x \to \infty} x \tan \left( \frac{1}{x} \right) = $ _____
$\int_{-\pi/6}^{\pi/6} \frac{(\sin x)^5 (\cos x)^3}{x^4} dx =$
Evaluate $\oint_C (y^2 dx - x^3 dy)$, where $C$ is the positively oriented circle of radius 2 centered at origin.
$f(x) = 2x^2 - 2x + 6$ will have a minimum value at $x=$ _____
If $f(x)$ is differentiable function in x then it is
As per Green's theorem $\oint_C Mdx + Ndy = \iint_R (_____)dxdy$
Augmented matrix of equations $x - y + z = 9; 2x - 3y + 4z = 25; 2x + 6y + 4z = 10$ is reduced to Echelon form as $\begin{bmatrix} 1 & -1 & 1 & 9 \\ 0 & -2 & 3 & 16 \\ 0 & 0 & 7 & 28 \end{bmatrix}$. Then the solution set $X = \begin{bmatrix} x \\ y \\ z \end{bmatrix}$ is
The rank of the matrix $A = \begin{bmatrix} 1 & 2 & 3 \\ 1 & 4 & 2 \\ 2 & 6 & 5 \end{bmatrix}$ is
For the matrix $\begin{bmatrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{bmatrix}$ which of the following is not an Eigen Vector