List of top Mathematics Questions asked in MHT CET

Evaluate the integral: \[ \int \frac{\sqrt{\tan x}}{\sin x \cos x} \, dx \]
Population of Town A and B was 20,000 in 1985. In 1989, the population of Town A was 25,000, and Town B had 28,000. What will be the difference in population between the two towns in 1993?
Given the equation: \[ 81 \sin^2 x + 81 \cos^2 x = 30 \] Find the value of \( x \).
If $ f(x) = 2x^2 - 3x + 5 $, find $ f(3) $.
Solve for \( x \): \( \log_2 (x-1) = 3 \).
Find the smallest angle of the triangle whose sides are \( 6 + \sqrt{12}, \sqrt{48}, \sqrt{24} \).
If \( A = \begin{bmatrix} 2 & 1
3 & 4 \end{bmatrix} \), then the determinant of matrix \( A \) is:
Find the area of a triangle with vertices \( A(2, 3) \), \( B(5, 11) \), and \( C(8, 7) \).
If $ \mathbf{a} $ and $ \mathbf{b} $ are non-coplanar unit vectors such that $ \mathbf{a} \times (\mathbf{b} \times \mathbf{c}) = \frac{\mathbf{b}}{2} $ then the angle between $ \mathbf{a} $ and $ \mathbf{b} $ is:
The maximum value of the function \( f(x) = -2x^2 + 4x + 1 \) occurs at:
If \( \mathbf{a} = 3\hat{i} + 4\hat{j} \) and \( \mathbf{b} = 2\hat{i} - \hat{j} \), find \( \mathbf{a} \cdot \mathbf{b} \) (the dot product).
If \( \tan \theta = 2 \), then the value of \( \sec^2 \theta \) is:
The distance between the points \( A(3, 4) \) and \( B(-1, -2) \) is:
Solve for $ x $ in the equation $ 2x - 3 = 5x + 12 $.
Find the roots of the quadratic equation \( 2x^2 - 4x - 6 = 0 \).
Find the value of \( \frac{5}{6} + \frac{3}{4} \).
Find the solution $ \frac{d^2y}{dm^2} - k^3 \frac{dy}{dm} = y \cos m, \quad y(0) = 1 $
Evaluate the integral: \[ \int \sqrt{x^2 + 3x} \, dx \]
If \( \mathbf{a} \) and \( \mathbf{b} \) are two non-zero vectors such that the angle between them is \( 60^\circ \), what is the probability that the dot product \( \mathbf{a} \cdot \mathbf{b} \) is positive?
Find the value of \( x \) if \( \sin(2x) = 1 \).
Find the sum of the first 20 terms of the arithmetic progression: \( 2, 5, 8, 11, \dots \).

If a random variable X has the following probability distribution values:

X01234567
P(X)1/121/121/121/121/121/121/121/12

Then P(X ≥ 6) has the value:

Given the vectors: \[ \mathbf{a} = i + 3j - k, \quad \mathbf{b} = 3i - j + 2k, \quad \mathbf{c} = i + 2j - 2k \] and the following information: \[ \frac{\mathbf{a} \cdot \mathbf{c}}{|\mathbf{c}|} = \frac{10}{3} \] Find the value of \( \alpha + \beta \) and the projection of \( \mathbf{a} \) on \( \mathbf{c} \).
Evaluate the following integrals: \[ \int \frac{(x^4 + 1)}{x(2x + 1)^2} \, dx \] and \[ \int \frac{1}{x^4 + 5x^2 + 6} \, dx \]
Given that: \[ \cot \left( \frac{A + B}{2} \right) \cdot \tan \left( \frac{A - B}{2} \right) \] and the equation involving coordinates: \[ \frac{x}{2} + \frac{y}{3} + \frac{2}{6} - 1 = 0 \] Find the area of \( \Delta ABC = 2 \).