List of top Engineering Mathematics Questions

If \(f = \text{Tan}^{-1}(xy)\) then \((\frac{\partial f}{\partial x})_{(1,2)}\) = _____ .

Line of Regression of y on x
The general solution of the differential equation \( x^2 \frac{d^2y}{dx^2} - 2x \frac{dy}{dx} + 2y = 4 \) is
Auxiliary Equation for the Cauchy Euler Equation \( (x^2 D^2 + xD + 4)y = 0 \) is ____ .
Let S be a closed surface for which \( \oiint_S \vec{r} \cdot \hat{n} \, dS = 1 \), then the volume enclosed by the surface is ____ .
In Method of Variation of Parameters, \( A = -\int \frac{y_2 R dx}{W} \). If \( V = \sin x, R = \sec x, W = 1 \) then A= ____ .
Cauchy Riemann Equations for an Analytic function are
For the function \( \frac{\sin z}{z^4} \), the point z = 0 is
The system of equations \(3x + 2y + z = 0, x + 4y + z = 0, 2x + y + 4z = 0\) is
If \( A = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \), \( B = \begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix} \) and \( C = \begin{bmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{bmatrix} \) then
The system AX=B has a unique solution if
The particular integral for the differential equation \( (D^2 - 2D + 1)y = x^2 e^{3x} \) is
Laplace transform of \( g(t) = \begin{cases} \cos(t-\frac{\pi}{3}), & \text{if } t>\frac{\pi}{3} \\ 0, & \text{if } t<\frac{\pi}{3} \end{cases} \) is
By eliminating a & b from z = ax + by + (a/b) then, P.D.E formed is _____
The Laplace transform of the function f(t) = t sin t 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 the mean and variance of a binomial variate are 12 & 4, then the distribution is _____
Probability that a leap year has 53 Sundays 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)
If any function is even, in Fourier series it contains
If \(\lambda\) is an eigenvalue of a non-singular matrix A . Then the eigenvalue of (adjA) is
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 \( c \).