List of top Questions asked in MHT CET

Which of the following is not used as a parameter for the classification of polymers?

Consider two matrices \(A=\begin{bmatrix}3 & -4 1 & -1\end{bmatrix}\) and \(B=\begin{bmatrix}6 & -13 5 & -10\end{bmatrix}\). If the following matrix equation holds true: \[ \left((A^{-1})^2 + B\right)\begin{bmatrix}x y\end{bmatrix} = \begin{bmatrix}0 0\end{bmatrix} \] Find the values of \(x\) and \(y\).

Evaluate the following indefinite integral: \[ \int \sin(\log x)\,dx \]

Find the unit vector perpendicular to both \( \vec{a} = 2\hat{i} - \hat{j} + \hat{k} \) and \( \vec{b} = \hat{i} + 2\hat{j} - 3\hat{k} \).

If \( y = \sin^{-1}(3x - 4x^3) \), find \( \dfrac{dy}{dx}. \)

Identify the major product formed when Ethyl Bromide reacts with alcoholic KOH.

What is the order of the differential equation \( \dfrac{d^2 y}{dx^2} + \left(\dfrac{dy}{dx}\right)^3 = 0 \)?

Find the slope of the normal to the curve \(y = 2x^2 + 3\sin x\) at \(x = 0\).

Evaluate \( \int \log x \, dx \).

What is the energy of a photon of frequency \( \nu \)?

Name the phenomenon that proves the transverse nature of light.

In an AC circuit, what is the power factor of a pure resistor?

What is the value of escape velocity on the Earth's surface?

What happens to the resistance of a wire if its radius is halved?

What is the SI unit of molar conductivity?

What is the oxidation state of Phosphorus in \(H_3PO_4\)?

Identify the product when Phenol reacts with Bromine water.

Which reagent is used in the Reimer--Tiemann reaction to convert phenol to salicylaldehyde?

Find the area of the region bounded by the curve \(y^2 = 4x\) and the line \(x = 3\).

What is the oxidation state of Phosphorus in \( H_3PO_4 \)?

A stone is dropped from a height of \(20\,\text{m}\); calculate its velocity just before it hits the ground \((g = 10\,\text{m/s}^2)\).

A metal has BCC structure. Atomic radius \(=173\,\text{pm}\) and molar mass \(M=56\,\text{g mol}^{-1}\). The density of the metal is:

Evaluate the integral: \( \displaystyle \int \frac{4x^2 \cot^{-1}(x^3)}{1+x^6}\,dx \) (where \(C\) is a constant of integration).

What is the difference in the oxidation number of Manganese (Mn) between \( \text{KMnO}_4 \) and \( \text{MnO}_2 \)?

Find the osmotic pressure of a \(0.1\,M\) glucose solution at \(27^\circ C\) \((R = 0.0821\,L\,atm\,mol^{-1}K^{-1})\).