List of top Mathematics Questions asked in MHT CET

If \( \sin \theta = \frac{3}{5} \), find the value of \( \cos \theta \).
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?
Solve for $ x $ in the equation $ 2x - 3 = 5x + 12 $.
Given that: \[ x = a \sin(2t) (1 + \cos(2t)), \quad y = a \cos(2t) (1 - \cos(2t)) \] Find \(\frac{dy}{dx}\).
If $ f(x) = 3x^2 + 5x - 7 $, find $ f(2) $.
In how many ways can 5 people be arranged in a row?
The value of the definite integral \( \int_0^{\pi} \sin^2 x \, dx \) is:
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 $ x = 2 $, what is the value of $ 3x^2 - 5x + 7 $?
Find the value of \( \tan 45^\circ \).
Find the derivative of the function \( f(x) = 3x^2 - 5x + 7 \).
Find the value of the integral: ∫ (2x + 3)/((xy)(x^2 + 1)) dx
Find the roots of the quadratic equation \( x^2 - 5x + 6 = 0 \).
In a dataset of 50 values, the mean is 40 and the variance is 25. What is the probability that a randomly selected value from this dataset is between 35 and 45?
Find the area of a circle with radius 7 cm.
Find the length of the diagonal of a rectangle with length 6 cm and breadth 8 cm.
If the roots of the quadratic equation \( x^2 - 5x + 6 = 0 \) are \( p \) and \( q \), then what is the value of \( p + q \)?
The integral $ \int e^x \left( \frac{x + 5}{(x + 6)^2} \right) dx $ is:
Find the value of \( \log_3 81 \).
Solve for $ x $ in the equation $ \frac{1}{x+3} + \frac{1}{x+5} = \frac{1}{6} $.
Series Expansion $ n^6 + \frac{1}{2} n^4 + \frac{1}{3} n^2 + \cdots + \frac{1}{n} C_n + 1 \quad n \to \infty $
Find the area of a circle whose radius is 7 cm.
A die is rolled once. What is the probability of rolling a number greater than 4?
In the word "UNIVERSITY", find the probability that the two "I"s do not come together.
Principal Solution of $ (5 \sin \theta)(2 \cos \theta + 1) = 0 $