List of top Engineering Mathematics Questions

Let \[ f(x) = \begin{cases} 1 + \dfrac{2x}{\pi}, & -\pi \le x \le 0
1 - \dfrac{2x}{\pi}, & 0<x \le \pi \end{cases} \] The constant term of the Fourier series of \(f(x)\) is:
The particular integral of \[ (D^2 - 6D + 13)\, y = 8e^{3x} \sin 2x \] is:
The maximum value of the directional derivative of \( \varphi = x^2 yz \) at the point \( (1, 4, 1) \) is:
The characteristic polynomial of a \(3 \times 3\) matrix \( A \) is \[ |A - \lambda I| = \lambda^3 - 9\lambda^2 + 23\lambda - 15. \] Let \( X = \text{trace}(A) \) and \( Y = \det(A) \), then:
For two events A and B, let $P(A)=\frac{1}{3}$, $P(B)=\frac{1}{4}$ and $P(A \cup B)=\frac{1}{2}$ then $P(A/B)$ is
A biased coin was thrown 300 times and the tail turned up 120 times, then the standard error of the observed proportion of tails is
The equation $x^4 - x - 10 = 0$ is to be solved using the Newton-Raphson method. If $x = 2$ is taken as the initial approximation of the equation, then the next approximation of the solution is
If $f(x) = \begin{cases} -\pi, & \text{in } -\pi<x<0 \\ x, & \text{in } 0<x<\pi \end{cases}$ then the constant term of the Fourier series is
The rank of the matrix A = $ \begin{bmatrix} 1 & 3 & 4 & 3 \\ 3 & 9 & 12 & 9 \\ -1 & -3 & -4 & -3 \end{bmatrix} $ is
If $u = \frac{x+y}{x-y}$ and $v = \frac{xy}{(x-y)^2}$ are functionally dependent, then the relation between $u$ & $v$ is
Newton-Raphson iterative formula for finding \[ \frac{1}{\sqrt{N}}, (N>0) \] is
Among the following, Rolle's theorem is not applicable for
The mean and variance of a random variable \( X \) having a Binomial distribution are 4 and 2 respectively, then \( P(X=1) \) is
If \[ f(x) = \begin{cases} -\pi, & -\pi<x<0 \\ x, & 0<x<\pi \end{cases} \] then the constant term of the Fourier series is
The integrating factor of \[ \frac{dy}{dx} + y \cot x = 2x + x^2 \cot x \] is
Particular integral of \[ \frac{dy}{dx} + y = e^{x} \] is
If the function \( u = \sin^{-1} \left( \frac{x^3 + y^3}{x + y} \right) \), then \[ x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y} \] is
Consider $ \frac{dy}{dx} = x^2 - y, y(0)=1 $ using Euler's method with step size of 0.1. Then the value of $ y(0.1) $ is
The value of the integral $ \int_C \frac{e^{2z}}{(z-1)(z-2)}dz $ where C is the circle $ |z|=3 $ is

Given the probability density function $ f(X=x)= \begin{cases} 0, & x<2 \\ \frac{3+2x}{18}, & 2\leq x\leq4 \\ 0, & x>4 \end{cases} $ then the probability that X lies between 2 and 3 is

If the chance that a bus arrives safely at a bus stand is $ \frac{9}{10} $, then the probability that out of 5 buses at least 4 will arrive safely is
Using Laplace transformation, the value of $ \int_{0}^{\infty} \frac{\sin 2t}{t} dt $ is
If Rolle’s theorem is applied for $ f(x) = x^3 - x $ in $ [-1,1] $, then the values of ‘c’ of this theorem are:
The value of $\int_0^\infty e^{-x^2} \, dx$ is:
The necessary condition for the equation $ M(x,y)dx + N(x,y)dy = 0 $ to be exact is