Mathematics

Periodic function $f(x)$ is given below. $f(x) = \begin{cases} -1, & \text{when} & -\pi < x < 0 \\ 1, & \text{when} & 0 < x < \pi \end{cases} ; f(x + 2\pi) = f(x)$ The CORRECT opti...

A partial differential equation is given below. $\frac{\partial^2 u}{\partial x^2} - \frac{\partial^2 u}{\partial y^2} = 0$ Possible solution(s) is/are:

An ordinary differential equation is given below. $x^2 \frac{d^2y}{dx^2} = 6y$ Considering $a$ and $b$ as arbitrary constants, the general solution of the equation is

Which of the following equations belong/belongs to the class of second-order, linear, homogeneous partial differential equations:

The "order" of the following ordinary differential equation is ______. $d^3y/dx^3 + (d^2y/dx^2)^6 + (dy/dx)^4 + y = 0$

The value of $\lim_{x\to\infty} (x - \sqrt{x^2 + x})$ is equal to

Pick the CORRECT solution for the following differential equation $\frac{dy}{dx} = e^{x-y}$

The statements P and Q are related to matrices A and B, which are conformable for both addition and multiplication. P: (A + B)ᵀ = Aᵀ + Bᵀ Q: (AB)ᵀ = AᵀBᵀ Which one of the following...

For the following partial differential equation, $x \frac{\partial^2 f}{\partial x^2} + y \frac{\partial^2 f}{\partial y^2} = \frac{x^2 + y^2}{2}$ which of the following option(s)...

In the differential equation $\frac{dy}{dx} + \alpha xy = 0$, $\alpha$ is a positive constant. If $y = 1.0$ at $x = 0.0$, and $y = 0.8$ at $x = 1.0$, the value of $\alpha$ is _____...

x : y : z = $\frac{1}{2} : \frac{1}{3} : \frac{1}{4}$ What is the value of $\frac{x+z-y}{y}$?

Consider the following expression: $z = \sin(y+it)+\cos(y-it)$ where z, y, and t are variables, and $i=\sqrt{-1}$ is a complex number. The partial differential equation derived fro...

$\int \left(x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} + \dots\right) dx$ is equal to

A function, λ, is defined by λ(p,q) = { (p-q)², if p≥q, { p+q, if p <q. The value of the expression λ(-(-3+2),(-2+3)) / λ(-(-2+1)) is:

Consider the limit: $\lim_{x\to 1} \left(\frac{1}{\ln x} - \frac{1}{x-1}\right)$ The limit (correct up to one decimal place) is _________

The volume determined from $\iiint_V 8 xyz \, dV$ for $V = [2, 3]\times [1, 2] \times [0,1]$ will be (in integer) _________

Suresh wanted to lay a new carpet in his new mansion with an area of 70 x 55 sq. mts. However an area of 550 sq. mts. had to be left out for flower pots. If the cost of carpet is R...

A retaining wall with measurements 30m x 12m x 6m was constructed with bricks of dimensions 8cm x 6cm x 6cm. If 60% of the wall consists of bricks, the number of bricks used for th...

The value of the integral $\int_0^\pi x \cos^2x \,dx$ is

The value (up to two decimal places) of a line integral $\int_{C} \mathbf{F}(\mathbf{r}) \cdot d\mathbf{r}$, for $\mathbf{F}(\mathbf{r})=x^{2}\hat{i}+y^{2}\hat{j}$ along C which is...