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:
The limit of \( \lim_{x \to 0} \frac{\sin x}{x} \) is:
Binomial Expansion Series $ \left( \frac{(1 + x)}{(n + 1)} \right)' = n_0 x + n_1 \frac{x^2}{2} + n_2 \frac{x^3}{3} + \cdots + n_n \frac{x^n}{n+1} $
Curves Represented
A bag contains 5 red balls, 7 green balls, and 8 blue balls. One ball is drawn at random. What is the probability that the ball is either red or green?
Find the roots of the quadratic equation \( x^2 - 5x + 6 = 0 \).
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 two dice are rolled, what is the probability of getting a sum of 7?
Find the value of the following expression: \[ \sin^2(30^\circ) + \cos^2(60^\circ) \]
Evaluate the integral: \[ \int \frac{x^2 + 2x}{\sqrt{x^2 + 1}} \, dx \]
Find the smallest angle of the triangle whose sides are \( 6 + \sqrt{12}, \sqrt{48}, \sqrt{24} \).
If \( P(A \cap B) = \frac{2}{25} \) and \( P(A \cup B) = \frac{8}{25} \), then find the value of \( P(A) \).
Evaluate the integral: \[ \int \sqrt{x^2 + 3x} \, dx \]
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?
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?
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.
Find the value of the following expression: \[ \tan^2(\sec^{-1}4) + \cot(\csc^{-1}3) \]
Given that: \[ x = a \sin(2t) (1 + \cos(2t)), \quad y = a \cos(2t) (1 - \cos(2t)) \] Find \(\frac{dy}{dx}\).
Find the value of \( \log_3 81 \).
Find the value of \( x \) if \( \sin(2x) = 1 \).
Find the sum of the first 20 terms of the arithmetic progression: \( 2, 5, 8, 11, \dots \).
Solve the system of equations: \[ x + y = 10 \] \[ 3x - y = 5 \]
Find the length of the diagonal of a rectangle with length 6 cm and breadth 8 cm.
If \( \log_2 x = 5 \), what is the value of \( x \)?