List of top Mathematics Questions asked in MHT CET

Evaluate the integral: \[ \int \frac{1}{\sin^2 2x \cdot \cos^2 2x} \, dx \]
Choose a randomly selected leap year, in which 52 Saturdays and 53 Sundays are to be there. Given the following probability distribution:
Find the mean and standard deviation.
If \( \tan^{-1} (\sqrt{\cos \alpha}) - \cot^{-1 (\cos \alpha) = x \), then what is \( \sin \alpha \)?}
There are 6 boys and 4 girls. Arrange their seating arrangement on a round table such that 2 boys and 1 girl can't sit together.
If \( \tan(\pi \cos x) = \cot(\pi \sin x) \), then what is \( \sin \left( \frac{\pi}{2} + x \right) \)?
A die was thrown \( n \) times until the lowest number on the die appeared. If the mean is \( \frac{n}{g} \), then what is the value of \( n \)?
Evaluate the integral: \[ \int \frac{\sqrt{\tan x}}{\sin x \cos x} \, dx \]
Find the value of the following expression: \[ \sin^2(30^\circ) + \cos^2(60^\circ) \]
The integral $ \int e^x \left( \frac{x + 5}{(x + 6)^2} \right) dx $ is:

The integral $ \int_0^1 \frac{1}{2 + \sqrt{2e}} \, dx $ is:

The integral $ \int e^x \left( \frac{x + 5}{(x + 6)^2} \right) dx $ is:
In $ \triangle ABC $, with usual notations, $ \sin \left( \frac{A}{2} \right) \cdot \sin \left( \frac{C}{2} \right) = \sin \left( \frac{B}{2} \right) \quad \text{and} \quad 2s \text{ is the perimeter of the triangle. Find the value of } s. $ Then the value of $ s $ is:
Evaluate the limit $ \lim_{n \to \infty} \frac{6^n - 9x - 7^n + 1}{\sqrt{2} - \sqrt{11} + \cos n} $

The eccentricity of the curve represented by $ x = 3 (\cos t + \sin t) $, $ y = 4 (\cos t - \sin t) $ is:

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 $
If $ y = \frac{b}{a} $, then $ \frac{dy}{dx} $ 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} $
Principal Solution of $ (5 \sin \theta)(2 \cos \theta + 1) = 0 $
Curves Represented
Which of the following expressions represents the Principal Solution
Evaluate the definite integral: \( \int_{-2}^{2} |x^2 - x - 2| \, dx \)
Find the value of the following expression: \[ \tan^2(\sec^{-1}4) + \cot(\csc^{-1}3) \]
If \( \mathbf{a} = \frac{1}{\sqrt{10}} (4\hat{i} - 3\hat{j} + \hat{k}) \) and \( \mathbf{b} = \frac{1}{5} (\hat{i} + 2\hat{j} + 2\hat{k}) \), then the value of \[ (2\mathbf{a} - \mathbf{b}) \cdot \left[ (\mathbf{a} \times \mathbf{b}) \times (\mathbf{a} + 2\mathbf{b}) \right] \]
Find the smallest angle of the triangle whose sides are \( 6 + \sqrt{12}, \sqrt{48}, \sqrt{24} \).
Evaluate the integral: \[ \int \frac{x^2 + 2x}{\sqrt{x^2 + 1}} \, dx \]