List of top 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

Solution of \( (2y - x) \frac{dy}{dx} = 1 \) is

The integrating factor of \( y + \frac{d}{dx}(xy) = x(\sin x + \log x) \) 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

The probability distribution of a random variable X is given by

Then the variance of X 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}

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 \( a = \)}

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 \( \frac{\text{cosec}^2 \theta}{\sqrt{10}} = \)}

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

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

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

\( f(x) = \begin{cases} 3-x, & -1<x<0 \\ 1+\frac{5x}{3}, & -3 \le x \le 2 \end{cases} \) 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 }

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

A first order reaction is 50% completed in 16 minutes. Find the percentage of reactant reacting in 32 minutes.

A hypothetical galvanic cell is A$_{(s)}$ | A$^+$(1M) || B$^{+2}$(1M) | B$_{(s)}$ and emf of cell is positive. What is the possible cell reaction?

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

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

The standard emf for cell, Cd$_{(s)}$ | Cd$^{+2}$(1M) || Cu$^{+2}$(1M) | Cu$_{(s)}$ is 0.74 V.
If concentration of Cd$^{+2}_{(aq)}$ and Cu$^{+2}_{(aq)}$ decreases by 10 times at 298 K. Calculate emf of cell.