List of top Questions asked in MHT CET

Principal Solution of $ (5 \sin \theta)(2 \cos \theta + 1) = 0 $

Curves Represented

Which of the following expressions represents the Principal Solution

In the reaction \( \text{Zn} + 2\text{Ag}^+ \rightarrow \text{Zn}^{2+} + 2\text{Ag} \), what is the oxidation state of zinc in \( \text{Zn} \) and \( \text{Zn}^{2+} \)?

The enthalpy change for the reaction \( \text{N}_2(g) + 3\text{H}_2(g) \rightarrow 2\text{NH}_3(g) \) is \( -92.4 \, \text{kJ/mol} \). What is the enthalpy change when 4 moles of nitrogen react?

Which of the following elements has the highest electronegativity?

What is the pH of a solution with a hydrogen ion concentration of \( 1 \times 10^{-5} \, \text{mol/L} \)?

In the reaction \( 2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O} \), if 4 moles of hydrogen react with excess oxygen, how many moles of water are produced?

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: \[ \int \sqrt{x^2 + 3x} \, dx \]

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 \[ (2\mathbf{a} - \mathbf{b}) \cdot \left[ (\mathbf{a} \times \mathbf{b}) \times (\mathbf{a} + 2\mathbf{b}) \right] \]

A water tank is open at the top and has a hole of area \( 10^{-4} \, \text{m}^2 \) at the bottom. The height of the water column is 5 m. What is the speed of the water flowing out of the hole? (Take \( g = 10 \, \text{m/s}^2 \))

A concave mirror has a focal length of 15 cm. An object is placed 30 cm from the mirror. What is the image distance?

A coil has 200 turns and an area of \( 0.01 \, \text{m}^2 \). If the magnetic field changes from 0 to 0.5 T in 0.1 seconds, what is the induced emf in the coil?

A gas expands from a volume of 2 m³ to 4 m³ against a constant pressure of 5 atm. How much work is done by the gas during expansion? (1 atm = \( 1.01 \times 10^5 \, \text{Pa} \))

A body of mass 10 kg is at a height of 5 m above the surface of the Earth. What is the gravitational potential energy of the body? (Take \( g = 10 \, \text{m/s}^2 \))

Two point charges \( +2 \, \mu\text{C} \) and \( -3 \, \mu\text{C} \) are placed 10 cm apart in vacuum. What is the electrostatic force between them?

A force of 20 N is applied to a body at an angle of \( 30^\circ \) to the horizontal, moving the body a distance of 5 m. What is the work done by the force?