List of top Questions asked in MHT CET

Evaluate the following integrals: \[ \int \frac{(x^4 + 1)}{x(2x + 1)^2} \, dx \] and \[ \int \frac{1}{x^4 + 5x^2 + 6} \, dx \]
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.
A simple pendulum has a length of $ L = 2 \, \text{m} $. What is the time period of the pendulum? (Assume $ g = 9.8 \, \text{m/s}^2 $)
A body of mass $ m = 2 \, \text{kg} $ is moving with a velocity of $ 5 \, \text{m/s} $. What is the kinetic energy of the body?
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?
Which organelle is primarily responsible for producing ATP in a cell?
Solve for \( x \): \( \log_2 (x-1) = 3 \).
A car accelerates uniformly from rest to a velocity of \( 25 \, \text{m/s} \) in \( 10 \, \text{seconds} \). What is the acceleration of the car?
A 10 kg box is pulled with a horizontal force of 50 N on a surface offering a frictional force of 20 N. What is the net acceleration of the box? (Take \( g = 10 \, \text{m/s}^2 \))
Evaluate the integral: \[ \int \frac{\sqrt{\tan x}}{\sin x \cos x} \, dx \]
How many molecules of carbon dioxide are formed when 0.6 g carbon is burnt in air?
In an LC circuit, the inductance \( L \) is \( 2 \, \text{H} \) and the capacitance \( C \) is \( 4 \, \mu\text{F} \). What is the frequency of oscillation of the circuit?
A concave mirror has a focal length of 20 cm. An object is placed 60 cm in front of the mirror. Find the image distance.
What is the genotype of Drosophila showing normal wings?
A car of mass 1000 kg is moving in a circular path of radius 50 m with a speed of 20 m/s. Calculate the centripetal force acting on the car.
A body of mass 0.2 kg is attached to a light string of length 1 m and revolved in a vertical circle. What is the minimum speed at the lowest point so that the body can complete the circular motion? (Take \( g = 10 \, \text{m/s}^2 \))
A man with blood group AB marries a woman with blood group O. What is the probability that their child will have blood group A?
A gas absorbs \( 100 \, \text{J} \) of heat while performing \( 40 \, \text{J} \) of work on its surroundings. Calculate the change in internal energy of the gas.
For a reaction, the rate law is given by \( \text{rate} = k[A]^2[B] \). If the concentration of \( A \) is doubled and the concentration of \( B \) is halved, how will the rate of the reaction change?
The wavelength of the light emitted by a hydrogen atom during a transition from \( n = 3 \) to \( n = 2 \) is \( 656.3 \, \text{nm} \). What is the energy of the photon emitted during this transition?
In the reaction \( 2 \, \text{H}_2 + \text{O}_2 \rightarrow 2 \, \text{H}_2\text{O} \), how many moles of water are produced when 4 moles of hydrogen react with excess oxygen?
A cylindrical pipe has a radius of \( 0.1 \, \text{m} \). If the speed of water flowing through the pipe is \( 2 \, \text{m/s} \), calculate the volume flow rate of water through the pipe.
If \( \tan^{-1} (\sqrt{\cos \alpha}) - \cot^{-1 (\cos \alpha) = x \), then what is \( \sin \alpha \)?}
Which hormone converts into amino acid?
Given the equation: \[ 81 \sin^2 x + 81 \cos^2 x = 30 \] Find the value of \( x \).