List of top Questions asked in MHT CET

Evaluate the integral: \[ \int_0^{\frac{\pi}{2}} \frac{dx}{1 + \cos x} \]

The integral \[ \int_0^{\frac{\pi}{2}} \frac{1 - \cot x}{\csc x + \cos x} \, dx = \]

Rate of radiation by a black body is $R$ at temperature $T$. Another body has the same area but emissivity is $0.2$ and temperature is $3T$. Its rate of radiation is

Two rings of radius $ R $ and $ nR $ made of the same material have the ratio of moment of inertia about an axis passing through their centre and perpendicular to the plane as $ 1 : 8 $. The value of $ n $ is (mass per unit length is constant).

The ratio of energy required to raise a satellite of mass $ m $ to a height $ h $ above the earth's surface to that required to put it into the orbit at same height is

What is the bond order of B$_2$ molecule?

Using Bohr’s quantization condition, what is the rotational energy in the second orbit for a diatomic molecule? (I = moment of inertia of diatomic molecule, $ h $ = Planck’s constant)

The domain of the real valued function \[ f(x) = \frac{x + 2}{9 - x^2} \] is

An iron rod is placed parallel to the magnetic field of intensity 2000 $ A/m $. The magnetic flux through the rod is $ 6 \times 10^{-4} \, Wb $ and its cross-sectional area is $ 3 \, cm^2 $. The magnetic permeability of the rod in $ \frac{Wb}{A \cdot m} $ is

In the equation $ P = \frac{C+S}{D} $, $ P $ and $ S $ represent pressure and distance respectively. The dimensions of $ \frac{P}{D} $ are

If the plane \[ 2x + 3y + 5z = 1 \] intersects the coordinate axes at the points A, B, C, then the centroid of $ \triangle ABC $ is

In series LCR circuit, resistance is 18 $ \Omega $ and impedance is 33 $ \Omega $. An r.m.s. voltage of 220 V is applied across the circuit. The true power consumed in a.c. circuit is

The rate of decay of mass of a certain substance at time $ t $ is proportional to the mass at that instant. The time during which the original mass of $ m_0 $ gram will be left to $ m_1 $ gram is
\[ k \text{ is constant of proportionality} \]

The joint equation of the lines through the origin trisecting angles in the first and third quadrant is

Among the given statements below
(a) $ \neg p \vee (\neg p \vee q) $
(b) $ \neg q \wedge (\neg p \vee \neg q) $
(c) $ (\neg p \vee \neg q) \wedge (p \vee \neg q) $
(d) $ (\neg p \vee \neg q) \vee (p \vee \neg q) $
.............. is a tautology.

The rate of growth of bacteria is proportional to the number present. If initially there were 1000 bacteria and the number doubles in 1 hour, then the number of bacteria after $ 2\frac{1}{2} $ hours are (Given $ \sqrt{2} = 1.414 $)

Which among the following compounds contains phantom atom?

Identify the product A in the following reaction.
\[ (CH_3)_3C{-}OH \xrightarrow[\;573\ \text{K}\;]{Cu} A \]

Which of the following is used as an antiseptic in soap?

Identify compound ‘B’ in following series of reactions?

Identify the formula of lanthanoid oxide formed when lanthanoid (Ln) is burnt in oxygen.

Which of the following is a cationic detergent?

Which of the following is NOT an antiseptic?

Identify the catalyst X used in the following reaction:
CH$_3$CH$_2$Br + 2[H] $\xrightarrow{X}$ CH$_3$CH$_3$ + HBr

Binding energy of a revolving satellite at height $h$ is $3.5\times10^8\,\text{J}$. Its potential energy is