List of top Mathematics Questions

A geometric progression has an even number of terms. If the sum of all terms is five times the sum of all odd terms, then the common ratio is equal to

If \(\frac{1}{8!} + \frac{1}{9!} = \frac{x}{12!}\), then the value of \(x\) is equal to

If $a,b,c$ are three unequal numbers such that $a,b,c$ are in arithmetic progression and $b-a, c-b, a-b$ are in geometric progression, then $a:b:c$ is

The number of ways in which we can choose a committee from 3 men and 6 women so that the committee includes at least two men and exactly twice as many women as men is

In a geometric progression of positive terms, if any term is equal to the sum of the next two terms, then the common ratio of the geometric progression is equal to

If $z(3 - i) = 2 + i$, then $z^2 =$

The imaginary part of \(\frac{1 - i\sqrt{3}}{1 + i\sqrt{3}}\) is

The sum of $i^2 + i^4 + \cdots$ upto 25 terms is equal to

If $|z + 4| = 2|z + 1|$, where $z$ is a complex number then $|z|$ is equal to

The domain of \(f(x) = \frac{x^2 + 1}{x^2 + x + 1}\) is

The number of elements in the set \(\{(x,y): 2x^2 + 3y^2 = 35, x,y \in \mathbb{Z}\}\), where \(\mathbb{Z}\) is the set of all integers, is

Let \(R\) be a relation in \(\mathbb{N}\) defined by \(\{(x,y): x + 3y = 10, x,y \in \mathbb{N}\}\). Then the range of \(R\) is

Let $A$ and $B$ be two sets of having 3 and 2 elements respectively. Then the number of subsets of $A \times B$ having at least three elements is

$$ \int \frac{dx}{x(x^{10}+1)} = $$

$$ \int \frac{1}{(x-3)(x-7)} \, dx = ? $$

$$ \int_{0}^{\pi/4} (\tan^8 x + \tan^6 x) \, dx = ? $$

$$ \int e^x \left( \log x + \frac{1}{x^2} \right) dx = ? $$

$$ \int e^x (\tan x + \sec^2 x) \, dx = ? $$

$$ \int_{-\pi/4}^{\pi/4} \sin^{103} x \cos^{101} x \, dx = ? $$

$$ \lim_{x \to 0} \frac{1 - \cos x}{x^2} = $$

$$ \lim_{x \to \infty} \left[ \frac{1^x + 2^x + 3^x + \cdots + n^x}{n} \right]^{1/x} = $$

Let $A = \{x : x \in \mathbb{R}, \, x \text{ is not a positive integer}\}$. Define $f: A \to \mathbb{R}$ as $f(x) = \dfrac{2x}{x-1}$, then $f$ is:

The number of bijective functions from set $A$ to itself when $A$ contains $97$ elements, is:

Domain of $\cos^{-1}[x]$ is, where $[.]$ denotes greatest integer function:

Given $0 \le x \le \dfrac{1}{2}$ then the value of $\tan \left[ \sin^{-1} \left( \dfrac{x}{\sqrt{2}} + \dfrac{\sqrt{1-x^2}}{\sqrt{2}} \right) - \sin^{-1} x \right]$ is: