List of top Questions asked in MHT CET

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

Which among the following observations suggests that glucose also exists in cyclic form?

Which among the following carbocation is most reactive?

The rate constant for the first order reaction is \(1.15 \times 10^{-3} \, \text{s}^{-1}\). How long will 5 g of the reactant take to reduce to 3 g?

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 \]

If \(f'(x) = k(\cos x + \sin x)\) and \(f(0) = 9,\ f\!\left(\dfrac{\pi}{2}\right) = 15\), then \(f(x)=\)

If \( f(x) = \frac{x^2 + 2{18} \), for \( -2<x<4 \), and 0 otherwise, is the p.d.f. of a random variable \( X \), then the value of \( P(|X|<2) \) is}

Energy of the incident photon on the metal surface is ' 3W ' and then ' 5W ', where 'W' is the work function for that metal. The ratio of velocities of emitted photoelectrons is

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?

Which of the following hydride is deficient in hydrogen?

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

An electron (\( e \)) is revolving in a circular orbit of radius \( r \) in a hydrogen atom. The angular momentum \( M \) of the electron is
\textit{(where \( M \) = magnetic dipole moment associated with it and \( m \) = mass of the electron)}

A metal rod of Young’s modulus $Y$ and coefficient of linear expansion $\alpha$ has its temperature raised by $\Delta \theta$. The linear stress to prevent the expansion of rod is ($L$ and $\ell$ are original length of rod and expansion respectively)

A stone is tied at the end of a rope of length 1 m and whirled in a vertical circle. The ratio of velocity at the highest point to the lowest point will be

The area bounded by the parabola \( y^2 = 16x \) and its latus-rectum in the first quadrant is

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

A circular coil of radius \( R \) is carrying a current \( I_1 \) in anticlockwise sense. A long straight wire is carrying current \( I_2 \) in the negative direction of x-axis. Both are placed in the same plane and the distance between the centre of coil and straight wire is \( d \). The magnetic field at the centre of coil will be zero for the value of \( d \) equal to

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

If \( \frac{1}{4}, a, b, \frac{1}{19} \) form a harmonic progression (H.P.), then the values of \( a \) and \( b \) are respectively

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

How many hydroxy groups are present in hydroxyquinol?

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

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

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}

Evaluate $\displaystyle \int \frac{dx}{1+\sqrt{x}}$