List of top Mathematics Questions asked in MHT CET

The line passing through the points \( (a, 1, 6) \) and \( (3, 4, b) \) crosses the \( yz \)-plane at \( (0, \frac{17}{2}, -\frac{13}{2}) \), then the value of \( (3a + 4b) \) is

The rate of change of volume of spherical balloon at any instant is directly proportional to its surface area. If initially its radius is 3 cm, after 2 minutes its radius becomes 9 cm, then radius of balloon after 4 minutes is

If \( \bar{a} = 2\hat{i} + 3\hat{j} + 4\hat{k}, \bar{b} = \hat{i} - 2\hat{j} - 2\hat{k}, \bar{c} = -\hat{i} + 4\hat{j} + 3\hat{k} \) and if \( \bar{d} \) is vector perpendicular to both \( \bar{b} \) and \( \bar{c} \), \( \bar{a} \cdot \bar{d} = 18 \), then \( |\bar{a} \times \bar{d}|^2 = \)}

If \( (\cos^{-1} x)^2 - (\sin^{-1} x)^2>0 \), then}

The probability distribution of a random variable X is given by

Then the variance of X is

A random variable X has following p.d.f. \( f(x) = kx(1 - x), 0 \le x \le 1 \) and \( P(x>a) = \frac{20}{27} \), then \( a = \)}

Let \( \bar{a} = \hat{i} + \hat{j}, \bar{b} = 2\hat{i} - \hat{k}, \bar{c} = 3\hat{i} - \hat{j} + \hat{k} \), then vector \( \bar{p} \) satisfying \( \bar{p} \cdot \bar{a} = 0 \) and \( \bar{p} \times \bar{b} = \bar{c} \times \bar{b} \) is

If \( X \sim B(6, \frac{1}{2}) \), then \( P(|X - 2| \le 1) = \)}

If \( \theta \) is the angle between the lines whose direction cosines are given by \( 6mn - 2nl + 5lm = 0 \) and \( 3l + m + 5n = 0 \), then \( \sin \theta = \)}

The equation \( x^2 - 3xy + \lambda y^2 + 3x - 5y + 2 = 0 \), where \( \lambda \) is a real number represents a pair of lines. If \( \theta \) is the acute angle between the lines, then \( \frac{\text{cosec}^2 \theta}{\sqrt{10}} = \)}

The number of values of \( x \) in the interval \( [0, 3\pi] \) satisfying the equation \( 2 \sin^2 x + 5 \sin x - 3 = 0 \) is

If \( A = \begin{bmatrix} 1 & -1 & 1 \\ 0 & 2 & -3 \\ 2 & 1 & 0 \end{bmatrix} \), \( B = \text{adj } A \) and \( C = 5A \), then \( \frac{|\text{adj } B|}{|C|} = \)}

Consider the statements given by following
(A) If 4+3 = 8, then 5+3=9
(B) If 6 + 4 = 10, then moon is flat
(C) If both (A) and (B) are true, then 5 + 6 = 17
Then which of the following statement is correct?

Let A = \( \lim_{x \to 0^+} (1 + \tan^2 \sqrt{x})^{\frac{1}{2x}} \), then log\(_e\) A =}

The foci of the conic \( 25x^2 + 16y^2 - 150x = 175 \) are

\( f(x) = \begin{cases} 3-x, & -1<x<0 \\ 1+\frac{5x}{3}, & -3 \le x \le 2 \end{cases} \) and \( g(x) = \begin{cases} -x, & -2 \le x \le 3 \\ x, & 0 \le x \le 1 \end{cases} \)
then range of (fog)(x) is }

The equations of the tangents to the circle \( x^2 + y^2 = 36 \) which are perpendicular to the line \( 5x + y - 2 = 0 \) are

Let A \( \equiv \) (0,0), B(3, 0), C(0, -4) are vertices of \( \triangle \)ABC, then the co-ordinates of incentre of \( \triangle \)ABC is

If sin \( \theta \) = \( \frac{1}{2}\left(x + \frac{1}{x}\right) \), then sin \( 3\theta + \frac{1}{2}\left(x^3 + \frac{1}{x^3}\right) \) =}

Argument of the complex number z = \( \frac{13-5i}{4-9i} \), i = \( \sqrt{-1} \) is

The function f(x) = 2x - \(|x - x^2|\) is

If the shortest distance between the lines $\bar{r}_1 = \alpha\hat{i} + 2\hat{j} + 2\hat{k} + \lambda(\hat{i} - 2\hat{j} + 2\hat{k}), \lambda \in \mathbb{R}, \alpha > 0$ and $\bar{r}_2 = -4\hat{i} - \hat{k} + \mu(3\hat{i} - 2\hat{j} - 2\hat{k}), \mu \in R$, is $9$, then the value of $\alpha$ is

The lines $\frac{x-3}{1} = \frac{y-2}{1} = \frac{z-5}{-k}$ and $\frac{x-4}{k} = \frac{y-3}{1} = \frac{z-3}{2}$ are coplanar, hence $k =$}

If $A = \begin{bmatrix} 1 & 2 \\ -1 & 4 \end{bmatrix}$ and $A^{-1} = \alpha I + \beta A$, $\beta \in R$ where I is the identity matrix of order 2, then $4(\alpha + \beta) =$}

A plane passes through \( (2, 1, 2) \) and \( (1, 2, 1) \) and parallel to the line \( 2x = 3y \) and \( z = 1 \), then the plane also passes through the point