List of top Mathematics Questions asked in MHT CET

If $a = \lim_{n \rightarrow \infty} \frac{1+2+3+\ldots+n}{n^2}$ and $b = \lim_{n \rightarrow \infty} \frac{1^2+2^2+3^2+\ldots+n^2}{n^3}$, then

If lines represented by the equation $px^2 - qy^2 = 0$ are distinct, then

If $A = \begin{bmatrix} 1 & 0 & 2 \\ -1 & 1 & -2 \\ 0 & 2 & 1 \end{bmatrix}$ and $\text{adj } A = \begin{bmatrix} 5 & x & -2 \\ 1 & 1 & 0 \\ -2 & -2 & y \end{bmatrix}$, then the value of $x + y$ is

If $\vec{a}$, $\vec{b}$, $\vec{c}$ are mutually perpendicular vectors having magnitudes $1$, $2$, $3$ respectively, then $[\vec{a} + \vec{b} + \vec{c} \quad \vec{b} - \vec{a} \quad \vec{c}] =$

If the variance of the data $2, 4, 5, 6, 8, 17$ is $23.33$, then the variance of $4, 8, 10, 12, 16, 34$ will be

The equation of the perpendicular bisector of the line segment joining $A(-2, 3)$ and $B(6, -5)$ is

The indefinite integral $\int \frac{\sec^8 x}{\csc x}\,dx$ is equal to

If $y = \tan^{-1}\left(\sqrt{\frac{1 + \sin x}{1 - \sin x}}\right)$, where $0 \le x < \frac{\pi}{2}$, then $\frac{dy}{dx}$ at $x = \frac{\pi}{6}$ is

The shortest distance between lines $\vec{r} = (2\hat{i} - \hat{j}) + \lambda(2\hat{i} + \hat{j} - 3\hat{k})$ and $\vec{r} = (\hat{i} - \hat{j} + 2\hat{k}) + \mu(2\hat{i} + \hat{j} - 5\hat{k})$ is

A random variable $X \sim B(n, p)$. If the values of the mean and variance of $X$ are $18$ and $12$ respectively, then $n =$

The value of $\int_0^1 \tan^{-1}\left(\frac{2x - 1}{1 + x - x^2}\right)\,dx$ is

If $x = \frac{1 - t^2}{1 + t^2}$ and $y = \frac{2at}{1 + t^2}$, then $\frac{dy}{dx} =$

The domain of the function $f(x) = \sqrt{x - 1 + \sqrt{6 - x}}$ is

$\tan^{-1}\left(\tan \frac{5\pi}{6}\right) + \cos^{-1}\left(\cos \frac{13\pi}{6}\right) =$

The differential equation of all family of lines $y = mx + \frac{4}{m}$ obtained by eliminating the arbitrary constant $m$ is

The integral $\int \sin^{-1}\left(\frac{2x}{1 + x^2}\right)\,dx$ for $|x| < 1$ is equal to

The expression $[(p \wedge \sim q) \vee q] \vee (\sim p \wedge q)$ is equivalent to

The sum of three numbers is 6. Thrice the third number when added to the first number gives 7. On adding three times first number to the sum of second and third number we get 12. The product of these numbers is

If in $\Delta ABC$, with usual notations, the angles are in A.P., then $\frac{a}{c}\sin(2C) + \frac{c}{a}\sin(2A) =$

A coin is tossed three times. If $X$ denotes the absolute difference between the number of heads and the number of tails, then $P(X = 1) =$

The maximum value of $z = 10x + 25y$ subject to $0 \le x \le 3$, $0 \le y \le 3$, $x + y \le 5$ occurs at the point

If a plane meets the axes $X$, $Y$, $Z$ in $A$, $B$, $C$ respectively such that centroid of $\Delta ABC$ is $(1, 2, 3)$, then the equation of the plane is

If $\vec{a} + \vec{b} + \vec{c} = \vec{0}$ with $|\vec{a}| = 3$, $|\vec{b}| = 5$ and $|\vec{c}| = 7$, then the angle between $\vec{a}$ and $\vec{b}$ is