List of top Mathematics Questions

Find \((x + 1)^6 - (x - 1)^6\). Hence or otherwise evaluate \((\sqrt2 + 1)^6 + (\sqrt2 - 1)^6.\)
Let relation defined as $(x_1, y_1) \,R (x_2, y_2)\, x_1 ≤ x_2,\, y_1 ≤ y_2$ and given that
(a) R is reflexive but not symmetric.
(b) R is transitive. then
The number of words, with or without meaning, that can be formed using all the letters of the word ASSASSINATION so that the vowels occur together, is________
An A.P. consists of n (odd terms) and its middle term is m. Then the sum of the A.P. is
The value of $∫_0^{\frac{\pi}{4}} \frac{dx}{1+tanx} $
Place commas correctly and write the numerals:
(a) Seventy three lakh seventy five thousand three hundred seven.
(b) Nine crore five lakh forty one.
(c) Seven crore fifty two lakh twenty one thousand three hundred two.
(d) Fifty eight million four hundred twenty three thousand two hundred two.
(e) Twenty three lakh thirty thousand ten.
What will be the remainder when (428)2024 is divided by 21?
The value of \(\int \frac{ln\,x}{(1+ln\,x)^2}dx\)=?
The number of onto mappings from the set A = {1, 2, ....., 100} to set B = {1, 2} is:

Coefficient independent of x in the expansion of \([\frac{3x^{2}-1}{2x^{5}}]^{7}\) is?

The number of real roots of the equation

[ x |x| - 5 |x + 2| + 6 = 0 ] ,  is:

Let $S_1$ and $S_2$ be respectively the sets of all $a \in R -\{0\}$ for which the system of linear equations
$ a x+2 a y-3 a z=1$ 
$ (2 a+1) x+(2 a+3) y+(a+1) z=2$
$(3 a+5) x+(a+5) y+(a+2) z=3$
has unique solution and infinitely many solutions. Then
Let $f(x)=\int \frac{2 x}{\left(x^2+1\right)\left(x^2+3\right)} d x$. If $f(3)=\frac{1}{2}\left(\log _e 5-\log _e 6\right)$, then $f(4)$ is equal to
What letters of the English alphabet have reflectional symmetry (i.e., symmetry related to mirror reflection) about. 
  1. a vertical mirror 
  2.  a horizontal mirror 
  3.  both horizontal and vertical mirrors
A bag contains six balls of different colours.Two balls are drawn in succession with replacement. The probability that both the balls are of the same colour is p. Next four balls are drawn in succession with replacement and the probability that exactly three balls are of the same colour is $q$ .If $p: q=m: n$, where $m$ and $n$ are coprime, then $m+n$ is equal to______
$50^{\text {th }}$ root of a number $x$ is 12 and $50^{\text {th }}$ root of another number $y$ is 18 Then the remainder obtained on dividing $(x+y)$ by 25 is_____

Let: $\vec{a}=\hat{i}+2 \hat{j}+3 \hat{k}, \vec{b}=\hat{i}-\hat{j}+2 \hat{k}$ and $\vec{c}=5 \hat{i}-3 \hat{j}+3 \hat{k}$ be there vectors If $\vec{r}$ is a vector such that, $\vec{r} \times \vec{b}=\vec{c} \times \vec{b}$ and $\vec{r} \cdot \vec{a}=0$, then $25|\vec{r}|^2$ is equal to

$\displaystyle \lim _{n \rightarrow \infty}\left[\frac{1}{1+n}+\frac{1}{2+n}+\frac{1}{3+n}+\ldots+\frac{1}{2 n}\right]$ is equal to
The mean and variance of $5$ observations are $5$ and $8$ respectively If $3$ observations are $1,3,5$, then the sum of cubes of the remaining two observations is
Let $S$ be the set of all solutions of the equation $\cos ^{-1}(2 x)-2 \cos ^{-1}\left(\sqrt{1-x^2}\right)=\pi$, $x \in\left[-\frac{1}{2}, \frac{1}{2}\right]$ Then $\displaystyle\sum_{x \in S} 2 \sin ^{-1}\left(x^2-1\right)$ is equal to
Let \(S=x: x∈R\) and $\left(\sqrt{3}+\sqrt{2})^{x^2-4}+(\sqrt{3}-\sqrt{2})^{x^2-4}=10\right\}$Then $n(S)$ is equal to
The sum to $10$ terms of the series $\frac{1}{1+1^2+1^4}+\frac{2}{1+2^2+2^4}+\frac{3}{1+3^2+3^4}+\ldots $ is
Let $x=(8 \sqrt{3}+13)^{13}$ and $y=(7 \sqrt{2}+9)^9$ If $[t]$ denotes the greatest integer $\leq t$, then
The parabolas : $a x^2+2 b x+c y=0$ and $d x^2+2 e x+f y=0$ intersect on the line $y=1$ If $a, b, c, d, e, f$ are positive real numbers and $a, b, c$ are in GP, then
Let $\lambda \in R , \vec{a}=\lambda \hat{i}+2 \hat{j}-3 \hat{k}, \vec{b}=\hat{i}-\lambda \hat{j}+2 \hat{k}$.If $((\vec{a}+\vec{b}) \times(\vec{a} \times \vec{b})) \times(\vec{a}-\vec{b})=8 \hat{i}-40 \hat{j}-24 \hat{k}$, then $|\lambda(\vec{a}+\vec{b}) \times(\vec{a}-\vec{b})|^2$ is equal to