List of top Questions asked in MHT CET

A particle is moving with a constant velocity of 5 m/s in a circular path of radius 2 m. What is the centripetal acceleration of the particle?
Solve for \( x \): \( \log_2 (x-1) = 3 \).
If $ f(x) = 2x^2 - 3x + 5 $, find $ f(3) $.
A mass of 0.5 kg is attached to a spring of force constant 200 N/m. What is the time period of oscillation?
The maximum value of the function \( f(x) = -2x^2 + 4x + 1 \) occurs at:
A 5 kg block is placed on a horizontal surface. A force of 10 N is applied to the block. The coefficient of friction between the block and the surface is 0.2. Find the acceleration of the block.
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:
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?
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).
Which of the following is a primary alcohol?
For a reaction A $\rightarrow$ B, the rate doubles when temperature increases from 298 K to 308 K. What is the activation energy (Ea)?
A solution is made by mixing 100 mL of 0.1 M HCl and 100 mL of 0.2 M NaOH. pH of resulting solution is:
A sample of gas occupies 10 L at 300 K and 2 atm. What will be its volume at 400 K and 1 atm?
What is the molar mass of the third member of the homologous series if the molar mass of the first member is 46 g?
How many isomers are possible for C$_4$H$_8$Cl$_2$ (including chain and positional)?
Which of the following reagents is used in Rosenmund reduction?
Three-point charges \( Q \), \( q \), and \( -q \) are kept at the vertices of an equilateral triangle of side \( L \). What is the total electrostatic potential energy of the system?
The reverse saturation current (I0) of a silicon diode at 27°C is \( 10^{-6} \) A. What will be the approximate value of I0 at 67°C? (Assume \( I_0 \) doubles for every 10°C rise in temperature)
A photon and an electron have the same energy \( E \). If \( \lambda_p \) is the wavelength of the photon and \( \lambda_e \) is the de Broglie wavelength of the electron, then the ratio \( \frac{\lambda_p}{\lambda_e} \) is:
What is the ratio of the wavelength of the Lyman series limit to that of the Paschen series limit in the hydrogen spectrum?
Two black bodies emit the same amount of radiation per second. The radius of the first is \( R_1 = 2 \, \text{m} \) and its temperature is \( T_1 = 400 \, \text{K} \). If the second body has a radius \( R_2 = 4 \, \text{m} \), what is its temperature \( T_2 \) in Kelvin?
An AC voltage \( V = 50\sqrt{2} \sin(100t) \) is applied across a capacitor of capacitance \( C = 1 \mu F \). What is the rms value of the current through the capacitor?
At a height \( h \) above the Earth's surface, the acceleration due to gravity becomes \( \frac{g}{\sqrt{3}} \). What is the value of \( h \) in terms of the Earth's radius \( R \)?
The mass of an object is measured as \( (28 \pm 0.01) \) g and its volume as \( (5 \pm 0.1) \) cm\(^3\). What is the percentage error in density?
Two spherical black bodies radiate the same amount of heat per second. If their temperatures are \( T_1 \) and \( T_2 \), and their radii are \( R_1 \) and \( R_2 \), respectively, find the relation between their temperatures and radii.