List of top Questions asked in MHT CET

A bar of iron having magnetic moment 2.4 Am$^2$ weighs 66 g. If the density of the material of the bar is 7700 kg/m$^3$, the intensity of magnetisation in Am$^{-1}$ is ______.
A source of sound emits sound wave of frequency 'f' and moves towards an observer with a velocity $V/3$ where $V$ is the velocity of sound. If the observer moves away from the source with a velocity $V/5$ the apparent frequency heard by him will be ______.
A sphere of mass 'm', moving with velocity '3u' collides head-on with another identical sphere at rest. If 'e' is coefficient of restitution then what will be the ratio of velocity of the second sphere to that of first sphere after collision?
In Paschen series, wavelength of first line is '$\lambda_1$' and for Brackett series, wavelength of first line is '$\lambda_2$' then ratio $\frac{\lambda_1}{\lambda_2}$ is ______.
Moment of inertia of the rod about an axis passing through the centre and perpendicular to its length is '$I_1$'. The same rod is bent into a ring and its moment of inertia about the diameter is '$I_2$'. Then $I_1/I_2$ is ______.
An air column is of length 17 cm. The ratio of frequencies of 5th overtone if the air column is closed at one end to that open at both ends is (velocity of sound in air = 340 ms$^{-1}$) ______.
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 ______.
A magnetic field $4 \times 10^{-2}$ T acts at right angles to a coil of area $100$ cm$^2$ with 50 turns. The average e.m.f. induced in the coil is 0.1 V, when it is removed from the field in time 't'. The value of 't' is ______.
The general solution of the differential equation $\frac{dy}{dx} = \cot x \cdot \cot y$ is ______.
The ratio of energies of photons produced due to transition of electron of hydrogen atom from its (i) third to 2nd energy level and (ii) highest energy level to 3rd level is ______.
A boy throws a ball vertically upwards from a bridge with velocity 5 m/s. It strikes water surface after 2 s. The height of the bridge is (Take g = 10 m/s$^2$) ______.
In Sonometer experiment, the frequency of a tuning fork used is 288 Hz. Harmonics will 'NOT' be produced at the frequency ______.
In series LCR circuit C = 2$\mu$F, L = 5mH and R = 5$\Omega$. The ratio of energy stored in the inductor to that in capacitor, when maximum current flows through the circuit is ______.
The probability that a person is not a sportsperson is $1/6$. Then the probability that out of 6 members of the family, 5 are sportspersons is ______.
If $\tan(\pi \cos \theta) = \cot(\pi \sin \theta)$, then $\sin\left(\frac{\pi}{4} + \theta\right) = $ ______.
If the foot of the perpendicular drawn from the origin to a plane is P(-1, -1, 2), then the equation of the plane is ______.
The line MN whose equation is $x - y - 2 = 0$ cuts the X-axis at M and coordinates of N are (4, 2). The line MN is rotated about M through $45^{\circ}$ in anticlockwise direction. The equation of the line MN in the new position is ______.
The money invested in a company is compounded continuously. If Rs. 400 invested today becomes Rs. 800 in 6 years, then at the end of 30 years, it will become (in Rs.) ______.
The least distance of the point A(10, 7) from the circle $x^2 + y^2 - 4x - 2y - 20 = 0$ is length of seg AM. If MM' is the diameter of the circle, then the lengths of AM and AM' are respectively ______, ______ units.
If $\sin^{-1}(4x) + \sin^{-1}(4\sqrt{3}x) = -\frac{\pi}{2}$, then the value of $x$ is ______.
If $f(x) = \sqrt{1 + \cos^2(x^2)}$, then $f'(\frac{\sqrt{\pi}}{2})$ is ______.
The equation of the directrix of the parabola $y^2 + 4y + 4x + 2 = 0$ is ______.
Let $\vec{a} = \alpha\hat{i} + 3\hat{j} - \hat{k}$, $\vec{b} = 3\hat{i} - \hat{j} + \beta\hat{k}$ and $\vec{c} = \hat{i} + 2\hat{j} - 2\hat{k}$ where $\alpha, \beta \in \mathbb{R}$, be three vectors. If the projection of $\vec{a}$ on $\vec{c}$ is $\frac{10}{3}$ and $\vec{b} \times \vec{c} = -6\hat{i} + 10\hat{j} + 7\hat{k}$, then the value of $(\alpha + \beta)$ is ______.
In a triangle ABC, with usual notations, if $a = 5$, $b = 7$, $\sin A = \frac{3}{4}$, then total number of triangles possible are ______.
$\int_0^1 \tan^{-1} x \, dx = $ ______.