List of top Mathematics Questions

The $3^{\text{rd}}$ and $6^{\text{th}}$ terms of a G.P. are, respectively 108 and -32. Then the first term is

The imaginary part of $\frac{\cos 50^{\circ}+i\sin 50^{\circ}}{\cos 50^{\circ}-i\sin 50^{\circ}}$ is equal to

The domain of the function $f(x)=\sin^{-1}(\sqrt{2-x})$ is

The equation $\text{Im}(1-i)z=1$ represents the line

The inverse function of $f(x) = ax + 1$, $x \in \mathbb{R}$ is itself. Then the value of $a$ is

The range of $f(x)=[\cos x]$, where $[x]$ is the greatest integer less than or equal to $x$, is

If $f(x)=x+1$, and $g(x)=x^{3}$, then $f^{-1}(g(x))$ is equal to

Let $A=\{1,2,3\}$ and $B=\{1,2,3,4\}$ and let $R:A\rightarrow B$ be a relation. If $R=\{(1,2), (2,3), (3,4)\}$, then $R\circ R$ is

Evaluate the integral: \(\int \frac{x}{x + 2} \, dx\).

Let $\alpha, \beta$ be the roots of the equation $x^2 - x + p = 0$ and $\gamma, \delta$ be the roots of the equation $x^2 - 4x + q = 0$; $p, q \in \mathbb{Z}$. If $\alpha, \beta, \gamma, \delta$ are in G.P., then $|p+q|$ equals :

Let \( A = \{1, 2, 3, 4, 5\} \) and \( B = \{a, b, c\} \). Then the number of functions which are not onto are:

A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is \(3/5\), then find the number of yellow balls.

The half of the average value of three number is 20. The second number is thrice the third number and first number is twice the second number. What is the sum of smallest and largest number?

The number of distinct real solutions of the equation \[ x|x + 4| + 3|x + 2| + 10 = 0 \] is

$\int_{0}^{5}\frac{(x+8)^{2026}}{(x+8)^{2026}+(13-x)^{2026}}dx$ is equal to

Let $[x]$ be the greatest integer function. Then $\int_{-4}^{4}(x-[x])dx$ is equal to

$\int\left(\frac{1}{1+e^{t}}\right)dt$ is equal to

$\int e^{x}(2e^{x}+\sin x+\cos x+2)dx$ is equal to

$\int_{\pi/6}^{\pi/3}\frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}}dx$ is equal to

$\int\frac{1}{(1+x^{2})\tan^{-1}\left(\frac{1+x}{1-x}\right)}dx$ is equal to

$\int_{0}^{1}\left(\frac{x^{15}}{1+x^{32}}\right)[\cos(\tan^{-1}x^{16})]dx$ is equal to

$\int \tan\frac{\theta}{2}\sin\theta\cos\theta\, d\theta$ is equal to

$\int\frac{y^{2}-3y+2}{y^{2}+y}dy$ is equal to

Consider the circle $x^{2}+y^{2}=1$. The point on the circle which is nearest from the point (1,1), is

If $|f(x_{1})-f(x_{2})|\le(x_{1}-x_{2})^{2},x_{1},x_{2}\in\mathbb{R}$ and if $f(0)=2026$, then $f(2025)$ is equal to