List of top Mathematics Questions asked in MHT CET

If \( f(x) = x^2 - 3x + 4 \) and \( f(x) = f(2x + 1) \), then \( x = \)

The minimum value for the LPP \( Z = 6x + 2y \), subject to \( 2x + y \geq 16, x \geq 6, y \geq 1 \) is

Write the statement in symbolic form 'Sandeep neither likes tea nor coffee but enjoys a soft drink'. Where \( p \): Sandeep likes tea, \( q \): Sandeep likes coffee, \( r \): Sandeep enjoys a soft drink

The principal value of \( \sin^{-1} \left( -\frac{1}{2} \right) \) is

Evaluate \( 2 \tan^{-1} \left( \frac{1}{3} \right) - \tan^{-1 \left( \frac{3}{4} \right) \)}

If \( f(x) = \frac{|x - 2|}{x - 2} \) for \( x \neq 2 \), and \( f(x) = 1 \) for \( x = 2 \), then which of the following statements is true?

If \( A(0, 4, 0) \), \( B(0, 0, 3) \), and \( C(0, 4, 3) \) are the vertices of \( \Delta ABC \), then its incenter is:

The probability distribution of a discrete r.v. \( X \) is: \[ \begin{array}{c|ccccc} X = x & 0 & 1 & 2 & 3 & 4 \\ P(X = x) & k & 2k & 4k & 2k & k \\ \end{array} \] Then, the value of \( P(X \leq 2) \) is:

If \( \frac{x}{x-y} = \log \left( \frac{a}{x-y} \right) \), then \( \frac{dy}{dx} = \)

The equation of the line passing through the points \( (3, 4, -7) \) and \( (6, -1, 1) \) is:

Evaluate the integral: \[ \int_{-1}^{1} \left[ \sqrt{1 + x + x^2} - \sqrt{1 - x + x^2} \right] dx \]

The co-ordinates of the foot of the perpendicular from the point \( (0, 2, 3) \) on the line
\[ \frac{x+3}{5} = \frac{y-1}{2} = \frac{z+4}{3} \]

The approximate value of \( \log_{10}99 \) is (Given \( \log_{10}e = 0.4343 \))

The maximum value of \(Z = 10x + 25y\) subject to \[ 0 \le x \le 3,\; 0 \le y \le 3,\; x + y \le 5,\; x \ge 0,\; y \ge 0 \] is

If \((\sim p \wedge q)\rightarrow r\) is false, then the truth values of \(p,q,r\) respectively are

Evaluate the integral: \[ \int \frac{\sin x}{\sin\left(x-\frac{\pi}{4}\right)}\,dx \]

The value of \(x\) such that the matrix \[ \begin{bmatrix} x & 2 & 3 \\ 4 & 5 & 6 \\ 2 & 3 & 5 \end{bmatrix} \] is not invertible is

If the population grows at the rate of 5% per year, the time taken for the population to become double is (Given \( \log 2 = 0.6912 \))

Evaluate the integral: \[ \int \left[ \log(1+\cos x) - x \tan\left(\frac{x}{2}\right) \right] dx \]

A die is thrown twice. If getting a number greater than four on the die is considered a success, then the variance of the probability distribution of the number of successes is

If $y = \left(\tan^{-1} x\right)^{2}$ then $ \left(x^{2} + 1\right)^{2} \frac{d^{2}y}{dx^{2} } + 2x \left(x^{2} + 1 \right) \frac{dy}{dx} = $

The maximum value of $2x + y$ subject to $3x + 5y \leq 26$ and $5x + 3y \leq 30, x \geq 0, y \geq 0$ is

Letters in the word HULULULU are rearranged. The probability of all three L being together is

If $f : R - \{2\} \to R$ is a function defined by $f(x) = \frac{x^2 - 4}{x - 2}$ , then its range is

If $\log_{10} \left(\frac{x^{3} - y^{3} }{x^{3} + y^3} \right) = 2$ then $ \frac{dy}{dx} = $