List of top Questions asked in MHT CET

Find the angle between non-zero vectors \( \mathbf{a} \) and \( \mathbf{b} \) if their dot product \( \mathbf{a}\cdot\mathbf{b} = 0 \).

If \( y = \sin^{-1}(3x - 4x^3) \), find the derivative \( \dfrac{dy}{dx} \) in its standard form.

Evaluate the integral: \[ \int \frac{2x}{x^2 - 5x + 4}\, dx \]

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

If \(A, B, C\) are vertices of a triangle with position vectors \(\vec{a}, \vec{b}, \vec{c}\) respectively, then find the position vector of the point \(D\) where the angle bisector from vertex \(A\) meets \(BC\).

Find the general solution for \(x\) if \( \cos 4x = \cos 3x \).

Find the approximate value of \(\sqrt[3]{63}\).

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

A \(1.5\,\text{kg}\) block is attached to a spring with spring constant \(k=100\,\text{N m}^{-1}\) and displaced by \(0.2\,\text{m}\). Calculate the potential energy stored in the spring.

The relation between molar conductivity \( \Lambda_m \), conductivity \( \kappa \), and concentration \( C \) of an electrolyte solution is:

If the statement $(p \wedge q) \rightarrow (r \vee \neg s)$ is False (F), then the truth values of $p, q, r$ and $s$ are respectively

Find the eigenvalues of the matrix \(A = \begin{pmatrix} 0 & 0 & -1 \\ 0 & -1 & 0 \\ 0 & 0 & -1 \end{pmatrix}\).

Evaluate the definite integral: \[ \int_{0}^{\frac{\pi}{2}} \sin^2 x \, dx \]

What product is formed when a ketone reacts with hydrazine \( (\mathrm{NH_2-NH_2}) \)?

Evaluate the integral: \[ \int_{0}^{\frac{\pi}{2}} \frac{dx}{1+(\cot x)^{101}} \]

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

If \( h(x) = \sqrt{4f(x) + 3g(x)} \), \( f(1)=4 \), \( g(1)=3 \), \( f'(1)=3 \), \( g'(1)=4 \), then \( h'(1) \) is equal to:}

Evaluate the integral: \[ \int \frac{x+1}{x(1+xe^x)^2}\,dx \]

Evaluate the integral: \[ \int_{1}^{4}\left(\frac{1}{\sqrt{x}}+\frac{1}{\sqrt{e^x}}\right)dx \]

If the concentration of an electrolyte solution decreases, the molar conductivity \( \Lambda_m \) will:

Identify the major product formed when phenol reacts with bromine water.

Find the oxidation state of Phosphorus in \( H_3PO_4 \) and \( H_3PO_3 \).

Which of the following polymers is prepared by condensation polymerization: Nylon-6,6 or Polythene?

Calculate the spin-only magnetic moment of a \( Mn^{2+} \) ion (Atomic number = 25).

What is the IUPAC name for the compound \( CH_3 - CH(OH) - CH_2 - CHO \)?