List of top Questions asked in MHT CET- 2020

The differential equation of the family of curves \( y = e^{x} (A \cos x + B \sin x) \), where \( A \) and \( B \) are arbitrary constants, is

The angle made by a vector \( \vec{B} = 3\hat{i} + 2\hat{j} + 4\hat{k} \) with the y-axis is

A bullet of mass $20\,\text{g}$ moving with a velocity of $200\,\text{m/s}$ strikes a target and is brought to rest in $\left(\dfrac{1}{50}\right)^{\text{th}}$ of a second. The impulse and average force of impact are respectively

In a semiconductor, the number of holes and number of free electrons are represented as \( n_h \) and \( n_e \), respectively. Which one of the following statements is TRUE for the semiconductor?

With usual notations, in triangle ABC, \( a = \sqrt{3} + 1 \), \( b = \sqrt{3} - 1 \) and \( \angle C = 60^\circ \), then \( A - B = \)

The letters of the word 'LOGARITHM' are arranged at random. The probability that the arrangement starts with a vowel and ends with a consonant is

If the angle between the lines whose direction ratios are \( 4, -3, 5 \) and \( 3, 4, k \) is \( \frac{\pi}{3} \), then \( k = \)

Identify the product C in the following reaction.
\[ \text{CH\(_3\)CH\(_2\)COOH} \xrightarrow{\text{NaOH}} A \xrightarrow{\text{CaO, }\Delta} B \xrightarrow{\text{HNO\(_3\)}} C \]

A capacitor is charged by a battery and energy stored is $U$. Now the battery is removed and the distance between plates is increased to four times. The energy stored becomes

When a beam of unpolarised monochromatic light is incident on a plane glass plate at a polarising angle, which one of the following statements is correct?

If the lines given by \( \vec{r} = 2\hat{i} + \lambda(\hat{i} + 2\hat{j} + m\hat{k}) \) and \( \vec{r} = \hat{i} + \mu(2\hat{i} + \hat{j} + 6\hat{k}) \) are perpendicular, then the value of \( m \) is

The increase in length of a wire on stretching is \(0.05%\). If its Poisson’s ratio is 0.4, then its diameter is reduced by

How many hydroxy groups are present in hydroxyquinol?

Two identical parallel plate air capacitors are connected in series to a battery of e.m.f. \( V \). If one of the capacitors is inserted in liquid of dielectric constant \( K \), then potential difference of the other capacitor will become

If rectangles are inscribed in a circle of radius \( r \) units, then the dimensions of the rectangle which has maximum area are

Two masses \( M_1 \) and \( M_2 \) are accelerated uniformly on a frictionless surface as shown in figure. The ratio of the tensions \( \left( \frac{T_1}{T_2} \right) \) is

One mole of a diatomic gas does a work $\frac{Q{3}$, when the amount of heat supplied is $Q$. In this process, the molar heat capacity of the gas is}

Which among the following carbocation is most reactive?

If the kinetic energy of a particle is increased to 16 times its previous value, the percentage change in the de-Broglie wavelength of the particle is

The coordinates of the foci of the ellipse \( 16x^2 + 9y^2 = 144 \) are

A potentiometer wire is 4 m long and potential difference of 3 V is maintained between the ends. The e.m.f. of the cell which balances against a length of 100 cm of the potentiometer wire is

One thousand small water drops of equal radii combine to form a big drop. The ratio of final surface energy to the total initial surface energy is

In conversion of moving coil galvanometer into an ammeter of required range, the resistance of ammeter so formed is

Sodium crystallizes in bcc structure with radius 1.86 \(\times\) 10\(^{-8}\) cm. What is the edge length of unit cell of sodium?

A torque of 50 Nm acts on a body for 8 seconds which is initially at rest. The change in its angular momentum is