List of top Mathematics Questions asked in MHT CET

If $\int\limits^{K}_0 \frac{dx}{2 + 18 x^2} = \frac{\pi}{24}$, then the value of K is

If $\vec{a} , \vec{b} , \vec{c}$ are mutually perpendicular vectors having magnitudes 1, 2, 3 respectively, then $[\vec{a} + \vec{b} + \vec{c} \, \, \vec{b} - \vec{a} - \vec{c}] = ?$

If $2 \sin \left( \theta + \frac{\pi}{3}\right) = \cos \left( \theta -\frac{\pi}{6}\right) , $ then $\tan \, \theta = $

The value of $\cos^{-1} \left(\cot\left(\frac{\pi}{2}\right)\right) + \cos^{-1} \left(\sin\left(\frac{2\pi}{3}\right)\right) $ is

If vector $\vec{r}$ with d.c.s. $l, m, n$ is equally inclined to the co-ordinate axes, then the total number of such vectors is

The equation of the plane through $(-1, 1 , 2 ) $ whose normal makes equal acute angles with co-ordinate axes is

$\Delta \, ABC$ has vertices at $A = (2, 3,5), B = (-1,3, 2)$ and $C = (\lambda , 5, \mu )$. If the median through A is equally inclined to the axes, then the values of $\lambda$ and $\mu$ respectively are

If $\int^{\pi/2}_{0} \log\cos x dx =\frac{\pi}{2} \log\left(\frac{1}{2}\right)$ then $ \int^{\pi/2}_{0} \log\sec x dx = $

The objective function of $LPP$ defined over the convex set attains its optimum value at

If $\int \sqrt{\frac{x - 5}{x -7}} dx = A \sqrt{x^2 - 12 x + 35 } + \log \, | x - 6 + \sqrt{x^2 - 12x + 35} | + C $ then $A = $

$\int^1_0 x \, \tan^{-1} x\,dx = $

The maximum value of $f(x) = \frac{\log \, x }{x} (x \neq 0 , x \neq 1)$ is

The number of principal solutions of $\tan 2 \theta = 1$ is

If $z_1$ and $z_2$ are z co-ordinates of the points of trisection of the segment joining the points $A(2, 1, 4), B _1 + z_2 =$

If the function \[ f(x) = \begin{cases} [ tan (\frac {\pi}{4}+x)]^{1/x} & \quad for\, x \neq 0\\ K \,\,\,\,\,\,\,\,\,\text{if } x =0 \end{cases} \] is continuous at $x = 0$, then $K = ?$

The area of the region bounded by the lines $y = 2x + 1, y = 3x + 1$ and $x = 4$ is

If $c$ denotes the contradiction then dual of the compound statement $\sim p \wedge ( q \vee c)$ is

The point on the curve $y = \sqrt{x - 1}$ where the tangent is perpendicular to the line $2x + y - 5 = 0 $ is

The objective function $z = 4x_1 + 5x_2$, subject to $2x_1 + x_2 \geq 7 , 2x_1 + 3x_2 \leq 15 , x_2 \leq 3, x_1 , x_2 \geq 0 $ has minimum value at the point

The differential equation of all parabolas whose axis is $y-axis$ is

The particular solution of the differential equation $xdy + 2ydx = 0$, when $x = 2, y = 1$ is

If $ 2 \,tan^{-1} (cos\,x) = tan^{-1} (2 \,cosec\,x)$ then $sin\,x + cos\,x $ is equal to

If $A=\begin{bmatrix}1&1&0\\ 2&1&5\\ 1&2&1\end{bmatrix}$, then $a_{11}A_{21} +a_{12}A_{22}+a_{13}A_{23} $ is equal to

$\int \frac{1}{\sqrt{8+2x-x^{2}}} dx$ is equal to

The approximate value of $f\left(x\right)= x^{3}+5x^{2}-7x +9$ at $x=1.1 $ is