List of top Questions asked in MHT CET

The resistance of a wire is \( 10 \, \Omega \) and the current passing through it is \( 2 \, \text{A} \). What is the potential difference across the wire?
Which organelle is primarily responsible for producing ATP in a cell?
Which of the following represents the correct IUPAC name for \( \text{CH}_3\text{CH}_2\text{OH} \)?

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:

Which of the following elements has the most electronegativity: Li, Na, K, or Rb?
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 \( \Delta ABC = 2 \).
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?
Evaluate the following integrals: \[ \int \frac{(x^4 + 1)}{x(2x + 1)^2} \, dx \] and \[ \int \frac{1}{x^4 + 5x^2 + 6} \, dx \]
The angle between the lines whose direction cosines satisfy the equations: \[ l + m + n = 0 \quad \text{and} \quad m^2 + n^2 - l^2 = 0 \] Find the angle between the two lines.
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.
Evaluate the integral: \[ \int \frac{1}{\sin^2 2x \cdot \cos^2 2x} \, dx \]
Given that \( \cot \left( \frac{A+B}{2} \right) \cdot \tan \left( \frac{A-B}{2} \right) = \), and the equation \( \frac{x}{2} + \frac{y}{3} + \frac{2}{6} - 1 = 0 \), find the area of \( \Delta ABC = 2 \).
If \( \tan^{-1} (\sqrt{\cos \alpha}) - \cot^{-1 (\cos \alpha) = x \), then what is \( \sin \alpha \)?}
If \( \tan(\pi \cos x) = \cot(\pi \sin x) \), then what is \( \sin \left( \frac{\pi}{2} + x \right) \)?
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.
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.

Which of the following compounds can exhibit geometrical isomerism, and why? 
1) 2-butene 
2) 1-butene ?
3) Pent-2-ene 
4) But-2-yne

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: