List of top Mathematics Questions asked in JKCET

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

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

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 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 probability that atleast one of the events $A$ and $B$ occurs is $ 0.5 $ . If $A$ and $B$ occur simultaneously with probability $ 0.2, $ then $ P({{A}^{c}})+P({{B}^{c}}) $ 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

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

If $ f(x)=\int_{1}^{x}{\sqrt{4-{{t}^{2}}}}\,\,\,dt, $ then real roots of the equation $ x-f'(x)=0 $ are

The value of $ \sum\limits_{n=0}^{\infty }{\frac{{{n}^{2}}+4}{n\,!}} $ is equal to

The equation of the plane perpendicular to the $z$-axis and passing through $ (2,-3,5) $ is

If $A$ is a square matrix of order $3$ and a is a real number, then determinant $ |\alpha \,\,\,A| $ is equal to

If $ {{4}^{x}}={{16}^{y}}={{64}^{z}}, $ then

The contrapositive statement of the proposition $ p\to \sim q $ is

The value of the integral $ \int{\frac{1}{{{e}^{2x}}+{{e}^{-2x}}}}\,\,dx $ is equal to

The number of straight lines which can be drawn through the point $ (-2,\,\,\,2) $ so that its distance from $ (-3,\,\,1) $ will be equal $6$ units is

The ratio in which ZX-plane divides the line segment AB joining the points $ A(4,2,3) $ and $ B(-2,4,5) $ is equal to

A force $2$ units acts along the line $ x-4=y-5. $ The moment of the force about the point $ (1,\,\,1) $ along $Z-axis$ is equal to

If $ f(x)\,=kx\,-\,\cos \,x $ is monotonically increasing for all $ x\in R, $ then

The value of $k$ for which the equation $ {{x}^{2}}-4xy-{{y}^{2}}+6x+2y+k=0 $ represents a pair of straight lines is

The three distinct points $ A(at_{1}^{2},\,2a{{t}_{1}}),\,\,B(at_{2}^{2},\,\,2a{{t}_{2}}) $ and $ C(0,\,a) $ (where $a$ is a real number) are collinear, if

The value of $ \cos \frac{\pi }{7}.\,\cos \frac{2\pi }{7}.\,\cos \frac{4\pi }{7} $ is equal to