List of top Mathematics Questions asked in JKCET

Let $ f(x)=\frac{k}{1+{{x}^{2}}},\,-\infty < x < \infty $ be the probability density of a random variable. Then, $k$ equals 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 $ {{4}^{x}}={{16}^{y}}={{64}^{z}}, $ then

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

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

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

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

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

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

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

The equation of the line passing through $ (0,0) $ and intersection of $ 3x-4y=2 $ and $ x+2y=-4 $ is

The number of lines making equal angles with the coordinate axes in three dimensional geometry is equal to

The length of the perpendicular distance of the point $ (-1,\,4,\,0) $ from the line $ \frac{x}{1}=\frac{y}{3}=\frac{z}{1} $ is equal to

The projection of a line segment $OP$ through origin $O$, on the coordinate axes are $8, 5, 6$. Then, the length of the line segment $OP$ is equal to

The vector equation of the straight line $ 6x-8=2y-7=3z $ is

if the straight lines $ 2x+5ay-1=0 $ and $ 3x+7y+7=0 $ are mutually perpendicular, then value of $a$ is

The unit normal vector to the plane $ 3x+2y-2z=8\sqrt{17} $ is

If $A$ is a square matrix of order $3$ and if $ \det \,(A)=3, $ then $ \det \,[adj\,\,\{adj\,(adj\,A)\}] $ is equal to

If $ {{\tan }^{-1}}\,(1-x),\,\,{{\tan }^{-1}}\,(x) $ and $ {{\tan }^{-1}}\,(1+x) $ are in $A.P.$, then the value of $ {{x}^{3}}+{{x}^{2}} $ is equal to

$ \int_{0}^{\pi /2}{\frac{{{\sin }^{100}}x}{{{\sin }^{100}}x+{{\cos }^{100}}x}\,\,dx} $ is equal to