List of top Questions asked in MHT CET

Evaluate the integral: \( \displaystyle \int \frac{x}{x+2}\,dx \)

Calculate the osmotic pressure of \(0.1\,M\) glucose at \(27^\circ C\).

Calculate the ratio of potential energy to kinetic energy at time \(t=\dfrac{T}{6}\) for a particle starting SHM from its mean position.

A cube of edge 4 cm has mass 256 g. The density of the material in SI unit is:

Find the general solution of the differential equation \(\dfrac{dy}{dx} + y\cot x = \csc x\).

Find the value of \(k\) if the function \(f(x) = \dfrac{k\sin x}{x}\) is continuous at \(x = 0\) and \(f(0)=3\).

What is the value of \( \sin^{-1}\left(\frac{1}{2}\right) + \cos^{-1}\left(\frac{1}{2}\right) \)?

Find the work done by a gas that expands from \(0.2\,\text{dm}^3\) to \(0.8\,\text{dm}^3\) against a constant pressure of \(2\) bar.

A ball is thrown upwards with a velocity of \(20\ \text{m/s}\); find the maximum height reached \((g = 10\ \text{m/s}^2)\).

Identify the co-ordinates of the point where the line joining \( (1,1,1) \) and \( (2,2,2) \) intersects the plane \( x+y+z=9 \).

Calculate \( y(\log 2) \) if \( \dfrac{dy}{dx} = y + 5 \) and \( y(0) = 4 \).

Find the value of \( k \) if the function \( f(x) = k\sin x + 2\cos x \) is increasing for all \( x \)

What is the hybridization of the central sulfur atom in \(SF_6\)?

Which reagent is used in the Lucas test to distinguish alcohols?

How many atoms are present in a unit cell of a body-centered cubic (BCC) lattice?

What is the major product when 2-bromopentane reacts with alcoholic KOH?

Find the moment of inertia of a uniform ring of mass \(M\) and radius \(R\) about a tangent perpendicular to its plane.

Calculate the energy stored in a \(10\,\mu F\) capacitor charged to \(50\,V\).

Calculate the de Broglie wavelength of an electron accelerated through a potential of \(100\,\text{V}\).

Find the direction cosines of a line that makes equal angles with the coordinate axes.

In a Binomial distribution with \(n=10\) and \(p=0.4\), find the variance.

Solve the differential equation \( \frac{dy}{dx} = \frac{1+y^2}{1+x^2} \) given \(y(0)=1\).

In the electrolysis of molten NaCl, the product obtained at the cathode is:

Rosenmund reduction is used to convert acyl chlorides into:

The Van't Hoff factor for a solution of $K_2SO_4$ in water is: