List of top Mathematics Questions asked in MHT CET

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 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 $A(2, 1, 4), B _1 + z_2 =$

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 $\int\frac{f\left(x\right)}{log \left(sin\,x\right)}dx = log\left[log\,sin\,x\right]+c$ then $f\left(x\right)=$

$\int \left(\frac{\left(x^{2}+2\right)a^{\left(x +tan^{-1}x\right)}}{x^{2}+1}\right)dx = $

If $r. v. x :$ waiting time in minutes for bus and $p.d.f.$ of $x$ is given by $f(x) = \begin{cases} \frac{1}{5} , & 0\le x\le5 \\[2ex] 0, & \text{otherwise} \end{cases}$ then probability of waiting time not more than $4$ minutes is = _______

If $A$ and $B$ are foot of perpendicular drawn from point $Q (a, b, c)$ to the planes $yz$ and $zx$, then equation of plane through the points $A, B$ and $O$ is ___________

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

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

If $p :$ Every square is a rectangle $q :$ Every rhombus is a kite then truth values of $p ? q$ and $p ? q$ are __________ and ___________ respectively.

The differential equation of the family of circles touching $y$-axis at the origin is

Direction cosines of the line $\frac{x+2}{2} = \frac{2y-5}{3}, z = -1$ is

If $r.v. X \sim B \left(n = 5, P=\frac{1}{3}\right)$ then $P(2 < X < 4) =$ ______________

The joint equation of lines passing through the origin and trisecting the first quadrant is ________

For what value of $k$, the function defined by $ f(x) = \begin{cases} \frac{log(1+2x)sin\,x^\circ}{x^2} & \text{for } x \ge \text {0}\\ k & \text{for } x = \text{ 0} \end{cases}$ is continuous at $x = 0$ ?

If Rolle�s theorem for $f\left(x\right)= e^{x} \left(sinx - cosx\right)$ is verified on $[\pi/4$, $5 \pi/4]$, then the value of $c$ is

$\int\left(\frac{4e^{2}-25}{2e^{x}-5}\right)dx = Ax+B \,\,log |2e^{x}-5|+c$ then

If Matrix $A = \begin{bmatrix}1&2\\ 4&3\end{bmatrix}$ such that $Ax = I$, then $X = $_______

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

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

Derivative of $log \left(sec\,\theta +tan \,\theta\right) $ with respect to $sec\, \theta$ at $\theta = \pi/4$ is

In $\Delta ABC \left(a-b\right)^{2} cos^{2} \frac{C}{2} + \left(a+b\right)^{2} sin^{2} \frac{C}{2} = $

Let $f(x) = \int \frac{x^2 - 3x + 2}{x^4 + 1} \, dx$, then the function decreases in the interval