List of top Questions asked in MHT CET

At any time \( t \), the co-ordinates of moving particle are \( x = at^2 \) and \( y = bt^2 \). The speed of the particle is

Which amino acid from following contains \(\text{--CH}_3\) as side chain?

Calculate the volume occupied by a particle in fcc unit cell if volume of unit cell is 1.6 \(\times\) 10\(^{-23}\) cm\(^3\).

Identify from following reactions that exhibits negative work done.

Which of the following molecules contains maximum number of electrons in antibonding molecular orbitals?

Three charges each of magnitude \(3\mu C\), are placed on the vertices of an equilateral triangle of side 6 cm . The net potential energy of the system will be nearly \(\left[ \frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \text{ SI unit} \right]\)}

A small spherical ball of radius ' r ' is rolling on a curved surface which is frictionless and has a radius of curvature ' R '. Its motion is simple harmonic. Then its time period of oscillation is proportional to ( g = acceleration due to gravity)}

A car is driven on the banked road of radius of curvature 20 m with maximum safe speed. In order to increase its safety speed by 20%, without changing the angle of banking, the increase in the radius of curvature will be [Assume friction is same on the road]}

The percentage error in the measurement of mass and speed of a particular body is 3% and 4% respectively. The percentage error in the measurement of kinetic energy is

The projection of the line segment joining P(2, -1, 0) and Q(3, 2, -1) on the line whose direction ratios are 1, 2, 2 is

The equation of the curve passing through $(2, \frac{9}{2})$ and having the slope $(1 - \frac{1}{x^2})$ at $(x, y)$ is

Four defective oranges are accidentally mixed with sixteen good ones. Three oranges are drawn from the mixed lot. The probability distribution of defective oranges is

The general solution of the differential equation $\frac{\text{d}y}{\text{d}x} + \sin \left( \frac{x+y}{2} \right) = \sin \left( \frac{x-y}{2} \right)$ is

The value of the integral $\int_1^2 \frac{x \text{ d}x}{(x+2)(x+3)}$ is

In a box containing 100 apples, 10 are defective. The probability that in a sample of 6 apples, 3 are defective is

Three urns respectively contain 2 white and 3 black, 3 white and 2 black and 1 white and 4 black balls. If one ball is drawn from each um, then the probability that the selection contains 1 black and 2 white balls is

$\int \text{e}^{2x} \frac{(\sin 2x \cos 2x-1)}{\sin^2 2x} \text{d}x =$

If four digit numbers are formed by using the digits 1, 2, 3, 4, 5, 6, 7 without repetition, then out of these numbers, the numbers exactly divisible by 25 are

An open tank with a square bottom is to contain 4000 cubic cm . of liquid. The dimensions of the tank so that the surface area of the tank is minimum, is

If the lengths of three vectors $\bar{a}, \bar{b}$ and $\bar{c}$ are 5, 12, 13 units respectively, and each one is perpendicular to the sum of the other two, then $|\bar{a} + \bar{b} + \bar{c}| = ..............$

$\int \sec^{\frac{2}{3}} x \cdot \csc^{\frac{4}{3}} x dx =$

If $f(x) = \begin{cases} \frac{1-\cos 4x}{x^2} & , \text{if } x<0 \\ a & , \text{if } x = 0 \\ \frac{(16+\sqrt{x})^{\frac{1}{2}}-4}{\sqrt{x}} & , \text{if } x>0 \end{cases}$ is continuous at $x = 0$, then a =}

Identify the correct symbolic representation for the circuit provided in the image.

If p : switch $S_1$ is closed, q : switch $S_2$ is closed, r : switch $S_3$ closed, then the symbolic form of the following switching circuit is equivalent to

In a triangle ABC with usual notations, if $3a = b + c$, then $\cot \frac{B}{2} \cdot \cot \frac{C}{2} =$