List of top Mathematics Questions

The two geometric means between 2 and 8 are $g_{1}$ and $g_{2}$. Then $g_{1}^{3}+g_{2}^{3}$ is equal to

Given that $i^{2}=-1$. If $z_{1}=(7+i\sqrt{5})^{2}+(7-i\sqrt{5})^{2}$ and $z_{2}=(3+2i)^{3}-(3-2i)^{3}$, then

If $z_{1}=1+3i$, $z_{2}=-3i+5$, then $(z_{1}\overline{z_{2}}+z_{2}\overline{z_{1}})+(z_{1}\overline{z_{2}}+z_{2}\overline{z_{1}})$ is equal to

The sum of the first $n$ terms in a G.P. is $s_{n}=100-100^{1-n}$. The common ratio $r$ is

Let $t_{1},t_{2},t_{3},\dots,t_{n}$ be in G.P. Then $(\frac{t_{4}}{t_{2}})^{3}$ is equal to

$\left|\frac{\cos\alpha+i\sin\alpha}{\sin\alpha-i\cos\alpha}\right|^{1000}+\left|\frac{\sin\alpha+i\cos\alpha}{\cos\alpha-i\sin\alpha}\right|^{2000}$ is equal to

Let $X=\{1,2,3,4,5,6,7}$. Let $R=\{(1,1), (1, 2), (1, 3), (5, 6), (6, 7), (7,5)\}$ be a relation on $X$. Then the relation $R$ will become reflexive if we include the pairs

Let $f(x)=\frac{2025x+2026}{2027x-2025},x\in\mathbb{R},x\ne\frac{2025}{2027}$ be a function. Then $f^{1000}(100)$, where $f^{2}(x)=f(f(x))$ is equal to

Given that $i^{2}=-1$. Then $(i^{1})(i^{2})(i^{3})\dots(i^{2026})$ is equal to

Let $f(x)=x^{2}+2x+3,x\le-1$. Then the domain of the inverse of $f(x)$ is

Let $X=\{a,b,c,d,e}$ and $A=\{a,b,c,d\}$. Let $P=\{B:B\subseteq X \text{ and } A\setminus B=\{d\}\}$. Then the number of elements in the set $P$ is

Let $X = \{a_1, a_2, a_3, \ldots, a_n\}$ be a set consisting of $n$ elements. The relation $R = \{(a_1,a_1),(a_2,a_2),(a_3,a_3),\ldots,(a_n,a_n)\}$ on the set $X$ is:

Let $f(x)=10x^2+ax,\; x\in \mathbb{R}$ be such that $a^2-400<0$. Let $g(x)=f(x)+f'(x)+f''(x)$. Then $g(x)$ is:

The minimum of $f(x) = \dfrac{x^{100} - 1}{x^{100} + 1}, \; x \in \mathbb{R}$ is:

Elimination of arbitrary constants $A$ and $B$ from $y = Ae^x + Be^{-2x}$ gives the differential equation:

Consider the Linear Programming Problem (LPP): Maximize $z = 30x + 60y$ subject to constraints $x + 2y \leq 12$, $2x + y \leq 12$, $4x + 5y \geq 20$, $x \geq 0$, $y \geq 0$. Then the number of corner points of the feasible region is

The solution of the differential equation $(x + 2y)dx + (2x - y)dy = 0$ is

$\displaystyle \int \frac{\sin(\cot^{-1}x)}{1+x^2} \, dx$ is equal to:

The value of $\displaystyle \int_{0}^{1} x(1-x)^4 \, dx$ is equal to:

$\displaystyle \int \left(\frac{1}{(1+x)^2} - \frac{2}{(1+x)^3}\right)e^x \, dx$ is equal to:

$\displaystyle \int \sqrt{1 + \sin\left(\frac{x}{8}\right)} \, dx =$

Let $f(x) = 1 + x\log\left(x + \sqrt{x^2+1}\right) - \sqrt{x^2+1}, \; x \geq 0$. Then:

Let $X = \{a,b,c,d,e,f\}$ and $Y = \{7,8,9,10,11\}$ be two sets. Which one of the following is true?

If $y = e^{-x^2}$, then $\dfrac{d^2y}{dx^2} + 2x\dfrac{dy}{dx}$ is equal to:

Let $y = \dfrac{3x^3 - 2x^2 + x}{|x|}, \; x \ne 0$. Then $\dfrac{dy}{dx}$ at $x=-2$ is equal to: