List of top Mathematics Questions

\(\lim\limits_{n\rightarrow \infin}\frac{\sum(n^4-2n^3+n^2)}{\sum ((3n)^4+n^3-n^2)}\) is equal to

If the orthocentre of triangle formed by (8, 3), (5, 1) and (h, k) is (6, 1), then (h, k) lie on

The locus of P such that the ratio of distance P from A(3, 1) and B(1, 2) is 5 : 4 is

Sides of a triangle are AB = 9, BC = 7, AC = 8. Then cos 3C equals to

If α, ß are the roots of the equation x² - √2 x - 8 = 0 and A_n = αⁿ + ßⁿ, n ∈ N, then the value of (A₁₀ - √2A₉) / 2A₈

Find the range of \(\frac{1}{7}-\sin5x\)

If \(\int\frac{dx}{a^2\sin x+b^2\cos^2x}=\frac{1}{12}\tan^{-1}(3\tan x)+c,\)then the maximum value of a sinx + bcosx is____

Let $ {{(1+x)}^{n}}=1+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+.....+{{a}_{n}}{{x}^{n}} $ .If $ {{a}_{1}},{{a}_{2}} $ and $ {{a}_{3}} $ are in $AP$, then the value of $n$ is

$\int \limits^{2017}_{2016} \frac{\sqrt{x}}{\sqrt{x} + \sqrt{4033 - x}} dx $ is equal to

$\int\frac{dx}{x-\sqrt{x}}$ is equal to

$\int\frac{2x+\sin2x}{1+\cos2x}\, dx$ is equal to

The coefficient of $x ^{49}$ in the product $\left(x-1\right)\left(x-2\right)\cdots\left(x-50\right)$ is

Let $t_n$ denote the $n^{th}$ term in a binomial expansion. If $ \frac{t_{6}}{t_{5}}$ in the expansion of $(a+ b)^{n+4}$ and $ \frac{t_{5}}{t_{4}}$ in the expansion of $(a + b)^n$ are equal, then $n$ is

If $ \tan \alpha =\frac{b}{a},a>b>0 $ and if $ 0

Let $u , v$ and $w$ be vectors such that $u + v + w = 0 .$ If $| u |=3,| v |=4$ and $| w |=5$ then $u \cdot v + v \cdot w + w \cdot u$ is equal to

Number of integral solutions of $ \frac{x+2}{{{x}^{2}}+1}>\frac{1}{2} $ is

The negation of $\left(p\vee\sim q\right)\wedge q$ is

Let $p$ : roses are red and q : the sun is a star. Then, the verbal translation of $ (-\text{ }p) \vee q $ is

If $y = x + \frac{1}{x}, x \ne 0$, then the equation $\left(x^{2}-3x+1\right)\left(x^{2}-5x+1\right)=6x^{2}$ reduces to

The value of $\sum\limits^{n}_{k=0}\left(i^{k}+i^{k+1}\right)$, where $i^2 = -1$, is equal to

$ \displaystyle\lim_{x\rightarrow0} \frac{1}{3-2^{\frac{1}{x}}}$ is equal to

Let $S_{1}$ be a square of side $5\,cm$. Another square $S_{2}$ is drawn by joining the midpoints of the sides of $S_{1}$ Square $S_{3}$ is drawn by joining the midpoints of the sides of $S_{2}$ and so on. Then (area of $S_{1}$ + area of $S_{2}$ + area of $S_{3}$ $+\ldots+$ area of $S_{10}$) =

If $f\left(x\right) = \int\limits^{sin\,x}_{2x}cos\left(t^{3}\right)dt$, then $f'{x}$ is equal to

$\int \frac{e^{x}}{x}\left(x\,log\,x+1\right)dx$ is equal to

The plane $ \overrightarrow{r}=s(\hat{i}+2\hat{j}-4\hat{k})+t(3\hat{i}+4\hat{j}-4\hat{k}) $ $ +(1-t)(2\hat{i}-7\hat{j}-3\hat{k}) $ is parallel to the line