List of top Mathematics Questions asked in MHT CET

If \( \vec{A} = 2\hat{i} + 3\hat{j} \) and \( \vec{B} = 4\hat{i} - \hat{j} \), then the dot product \( \vec{A} \cdot \vec{B} \) is:
Find the area of a triangle with base 12 cm and height 5 cm.
Solve for $ x $ in the equation $ \frac{1}{x+3} + \frac{1}{x+5} = \frac{1}{6} $.
If $ \tan \theta = \frac{3}{4} $, find the value of $ \sin \theta $.
Find the roots of the quadratic equation $ x^2 - 5x + 6 = 0 $.
Find the value of $ x $ that satisfies the equation $ 2x + 3 = 11 $.
Evaluate the expression: \[ f\left(f(f(x))\right) + \left(f(f(x))\right)^2 \quad \text{if} \quad x = 1 \]
Evaluate the determinant of the matrix: \[ \left| \begin{array}{cc} 1 & \tan x
-\tan x & 1 \end{array} \right| \]
Evaluate the integral: \( \int \sin^5 x \, dx \)
Find the value of \( \tan 45^\circ \).
Find the value of \( \frac{d}{dx} (3x^2 + 4x + 5) \).
Find the area of a circle whose radius is 7 cm.
Find the value of \( \log_2 32 \).
If the sum of the first \( n \) terms of an arithmetic progression (AP) is given by \( S_n = 3n^2 + 2n \), find the 4th term of the AP.
The sum of the ages of a father and his son is 60 years. The father is three times as old as the son. What is the son's age?
If \( \sin \theta = \frac{3}{5} \), find the value of \( \cos \theta \).
Find the value of \( \sin 30^\circ + \cos 60^\circ \).
The area of a triangle with base 12 cm and height 5 cm is?
If \( y = x^x + x^x \), then find \( \frac{dy}{dx} \):
If ∫ (2x + 3)/((x - 1)(x^2 + 1)) dx = log_x {(x - 1)^(5/2)(x^2 + 1)^a} - (1/2) tan^(-1)x + C, then the value of a is:
Find the value of the integral: ∫ (2x + 3)/((xy)(x^2 + 1)) dx
The limit of \( \lim_{x \to 0} \frac{\sin x}{x} \) is:
A die is rolled. What is the probability of getting a number less than or equal to 4?
The feasible region of the linear programming problem is determined by the system of inequalities: \[ x + y \leq 6, \quad x \geq 0, \quad y \geq 0. \] What is the maximum value of \( x + y \) in the feasible region?
In how many ways can 5 people be arranged in a row?