List of top Mathematics Questions asked in MHT CET

The solution set of the inequalities $4x+3y\le60$, $y\ge2x$, $x\ge3$, $x, y\ge0$ is represented by region

The statement $[(p\rightarrow q)\wedge\sim q]\rightarrow r$ is tautology, when $r$ is equivalent to

The variance of 20 observations is 5. If each observation is multiplied by 2, then variance of resulting observations is

If the line \( x - 2y = m \, (m \in \mathbb{Z}) \) intersects the circle \( x^{2} + y^{2} = 2x + 4y \) at two distinct points, then the number of possible values of \( m \) are

General solution of the differential equation $\cos x(1+\cos y)dx-\sin y(1+\sin x)dy=0$ is

The negation of the statement "The number is an odd number if and only if it is divisible by 3."

Two cards are drawn successively with replacement from well shuffled pack of 52 cards, then the probability distribution of number of queens is

For an initial screening of an entrance exam, a candidate is given fifty problems to solve. If the probability that the candidate can solve any problem is \( \frac{4}{5} \), then the probability that he is unable to solve less than two problems is

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

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

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

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

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

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

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

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

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

If $\underset{x\to \mathrm{\infty }}{lim}(\frac{x^2+x+1}{x+1}-px-q)=-3$, then $p$ and $q$ is:

The value of $\frac{d}{dx}{x}^{2x}=$

Consider the following statements:1. If $y=\ln (\sec x+\tan x)$, then $\frac{dy}{dx}=\sec x$.2. If $y=\ln (\mathrm{cosec}x-\cot x)$, then $\frac{dy}{dx}=\mathrm{cosec}x$.Which of the above is / are correct?

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

The integrating factor of the differential equation $2y\frac{dx}{dy}+x=5y^2$ is, $(y\ne 0)$:

If $\int \frac{x^2+1}{x(x+1{)}^2}dx=A\ln |x|+\frac{B}{1+x}+C$, where C is the constant of integration, then $A+B$ $=$