List of top Mathematics Questions asked in JKCET

If $\alpha$ and $\beta$ are roots of the quadratic equation $ {{x}^{2}}+4x+3=0, $ then the equation whose roots are $ 2\alpha \,\text{+}\,\beta $ and $ \alpha \,\text{+2}\,\beta $ is

If the third term of a $G.P.$ is $3$, then the product of its first $5$ terms is

The number of diagonals of a polygon of $20$ sides is

If $X$ and $Y$ are $ 2\times 2 $ matrices such that $ 2X+3Y=O $ and $ X+2Y=I, $ where $ O $ and $ I $ denote the $ 2\times 2 $ zero matrix and the $ 2\times 2 $ identity matrix, then $X$ is equal to

The value of $\begin{vmatrix} \log_5\,729 & \log_3\,5 \\[0.3em] \log_5\,27 & \log_9\,25 \end{vmatrix}.\begin{vmatrix} \log_3\,5 & \log_{27}\,5 \\[0.3em] \log_5\,9 & \log_5\,9 \end{vmatrix}=$

If $ f\,(x)=\underset{y\to x}{\mathop{lim}}\,\,\frac{{{\sin }^{2}}y-{{\sin }^{2}}x}{{{y}^{2}}-{{x}^{2}}}, $ then $ \int{4x\,\,f(x)\,\,dx} $ =

If the sum to $2n$ terms of the $ A.P. \text{ }2,\text{ }5,\text{ }8,11,... $ is equal to the sum to $n$ terms of the $\text{ }57,\text{ }59,\text{ }61,\text{ }63,\text{ }...\text{ }, $ then $n$ =

If the equation $ (a+1){{x}^{2}}-(a+2)x+(a+3)=0 $ has roots equal in magnitude but opposite in signs, then the roots of the equation are

If $ (3,\,\,3) $ is a vertex of a triangle and $ (-3,\,\,6) $ and $ (9,\,\,6) $ are the mid points of the two sides through this vertex, then the centroid of the triangle is

A point P moves so that the sum of its distances from $ (-ae,\,0) $ and $ (ae,\,0) $ is $ 2a $ . Then the locus of P is

If $ {{C}_{0}},{{C}_{1}},{{C}_{2}},.....{{C}_{n}} $ denotes the binomial coefficients in the expansion of $ {{(1+x)}^{n}}, $ then $ {{C}_{0}}+\frac{{{C}_{1}}}{2}+\frac{{{C}_{2}}}{3}+....+\frac{{{C}_{n}}}{n+1} $ is equal to

If $ x\ne 0,\,\left| \begin{matrix} x+1 & 2x+1 & 3x+1 \\ 2x & 4x+3 & 6x+3 \\ 4x+4 & 6x+4 & 8x+4 \\ \end{matrix} \right|=0, $ then $2x+1 $ is equal to

The number of permutations of 4 letters that can be made out of the letters of the word EXAMINATION is

The coefficient of $ {{x}^{r}} $ in the expansion of $ {{(1-x)}^{-2}} $ is

$ 3a{{\int_{0}^{1}{\left( \frac{ax-1}{a-1} \right)}}^{2}}\,\,dx $ is equal to

The distance between the parallel lines $ y=x+a,\,\,y=x+b $ is

The number of solutions of $ \sin x=\sin 2x $ between $ \frac{-\pi }{2} $ and $ \frac{\pi }{2} $ is

The foot of the perpendicular from $ (2,4,-1) $ to the line $ x+5=\frac{1}{4}(y+3)=-\frac{1}{9}(z-6) $

If $A$ is a square matrix. $A'$ its transpose, then $ \frac{1}{2}(A-A') $ is

If $ y={{\sec }^{-1}}\left( \frac{1}{\sqrt{1-{{x}^{2}}}} \right), $ then $ \frac{dy}{dx} $ is equal to

If $p^{th}$ term of an arithmetic progression is $q$ and the $q^{th}$ term is $p$, then $10^{th}$ term is

If $ \alpha ,\beta $ are the roots of the equation $ {{x}^{2}}+ax+b=0, $ then $ \frac{1}{{{\alpha }^{2}}}+\frac{1}{{{\beta }^{2}}} $ is equal to

The distance between the planes $ 2x-2y+z+3=0 $ and $ 4x-4y+2z+5=0 $ is

The vector equation of the line passing through the points $ (3,2,1) $ and $ (-2,1,3) $ is

If $ |a|<1, $ then $ 1+2a+3{{a}^{2}}+4{{a}^{3}}+..... $ is equal to