List of top Mathematics Questions asked in JKCET

The value of $ \left| \begin{matrix} {{a}^{2}} & 2ab & {{b}^{2}} \\ {{b}^{2}} & {{a}^{2}} & 2ab \\ 2ab & {{b}^{2}} & {{a}^{2}} \\ \end{matrix} \right| $ is

If $ \theta =\frac{\pi }{{{2}^{n}}+1}, $ then the value of $ {{2}^{n}}\cos \theta \,\cos \,2\theta \,\cos \,{{2}^{2}}\theta .....\cos {{2}^{n-1}}\theta $ is

Using the principal values, the value of $ {{\sin }^{-1}}\left\{ \sin \frac{5\pi }{6} \right\}+{{\tan }^{-1}}\left\{ \tan \frac{\pi }{6} \right\} $ = ?

The value of $ \frac{d}{dx}[{{x}^{n}}\,{{\log }_{a}}\,x{{e}^{x}}] $ is

If $ {{S}_{n}} $ denotes the sum of first $n$ terms of $A.P.$ $ , $ such that $ \frac{{{S}_{m}}}{{{S}_{n}}}=\frac{{{m}^{2}}}{{{n}^{2}}}, $ then $ \frac{{{a}_{m}}}{{{a}_{n}}} $ is equal to

A bag contains $50$ tickets numbered $1, 2, 3, ...,50$ of which five are drawn at random and arranged in ascending order of magnitude $ ({{x}_{1}}

$ \underset{x\to 0}{\mathop{\lim }}\,\,{{\left\{ \tan \left( \frac{\pi }{4}+x \right) \right\}}^{1/x}} $ is equal to

Five persons entered the lift cabin on the ground floor of an eight floor house. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first, then the probability of all $5$ persons leaving at different floors is

For the married couple living in Jammu, the probability that a husband will vote in an election is $ 0.5 $ and the probability that his wife will vote is $ 0.4 $ . The probability that the husband votes, given that his wife also votes is $ 0.7 $ . Then, the probability that husband and wife both will vote is

The sum of the series $ 5-\frac{10}{3}+\frac{20}{9}-\frac{40}{27}+.... $ is equal to

The value of the integral $ \int_{0}^{1}{x{{(1-x)}^{49}}\,dx} $ is equal to

If $ f(x)={{(1+x)}^{n}}, $ then the value of $ f(0)+f'(0)+\frac{f'\,'(0)}{2!}+.....+\frac{{{f}^{(n)}}(0)}{n!} $ is equal to

If $ ^{m+n}P{{ }_{2}}=90 $ and $ ^{m-n}P{{ }_{2}}=30, $ then $ (m,n) $ is given by (where, m and n are positive integers)

If the points $ (2a,\,a),\,(a,\,2a) $ and $ (a,\,\,a) $ form a triangle of area $ 32\text{ }sq $ units, then the centroid of the triangle is

Let $ P(x,y) $ be a point on the curve $ {{y}^{2}}=4x $ at which the tangent is perpendicular to the line $ 2x+y=-2. $ Then, the coordinates of the point $P$ are

Let \(f:R\to R\) be a function such that the third derivative of \(f(x)\) vanishes for all \(x\). If \(f(0)=1,\,f'(2)=4\) and \(f''(1)=2,\) then \(f(x)\) equals to

In the binomial expansion of $ {{(a-b)}^{n}},\,\,n\,\,\ge \,5, $ the sum of $5^{th}$ and $6^{th}$ term is zero. Then, $ \frac{a}{b} $ is equal to

If $ f(x)={{\log }_{e}}\,(1+x)-{{\log }_{e}}(1-x), $ then the value of $ \int_{-1/2}^{1/2}{f(x)\,\,\,dx} $ equals to

The angle between the two lines $ \frac{2-x}{1}=\frac{y}{2}=\frac{z+3}{1} $ and $ \frac{x-4}{4}=\frac{y-1}{1}=\frac{z-5}{2} $ is

The value of $a$ for which the volume of parallelepiped formed by the vectors $\hat {i}+a\hat{j} + \hat{k} \,\, \hat{j}+a\hat{k} $ and $ a\hat{i}+\hat{k} $ is minimum, is

If mean and variance of a binomial variate X are 2 and 1 respectively, then the probability that X takes a value atleast one is

Let $A$ and $B$ be two mutually exclusive events such that $ P(A\cap {{B}^{c}})=0.25 $ and $ P({{A}^{c}}\cap B)=0.5 $ . Then, $ P\{(A\cup {{B}^{c}})\} $ is equal to

If the product of $n$ positive real numbers is one, then their sum is

The sum of $n$ terms of the series $ \frac{3}{{{1}^{2}}{{.2}^{2}}}+\frac{5}{{{2}^{2}}{{.3}^{2}}}+\frac{7}{{{3}^{2}}{{.4}^{2}}}+..... $ is equal to

Let $ f(x)=\frac{k}{1+{{x}^{2}}},\,-\infty < x < \infty $ be the probability density of a random variable. Then, $k$ equals to