List of top Questions asked in MHT CET

For a first-order reaction, the slope of the graph between \(\log[A]\) vs time is equal to:
For all real x, the minimum value of the function f(x) = (1 - x + x^2) / (1 + x + x^2) is:
A charge of 2 $\mu C$ is placed in an electric field of intensity \( 4 \times 10^3 \, \text{N/C} \). What is the force experienced by the charge?
A 5-ohm resistor is connected to a 10 V battery. Calculate the current flowing through the resistor.
If y = tan-1 ((2 + 3x) / (3 - 2x)) + tan-1 (4x / (1 + 5x2)), then
dy/dx =
If \( \log_2 x = 5 \), what is the value of \( x \)?
A die is rolled once. What is the probability of rolling a number greater than 4?
If the roots of the quadratic equation \( x^2 - 5x + 6 = 0 \) are \( p \) and \( q \), then what is the value of \( p + q \)?
An object is placed at a distance of 10 cm from a concave mirror of focal length 15 cm. What is the image distance?
Given that: \[ x = a \sin(2t) (1 + \cos(2t)), \quad y = a \cos(2t) (1 - \cos(2t)) \] Find \(\frac{dy}{dx}\).
Find the length of the diagonal of a rectangle with length 6 cm and breadth 8 cm.
What is the pH of a 0.01 M solution of hydrochloric acid (HCl)?
A gas occupies a volume of 10.0 L at a pressure of 2.0 atm and a temperature of 300 K. What will the volume be if the pressure is increased to 4.0 atm and the temperature is increased to 600 K? (Assume the amount of gas remains constant.)
In a dataset of 50 values, the mean is 40 and the variance is 25. What is the probability that a randomly selected value from this dataset is between 35 and 45?
A radioactive substance has a half-life of 5 years. What is the probability that a single atom of this substance will decay within 5 years?
In the case of a particle in a one-dimensional infinite potential well (box), what is the probability of finding the particle in the first half of the box for the ground state?
For a system of particles in thermal equilibrium, what is the probability that a particle will have energy greater than \( E_0 \) according to the Boltzmann distribution?
In the word "UNIVERSITY", find the probability that the two "I"s do not come together.
Find the roots of the quadratic equation \( 2x^2 - 4x - 6 = 0 \).
Find the value of the determinant \( \begin{vmatrix} 2 & 3 \\ 4 & 5 \end{vmatrix} \).
Find the derivative of the function \( f(x) = 3x^2 - 5x + 7 \).
The enthalpy change for the reaction \( \text{C} + \text{O}_2 \rightarrow \text{CO}_2 \) is \( -393.5 \, \text{kJ/mol} \). What is the heat released when 2 moles of carbon react with excess oxygen?
A solution contains 10 g of NaOH dissolved in 500 mL of water. What is the molarity of the NaOH solution?
What is the total number of moles of gas in a 5 L container at 300 K and 2 atm pressure (Use the ideal gas law)?
What is the percentage composition of nitrogen in ammonium nitrate (\( \text{NH}_4\text{NO}_3 \))?