List of top Questions asked in MHT CET

Find the energy of a photon with a wavelength of \(4000\,\text{\AA}\). (Take \( h = 6.63 \times 10^{-34}\,\text{Js} \), \( c = 3 \times 10^8\,\text{m/s} \)).

Evaluate the definite integral: \( \displaystyle \int_{0}^{\pi/2} \frac{\sin^n x}{\sin^n x + \cos^n x}\, dx \).

Name the catalyst used in the manufacture of ammonia by Haber’s process.

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

Calculate the number of atoms per unit cell in a Face-Centered Cubic (FCC) crystal structure.

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

If the current in a coil changes from \(5\,\text{A}\) to \(2\,\text{A}\) in \(0.1\,\text{s}\) and an average emf of \(30\,\text{V}\) is induced, find the self-inductance.

What is the ratio of the surface area of two soap bubbles if their radii are in the ratio \(2:3\)?

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

Find the value of \(k\) if the function \(f(x)=\dfrac{k\sin x}{x}\) for \(x\neq0\) and \(f(0)=3\) is continuous at \(x=0\).

The probability of a shooter hitting a target is \( \frac{3}{4} \). Find the probability of hitting the target exactly 4 times in 5 shots.

If the vectors \(2i - j + k\), \(i + 2j - 3k\) and \(3i + aj + 5k\) are coplanar, find the value of \(a\).

When two sound waves having amplitudes 3 and 5 units are superimposed, find the ratio of maximum to minimum intensity of the resultant wave.

A wire of resistance \(R\) is stretched to triple its original length. Find the new resistance.

Calculate the osmotic pressure of a \(0.1\ \text{M}\) solution at \(27^\circ C\).

Identify the type of crystal defect found in \(NaCl\) crystals.

Calculate the pH of a \(0.001\,M\) \(NaOH\) solution at \(298\,K\).

Identify the product formed when Ethyl alcohol is heated with concentrated \( H_2SO_4 \) at \(443\,K\).

What is the oxidation number of Manganese (Mn) in the compound \( KMnO_4 \)?

What is the change in internal energy of a system if \(500\,\text{J}\) of heat is added and \(200\,\text{J}\) of work is done by the system?

Determine the centripetal force acting on a \(1000\,\text{kg}\) car moving at \(20\,\text{m/s}\) around a curve of radius \(50\,\text{m}\).

Calculate the moment of inertia of a uniform circular disc of mass \(M\) and radius \(R\) about its diameter.

Determine the distance of the point \( (1,2,3) \) from the plane \( 2x + 3y - z = 7 \).

Find the general solution of the differential equation \( \frac{dy}{dx} + y = e^{-x} \).

Find the truth value of the statement: "If 2 is even, then 5 is prime."