List of top Mathematics Questions asked in MHT CET

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

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

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 $ .

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

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

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

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

From a group of $ 8 $ boys and $ 3 $ girls, a commitee of $ 5 $ members to be formed. Find the probability that $ 2 $ particular girls are included in the committe is

A wire of length 20 units is divided into two parts such that the product of one part and the cube of the other part is maximum. The product of these parts is:

Find the centre and radius of $x^2+y^2+6y=0$.

Form the differential equation of $y=a{e}^{3x}\cos (x+b)$ Where $y^{\prime }=\frac{dy}{dx}$ and $y^n=\frac{d^{2}y}{d{x}^2}$?

The value of \( \sin(\cot^{-1}(x)) \) is:

The integral of \( \sec^{2/3}x \csc^{4/3}x \, dx \) from \( \pi/6 \) to \( \pi/3 \) is equal to:

If \( y = 5\cos x - 3\sin x \), then \( \frac{d^2y}{dx^2} + y \) equals:

It is known from past experience that in a certain plant there are on the average $4$ industrial accidents per month. Find the probability that there will be less than $4$ accidents in a given month. Given: $({\mathrm{e}}^{-4}=0.0183)$

Value of $\cos (-{1230}^{\circ })\times \cot (-{315}^{\circ })$ is:

If $f(x)$ and $g(x)$ are two probability density functions,$f(x)=\{\begin{array}{cc}\frac{x}{a}+1& :-a\le x<0\\ -\frac{x}{a}+1& 0\le x\le a\\ 0& \text{ otherwise }\end{array}$$g(x)=\{\begin{array}{cc}-\frac{x}{a}& :-a\le x\le 0\\ \frac{x}{a}& :0\le x\le a\\ 0& :\text{ otherewise }\end{array}$Which one of the following statements is true?

Find the value of $m$ for which the line $\overrightarrow{r}=(\hat{i}+2\hat{k})+\lambda (2\hat{i}-m\hat{j}-3\hat{k})$ is parallel to the plane $\overrightarrow{r}\cdot (m\hat{i}+3\hat{j}+\hat{k})=4$ ?

There are $7$ Men and $6$ Women. In how many ways can we select $5$ members in which at least $3$ men should be there: