List of top Mathematics Questions asked in MHT CET

Given the equation: \[ 81 \sin^2 x + 81 \cos^2 x = 30 \] Find the value of \( x \).
If the roots of the quadratic equation \( x^2 - 7x + 12 = 0 \) are \( \alpha \) and \( \beta \), then the value of \( \alpha + \beta \) is:
Find the sum of the first 20 terms of the arithmetic progression: \( 2, 5, 8, 11, \dots \).
A bag contains 5 red balls and 3 green balls. If two balls are drawn at random without replacement, what is the probability that both balls drawn are red?
If \( P(A \cap B) = \frac{2}{25} \) and \( P(A \cup B) = \frac{8}{25} \), then find the value of \( P(A) \).
If \( \tan^{-1} (\sqrt{\cos \alpha}) - \cot^{-1} (\cos \alpha) = x \), then what is \( \sin \alpha \)?
A boy tries to message his friend. Each time, the chance the message is delivered is \( \frac{1}{6} \), and the chance it fails is \( \frac{5}{6} \). He sends 6 messages. Find the probability that exactly 5 messages are delivered.
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) $.
Find the value of \( \tan 45^\circ \).
If $ x = 2 $, what is the value of $ 3x^2 - 5x + 7 $?
In how many ways can 5 people be arranged in a row?
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 value of the definite integral \( \int_0^{\pi} \sin^2 x \, dx \) is:
Find the length of the diagonal of a rectangle with length 6 cm and breadth 8 cm.
Find the value of the integral: ∫ (2x + 3)/((xy)(x^2 + 1)) dx
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 roots of the quadratic equation \( x^2 - 5x + 6 = 0 \).
Find the area of a circle with radius 7 cm.
Find the derivative of the function \( f(x) = 3x^2 - 5x + 7 \).
If the roots of the quadratic equation \( x^2 - 5x + 6 = 0 \) are \( p \) and \( q \), then what is the value of \( p + q \)?
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 $