List of top Mathematics Questions asked in MHT CET

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

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

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 ___________

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 $x = 0$ ?

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

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

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.

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

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

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

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

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

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

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

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 = _______

A point on $XOZ$ plane divides the join of $(5,-3,-2)$ and $ (1,2,-2)$ on

$ \int\limits_{5}^{10} \frac{1}{\left(x-1\right)\left(x-2\right)}dx $ is equal to

$ \int e^{x} \frac{\left(x-1\right)}{x^{2}} dx $ is equal to

$ \int\left[sin \left(log\,x\right)+cos\left(log\,x\right)\right]dx $ is equal to

Find the function $ f(x_1, x_2, x_3) $ satisfying $ f(x_1, x_2, x_3) = 1 $ at $ x_1 = 1, x_2 = x_3 = 0 $ .

Joint equation of pair of lines through $ (3, - 2) $ and parallel to $ x^2 - 4xy + 3y^2 = 0 $ is

For a certain function $ u_x $ , given that $ u_0 = 3, u_1 = 12, u_2 = 81, u_3 = 200, u_4 = 100, u_5 = 8 $ , then $ \Delta ^{5}u_{x} $ is equal to

The maximum value of $ z = 9x + 13y $ subject to $ 2x + 3y \le 18, 2x + y \le 10, x \ge 0, y \ge 0 $ is

$ \lim\limits _{x\to 1 } \left(log \,ex\right)^{1/log\,x} $ is equal

Given $ P(A \cup B ) = 0.6,P(A\cap B) = 0.2 $ , the probability of exactly one of the event occurs is