List of top Questions asked in MHT CET

For the curve \(y = 3x^3 - 3x^2 + 1\) at \(x = 1\), find the equation of the tangent.
A plane is formed by the axes whose centroid is \(\left(2, -\frac{2}{3}, \frac{1}{2}\right)\). Find the distance of the plane from the origin.
Evaluate: \(\int_0^3 \sqrt{9 - x^2} \, dx\).
If \(\tan^{-1}(-1) + \tan^{-1}(5) + \tan^{-1}(3) + \tan^{-1}\left(\frac{1}{4}\right) = \pi + \tan^{-1}\left(\frac{\alpha}{2}\right)\), find \(\alpha\).
Determine the shortest distance between the lines \( \dfrac{x-1}{2} = \dfrac{y-2}{3} = \dfrac{z-3}{4} \) and \( \dfrac{x-2}{3} = \dfrac{y-4}{4} = \dfrac{z-5}{5} \).
Evaluate the integral: \[ \int_{3}^{5} |x-4|\,dx \]
The limit of \( \lim_{x \to 0} \frac{\sin x}{x} \) is:
Plasmodium that affects humans
How many grams of NaOH are required to neutralize 25 mL of 0.1 M HCl solution?
Find the value of the determinant \( \begin{vmatrix} 2 & 3 \\ 4 & 5 \end{vmatrix} \).
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?
\(500 \text{ gram}\) of a diatomic gas is enclosed at a pressure of \(10^{5} \text{ Nm}^{-2}\). The density of the gas is \(5 \text{ kg m}^{-3}\). The energy of one mole of the gas due to its thermal motion is [consider the gas molecule as a rigid rotator].
Which of the following gases is most soluble in water?
A copper block of mass 2 kg is heated from 20°C to 100°C. If the specific heat capacity of copper is \( 400 \, \text{J/kg°C} \), how much heat energy is absorbed by the block? (Assume no phase change occurs.)
A circular coil has radius ' \(R\) '. The distance from centre on axis where induction is \(1/27\) th of its value at centre is.
If r.m.s. velocity of hydrogen molecules is 4 times that of an oxygen molecule at $47^{\circ}\text{C}$, the temperature of hydrogen molecules is (Molecular weight of Hydrogen and Oxygen are 2 and 32 respectively)}
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.
The temperature at which oxygen molecules will have same r.m.s. speed as helium molecules at 57$^\circ$C is (molecular masses of oxygen and helium are 32 and 4 respectively.) ______.
Calculate the volume occupied by a particle in fcc unit cell if volume of unit cell is $1.6 \times 10^{-23} \text{ cm}^3$.
Two stones of masses m and 3 m are whirled in horizontal circles, the heavier one in a radius $(\frac{r}{3})$ and lighter one in a radius r. The tangential speed of lighter stone is 'n' times the value of heavier stone. When the magnitude of centripetal force becomes equal the value of n is
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?
If $ f(x) = 3x^2 + 5x - 7 $, find $ f(2) $.
A body weighs 45 N on the surface of the earth. The gravitational force on a body due to earth at a height equal to half the radius of earth will be ______.
Evaluate the integral: \[ \int \frac{\sqrt{\tan x}}{\sin x \cos x} \, dx \]
The r.m.s. speed of gas molecules at 800 K will be