List of top Questions asked in MHT CET

Which of the following elements shows a +4 oxidation state with the given configuration?
Find the radius of a BCC molecule having an edge length of \( 2.0 \times 10^{-11} \) m.
What is the product obtained on the reaction of chlorobenzene with concentrated HNO3?
Which is the weakest ligand?
A medicine compound having an amide linkage was asked. Which of the following compounds contains an amide linkage?
Given the vectors: \[ \mathbf{a} = i + 3j - k, \quad \mathbf{b} = 3i - j + 2k, \quad \mathbf{c} = i + 2j - 2k \] and the following information: \[ \frac{\mathbf{a} \cdot \mathbf{c}}{|\mathbf{c}|} = \frac{10}{3} \] Find the value of \( \alpha + \beta \) and the projection of \( \mathbf{a} \) on \( \mathbf{c} \).
Given that: \[ \cot \left( \frac{A + B}{2} \right) \cdot \tan \left( \frac{A - B}{2} \right) \] and the equation involving coordinates: \[ \frac{x}{2} + \frac{y}{3} + \frac{2}{6} - 1 = 0 \] Find the area of \( \Delta ABC = 2 \).
Evaluate the following integrals: \[ \int \frac{(x^4 + 1)}{x(2x + 1)^2} \, dx \] and \[ \int \frac{1}{x^4 + 5x^2 + 6} \, dx \]
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 \( \tan(\pi \cos x) = \cot(\pi \sin x) \), then what is \( \sin \left( \frac{\pi}{2} + x \right) \)?
If \( \tan^{-1} (\sqrt{\cos \alpha}) - \cot^{-1} (\cos \alpha) = x \), then what is \( \sin \alpha \)?
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.
Population of Town A and B was 20,000 in 1985. In 1989, the population of Town A was 25,000, and Town B had 28,000. What will be the difference in population between the two towns in 1993?
Evaluate the limit $ \lim_{n \to \infty} \frac{6^n - 9x - 7^n + 1}{\sqrt{2} - \sqrt{11} + \cos n} $
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:

If a random variable X has the following probability distribution values:

X01234567
P(X)1/121/121/121/121/121/121/121/12

Then P(X ≥ 6) has the value:

If $ \mathbf{a} $ and $ \mathbf{b} $ are non-coplanar unit vectors such that $ \mathbf{a} \times (\mathbf{b} \times \mathbf{c}) = \frac{\mathbf{b}}{2} $ then the angle between $ \mathbf{a} $ and $ \mathbf{b} $ is:
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:

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

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} $
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 solution $ \frac{d^2y}{dm^2} - k^3 \frac{dy}{dm} = y \cos m, \quad y(0) = 1 $