List of top Mathematics Questions asked in JKCET

If $A$ and $B$ are square matrices of order $3$ such that $ det\text{ }A=1 $ and $ det\text{ }B=-1 $ then $ det\text{ (-10}\,\text{AB)} $ is equal to

Four arithmetic means between $-10$ and $25$ are inserted. Then the $5^{th}$ term in the series is

If $A$ and $B$ are square matrices of order 3 such that $det A = 1$ and $ det B = -1$, then $det (- 10 AB) = ? $

If $\begin{vmatrix} a_1 &b_1 &c_1 \\[0.3em] a_2 &b_2 &c_2 \\[0.3em] a_ 3&b_3 &c_3 \end{vmatrix}=\,\,\,\,3,\, $ then $ \begin{vmatrix} 3a_1 &9b_1 &3c_1 \\[0.3em] a_2 &3b_2 &c_2 \\[0.3em] 3a_ 3&9b_3 &3c_3 \end{vmatrix}=$,

The dual of the statement $ (\sim p)\wedge [(\sim q)\wedge (p\vee q)\wedge ( \sim r)] $ is

$ \int{{{x}^{2}}\,{{7}^{x}}\,\,dx} $ is equal to

The radius of the sphere $ |\,3\,\vec{r}+2\hat{i}-\hat{j}-4\hat{k}|=3 $ is

$ \underset{n\to \infty }{\mathop{\lim }}\,\,\,\frac{{{2}^{n+1}}+{{3}^{n+1}}}{{{2}^{n}}+{{3}^{n}}} $ is equal to

The foot of the perpendicular drawn from the origin to a plane is $ (1,-1,5) $ . The equation of the plane is

The centroid of the triangle formed by joining the mid points of the sides of a triangle with vertices $ (-1,-1),(2,4) $ and $ (-5,-6) $ is

If $ A+B+C=\pi , $ then $ \tan \frac{A}{2}\tan \frac{B}{2}+\tan \frac{B}{2}\tan \frac{C}{2}+\tan \frac{C}{2}+\tan \frac{C}{2}\tan \frac{A}{2} $ is equal to

The pair of straight lines $ {{x}^{2}}-3{{y}^{2}}=0 $ and the line $ x=1 $ form a triangle which is

$ \int_{0}^{x}{\log \,(\cot \,x\,+\,\tan t)\,dt} $ =

If $ {{\tan }^{-1}}\,2 $ and $ {{\tan }^{-1}}\,3 $ are two angles of a triangle, then the third angle is

The image of the point $ (6,3,9) $ in the straight line $ x-2=\frac{1-y}{2}=\frac{z}{2} $ is

The sum of the series $ \left( 1+\frac{{{({{\log }_{e}}\,n)}^{2}}}{2!}+\frac{{{({{\log }_{e}}n)}^{4}}}{4!}+... \right) $ is

If $ {{x}_{1}},{{x}_{2}},......{{x}_{18}} $ are observations such, that $ \sum\limits_{j=1}^{18}{({{x}_{j}}-8)=9} $ and $ \sum\limits_{j=1}^{18}{{{({{x}_{j}}-8)}^{2}}=45,} $ then the standard deviation of these observations is

The number of ways in which $5$ boys and $5$ girls can be seated for a photograph so that no two girls sit next to each other is

The term independent of $x$ in the expansion of $ {{\left( \sqrt{\frac{x}{3}}+\frac{3}{2{{x}^{2}}} \right)}^{10}} $ is

The number of solutions of the equation $ \sin \,x\,\,\cos \,\,3x=\sin \,3x\,\,\cos \,5x $ in $ \left[ 0,\frac{\pi }{2} \right] $ is

$ \frac{^{8}{{C}_{0}}}{6}{{-}^{8}}{{C}_{1}}{{+}^{8}}{{C}_{2}}\cdot 6{{-}^{8}}{{C}_{3}}{{.6}^{2}}+....{{+}^{8}}{{C}_{8}}{{\cdot 6}^{7}} $ is equal to

If $ (3+i)\,(z+\bar{z})-(2+i)(z-\bar{z})+14i\,=0, $ then $ z\bar{z} $ is equal to

The value of $ {{\cos }^{-1}}\,\left( \sin \,\frac{7\pi }{6} \right) $ is equal to

The point on the x-axis equidistant from the points $ (4,3,1) $ and $ (-2,\,-6,\,-2) $ is

In $ \Delta \,\,ABC $ if $ si{{n}^{2}}A+si{{n}^{2}}B+si{{n}^{2}}C=2, $ then the triangle is