List of top Questions asked in MHT CET

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 $\alpha$.

Given $\int_1^a (2x + 1) \, dx = 5$, find the sum of all values of $a$.

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: \[ \int_{3}^{5} |x-4|\,dx \]

There are 6 boys and 4 girls. Arrange their seating arrangement on a round table such that 2 boys and 1 girl can't sit together.

The r.m.s. speed of gas molecules at 800 K will be

How many isomers are possible for C$_4$H$_8$Cl$_2$ (including chain and positional)?

For the cell reaction, $ 2Al(s) + 3Cu^{2+}_{(aq)} \rightarrow 2Al^{3+}_{(aq)} + 3Cu(s) $, if $ \Delta G^\circ = -1158 \, \text{kJ} $, what is $ E_{\text{cell}} $?

A particular solution of $ 3e^x \tan y \, dx + (1 - e^x)\sec^2 y \, dy = 0 $ with $ y(1) = \frac{\pi}{4} $ is:

If $ \sin^{-1}x + \sin^{-1}y = \frac{\pi}{6} $ and $ \cot^{-1}\left(\frac{1}{2}\right) - \cot^{-1}\left(\frac{1}{y}\right) = 0 $, then calculate $ 2x^2 + y^2 - xy = ? $

If $ f(x) = \frac{k \sin x + 2 \cos x}{\sin x + \cos x} $ is strictly increasing for all real values of $ x $, then:

A random variable $ X $ has p.m.f. $ P(X = x) = \frac{{}^{4}C_x}{2^4}, \quad x = 0, 1, 2, 3, 4 $, and $ \mu $ and $ \sigma^2 $ are the mean and variance respectively of the random variable $ X $, then:

If $ \sin\left(\frac{\pi}{4}\cot\theta\right) = \cos\left(\frac{\pi}{4}\tan\theta\right) $, then the general solution of $ \theta $ is:

If $ A, B, C $ are mutually exclusive and exhaustive events of a sample space $ S $ such that $ P(B) = \frac{3}{2}P(A) $ and $ P(C) = \frac{1}{2}P(B) $, then $ P(A) = $ ______.

The equation of a progressive wave is $ Y = 3 \sin\left(kx - \frac{\pi}{3}\right) + \frac{1}{2} $, where $x$ and $y$ are in meter and time is in second. Which of the following is correct?

Heat is given to an ideal gas in an isothermal process. Then

Two long parallel wires carry currents $ I_1 $ and $ I_2 $ ($ I_1 > I_2 $). When currents are flowing in the same direction, the magnetic field at a point midway between the wires is $ 6 \times 10^{-6} \, \text{T} $. If the direction of $ I_2 $ is reversed, the field at the midpoint becomes $ 3 \times 10^{-5} \, \text{T} $. The ratio $ I_1 : I_2 $ is

A parallel plate capacitor has plate area 50 cm$^2$ and plate separation 3 mm. The space between the plates is filled with a dielectric medium of thickness 1 mm and dielectric constant 4. The capacitance becomes ( $ \epsilon_0 $ = permittivity of free space)

A vehicle starts from rest and accelerates along straight path at $ 2 \, \text{m/s}^2 $. At the starting point of the vehicle, there is a stationary electric siren. How far has the vehicle nearly gone when the driver hears the siren at 94% of its value when the vehicle was at rest? (speed of sound = 220 m/s)

When a light of wavelength $ \lambda $ falls on the emitter of a photocell, maximum speed of emitted photoelectrons is $ v $. If the incident wavelength is changed to $ \frac{2}{3} \lambda $, the maximum speed of emitted photoelectrons will be:

A pendulum bob has a speed of 4 m/s at its lowest position. The pendulum is 1 m long. When the length of the string makes an angle of 60° with the vertical, the speed of the bob at that position is (acceleration due to gravity, $ g = 10 \, \text{m/s}^2, \cos(60^\circ) = 0.5) $

What is the phase difference between the flux linked with a coil rotating in a uniform magnetic field and the induced e.m.f. produced in it?

The length of the simple pendulum is made 3 times the original length. If $ T $ is its original time period, then the new time period will be