List of top Mathematics Questions asked in MHT CET

If $A=\left[\begin{array}{cc}\cos 2\theta & -\sin 2\theta \\ \sin 2\theta & \cos 2\theta \end{array}\right]$ and $A+A^T=I$ Where $I$ is the unit matrix of $2\times 2$ and  $A^T$ is the transpose of $A$, then the value of $\theta$ is equal to:

Jobs arrive at a facility at an average rate of $5$ in an $8$ hour shift. The arrival of the jobs follows Poisson distribution. The average service time of a job on the facility is $40$ minutes. The service time follows exponential distribution. Idle time (in hours) at the facility per shift will be _______.

What is the acute angle between the lines represented by the equations $y-\sqrt{3}x-5=0$ and $\sqrt{3}y-x+6=0?$

The point which does not belong to the feasible region of the LPP:Minimize: $\mathrm{Z}=60\mathrm{x}+10\mathrm{y}$subject to $3\mathrm{x}+\mathrm{y}\ge 18$$2x+2y\ge 12$$x+2y\ge 10$$\mathrm{x},\mathrm{y}\ge 0$ is:

A circle with center $(4,-5)$ is tangent to the $y$ -axis in the standard $(x,y)$ coordinate plane. What is the radius of this circle?

Find ${\int }_0^2(x^2+1)dx$ as the limit of a sum :

The differential form of the equation $y^2+(x-b{)}^2=c$:

A line passes through $(1,1)$ and is perpendicular to the line $3x+y=7$. Its $x$-intercept is:

If $\left[\begin{array}{cc}2x+y& 4x\\ 5x-7& 4x\end{array}\right]=\left[\begin{array}{cc}7& 7y-13\\ y& x+6\end{array}\right]$, then $x+y=$

If $\overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}+2\hat{\mathrm{j}}-3\hat{\mathrm{k}}$, $\overrightarrow{\mathrm{b}}=3\hat{\mathrm{i}}-\hat{\mathrm{j}}+2\hat{\mathrm{k}}$ then the angle between $\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}},\overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}}$ is:

Let the random variables $X$ follow $B(6,p)$ If $16P(X=4)=P(X=2)$, then what is the value of $p$:

In this figure PQ ⊥ RS and RT ∥ PQ. if ∠PST = 68° then find reflexive ∠RTS.

The angle between the lines $x+y-3=0$ and $x-y+3=0$ is $\alpha$ and the acute angle between the lines $x-\sqrt{3}y+2\sqrt{3}=0$ and $\sqrt{3}x-y+1=0$ is $\beta$. Which one of the following is correct?

The value of $k$ which makes $f(x)=\{\begin{array}{l}\sin x,x\ne 0\\ k,x=0\end{array}$ continuous at $x=0$, is:

In the following trigonometry expression, find the value of (MN).$\frac{(1+\cos x)}{(1-\sin x)}(\sin x+\cos x-1{)}^2=M{\sin }^{N}x$

Let $\overrightarrow{a}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k},\overrightarrow{b}=b_1\hat{i}+b_2\hat{j}+b_3\hat{k}$ be three non-zero vectors such that $\overrightarrow{c}$ is a vector perpendicular to both $\overrightarrow{a}$ and $\overrightarrow{b}$. If the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is $\frac{\pi }{6}$ then $\left|\begin{array}{lll}{a}_1& b_1& c_1\\ a_2& b_2& c_2\\ a_3& b_3& c_3\end{array}\right|=?$

In a binomial distribution, the mean is $\frac{2}{3}$ and variance is $\frac{5}{9}$. What is the probability that random variable $D=2?$

What is ${\int }_0^a\frac{f(a-x)}{f(x)+f(a-x)}dx$ equal to?

What is the number of different messages that can be represented by three a’s and two b’s?

The solution of differential equation $dy=(4+y^2)dx$ is:

Find the angle between two vectors $(\overrightarrow{a}=2\hat{i}+\hat{j}-3\hat{k})$ and $(\overrightarrow{b}=3\hat{i}-2\hat{j}-\hat{k})$.

Consider a Poisson distribution for the tossing of a biased coin. The mean for this distribution is $\mu$. The standard deviation for this distribution is given by ______.

Find the area bounded between the curve $\mathrm{y}={\mathrm{x}}^2$ and $\mathrm{y}={\mathrm{x}}^3$.

If $\overrightarrow{OA}=\overrightarrow{a}$ and $\overrightarrow{OB}=\overrightarrow{b}$, then $\overrightarrow{BA}$ is:

What is the sum of the measures of the angles ∠A, ∠B, ∠C, ∠D, ∠E, and ∠F in the given figure?