List of top Mathematics Questions asked in MHT CET

Solve the system of equations: \[ x + y = 5 \] \[ 2x - y = 4 \]
Find the value of the determinant \( \begin{vmatrix} 2 & 3 \\ 4 & 5 \end{vmatrix} \).
Find the derivative of the function \( f(x) = 3x^2 - 5x + 7 \).
Solve for \( x \): \( \log_2 (x-1) = 3 \).
Find the area of a triangle with vertices \( A(2, 3) \), \( B(5, 11) \), and \( C(8, 7) \).
Find the roots of the quadratic equation \( 2x^2 - 4x - 6 = 0 \).
Find the value of \( \frac{d}{dx} (3x^2 + 4x + 5) \).
Find the value of \( \tan 45^\circ \).
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.
If \( \sin \theta = \frac{3}{5} \), find the value of \( \cos \theta \).
Find the value of \( \log_2 32 \).
Find the value of \( \frac{5}{6} + \frac{3}{4} \).
Find the area of a circle whose radius is 7 cm.
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?
Find the roots of the quadratic equation \( 2x^2 - 4x - 6 = 0 \).
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 the roots of the quadratic equation \( x^2 - 5x + 6 = 0 \) are \( p \) and \( q \), then what is the value of \( p + q \)?
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
If \( y = x^x + x^x \), then find \( \frac{dy}{dx} \):
Given \( f'(1) = 3 \), \( f(1) = 1 \), and
\[ y = f\left(f(f(x))\right) + \left(f(x)\right)^2, \] then find \( \frac{dy}{dx} \) at \( x = 1 \).
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: \( \int \sin^5 x \, dx \)