List of top Mathematics Questions asked in MHT CET

The maximum value of \( z = 3x + 5y \), subject to \( 3x + 2y \leq 18 \), \( x \leq 4 \), \( y \leq 6 \), \( x, y \geq 0 \) is

If \( \sin(x + y) + \cos(x + y) = \sin \left[ \cos^{-1} \left( \frac{1}{3} \right) \right] \), then \[ \frac{dy}{dx} = \]

For any non-zero vectors \( \vec{a} \) and \( \vec{b} \), \( \left| \vec{b} \times (\vec{a} \times \vec{b}) \right| = \)

Evaluate the integral \[ \int \frac{1 + 2e^{-x}}{1 - 2e^{-x}} \, dx \]

The area included between the parabolas \( y^2 = 5x \) and \( x^2 = 5y \) is

If \[ A = \{x, y, z\}, \quad B = \{1, 2\}, \text{ then the total number of relations from set } A \text{ to set } B \text{ are} \]

The approximate value of the function \[ f(x) = x^3 - 3x + 5 \quad \text{at} \quad x = 1.99 \] is

If \[ p \rightarrow \left( \sim p \vee q \right) \text{ is false, then the truth values of } p \text{ and } q \text{ are respectively} \]

The integral \[ \int_0^{\frac{\pi}{2}} \log \left( \frac{\sqrt{1 - \cos 2x}}{\sqrt{1 + \cos 2x}} \right) dx \] is

The Cartesian coordinates of the point on the parabola \[ y^2 = x \quad \text{whose parameter is} \quad \frac{-4}{3} \] are

The radius of the circle passing through the points \[ (5, 7), \quad (2, -2), \quad (-2, 0) \] is

In a triangle ABC, if \[ \frac{\sin A - \sin C}{\cos C - \cos A} = \cot B, \text{ then A, B, C are in} \]

If \[ \sin \theta = \frac{-12}{13}, \quad \cos \phi = \frac{-4}{5}, \quad \text{and} \quad \theta, \phi \text{ lie in the third quadrant, then } \tan(\theta - \phi) = \]

If \[ x \cos \theta + y \sin \theta = 5, \quad x \sin \theta - y \cos \theta = 3, \quad \text{then the value of} \, x^2 + y^2 \, \text{is} \]

If \[ \begin{vmatrix} a + b & b + c & c + a \\ b & c & a \\ c & a & b \end{vmatrix} \neq 0, \quad \text{then} \quad \begin{vmatrix} a + b & b + c & c + a \\ b & c & a \\ c & a & b \end{vmatrix} = \]

The angle between the line \[ \mathbf{r} = (i + j + k) + \lambda (3i + j + 3k) \] and the plane \[ \mathbf{r} \cdot (i + 2j + 3k) = 8 \] is

The equation of the tangent at \( P(-4, -4) \) on the curve \[ x^2 = -4y \] is

The minimum value of \( Z = 5x + 8y \) subject to \[ x + y \geq 5, \quad 0 \leq x \leq 4, \quad y \geq 2, \quad x \geq 0, \quad y \geq 0 \] is

If the angle between the lines given by the equation \[ x^2 - 3xy + Ay^2 + 3x - 5y + 2 = 0, \quad \lambda \geq 0, \quad \text{is} \, \tan^{-1} \left( \frac{1}{3} \right), \, \text{then} \, \lambda = \]

The probability that a bomb will miss the target is 0.2. Then the probability that out of 10 bombs dropped exactly 2 will hit the target is

If \[ \int \sqrt{x - 1} \left( \frac{x^2 + 1}{x^2} \right) dx = \frac{2}{3} (x - 1)^k + c, \quad \text{then the value of } k \text{ is} \]

If the p.m.f. of a random variable \( X \) is given by \[ P(X = x) = \frac{5}{25} \quad \text{if} \quad x = 0, 1, 2, 3, 4, 5 \] then which of the following is not true?

The points of discontinuity of the function \[ f(x) = \begin{cases} \frac{1}{x - 1} & \text{if } 0 \leq x \leq 2 \\ \frac{x + 5}{x + 3} & \text{if } 2<x \leq 4 \end{cases} \] in its domain are

The integrating factor of the differential equation \[ (1 + x^2) \, dt = \left( \tan^{-1} x - t \right) \, dx \text{ is} \]

The integral \[ \int \cot x \cdot \log \left[ \log (\sin x) \right] \, dx = \]