List of top Engineering Mathematics Questions

For a bivariate data $(x_i, y_i)$ ($i=1,2,3,\dots,10$), $\sum x_i y_i = 6200$, $\sum x_i = 400$, $\sum y_i = 1220$, $\sum x_i^2 = 1800$, then equation of line of best fit is?
Let $X$ be a discrete random variable with probability mass function $P(X=x_i)$ where $x \in \{x_1, x_2, \dots, x_n\}$. If $\sum_{i=1}^{n} (x_i-2)^2 P(X=x_i) = 28$ and $\sum_{i=1}^{n} (x_i+2)^2 P(X=x_i) = 12$. Then variance of $X$ is?
If the probability density function of a continuous random variable X is $f(X=x) = Ke^{-3x}$, $0<x<\infty$, then a solution of $\frac{P^2+1}{P} = \frac{K}{\sqrt{2}}$ is?
If for a progression, sum of the first $n$ terms is $2n^2+5n+6$ and $T_n$ is the $n^{th}$ term of the progression, then $\sum_{k=1}^{10} T_{3k} = $?
The complete solution of \( (mz-ny)\frac{\partial z}{\partial x} + (nx-lz)\frac{\partial z}{\partial y} = ly-mx \) is
Which of the following pair of functions are linearly dependent
The number of positive integral solutions of $x+y+z = 12$, $x \le y \le z$ is?
If $l>0, K<0$ are roots of $x^2 + x - 20 = 0$, the system of linear equations $3x - y + 4z = 3$, $x + 2y - 3z = -2$ and $6x + 5y + Pz = -3$ has?
Let \( \vec{F} \) be a vector point function defined inside and on the surface (S) of the sphere \( x^2+y^2+z^2=1 \). Then \( \oint_S (\text{Curl} \vec{F}) \cdot \hat{n} ds = \)
\( \int_{0}^{2} \int_{0}^{\sqrt{y}} e^{y/x} dx dy = \)
The system of equations \( \begin{bmatrix} -2 & 1 & 1 \\ 1 & -2 & 1 \\ 1 & 1 & -2 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} a \\ b \\ c \end{bmatrix} \) has
If \( \begin{bmatrix} \frac{1}{\sqrt{3}} & \frac{1+i}{\sqrt{3}} \\ \frac{1-i}{\sqrt{3}} & \frac{K}{\sqrt{3}} \end{bmatrix} \) is a unitary matrix, then the sum of all possible values of K is
The maximum area of a rectangle that can be inscribed in a circle of radius $R$ is
The value of \( \int_0^3 \int_0^0 (x^2 + 3y^2) \, dy \, dx \) is
If the mean and variance of a binomial variate are 12 & 4, then the distribution is _____
The value of the integral \[ \int_C \frac{2e^z}{(z-4)(z-2)} \, dz \] where \( C: |z| = 3 \) is
A continuous random variable \(X\) has a probability density function \( f(x) = 3x^2, \ 0 \leq x \leq 1 \). If \( P(X \leq a) = P(X>a) \), then the value of 'a' is
If the random variable \( X \) takes the values 1, 2, 3, and 4 such that \( 2P(X=1) = 3P(X=2) = P(X=3) = 5P(X=4) \), then the mean of \( X \) is
The equation \( x^3 - 6x - 4 = 0 \) has one real root between 2 and 3. The 2ndapproximation to the root of the equation by bisection method will be
The approximate solution of the initial value problem \( \frac{dy}{dx} = 1 + xy \), \( y(0) = 1 \) by Picard’s method will be
The particular integral of \( \frac{d^2y}{dx^2} + y = \cos(2x - 1) \) is
The value of \( \int_0^1 \int_y^{\sqrt{y}} yx \, dxdy \) is
The Laplace transform \( \mathcal{L}\{t^2 \sin 2t\} \) is
The divergence of the vector field \( \vec{F} = yz\,\hat{i} - zx\,\hat{k} \) at \( (-2, 0, 1) \) is
Evaluate \( \log_{e^{2000}} e^{2021} \cdot \log_{e^{2021}} e^{2022} \cdot \log_{e^{2022}} e^{2023} \cdot \log_{e^{2023}} e^{2024} \)