List of top Mathematics Questions asked in MHT CET

If \( y = \sin^{-1}\!\left(\dfrac{5x + 12\sqrt{1-x^2}}{13}\right) \), then \( \dfrac{dy}{dx} \) is equal to:

Find the value of \( k \) if the function \( f(x) = \dfrac{k\cos x}{\pi - 2x} \) is continuous at \( x = \dfrac{\pi}{2} \).

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 \( \vec{b} \).

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

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

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

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

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

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

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

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

Identify the truth value of the statement pattern \( (p \land \sim q) \rightarrow r \).

Find the area of the region bounded by the parabola \( y^2 = 4ax \) and its latus rectum.

Find the value of \( k \) if the function \( f(x) = \frac{k \cos x}{\pi - 2x} \) is continuous at \( x = \frac{\pi}{2} \).

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

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

If \( \vec{a} \) and \( \vec{b} \) are unit vectors and the angle between them is \(60^\circ\), find \( |\vec{a}-\vec{b}| \).

Find the general solution of the differential equation \( \dfrac{dy}{dx} + \dfrac{y}{x} = x^2 \).

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

In $\triangle ABC$, if $2a^2 = b^2 + c^2$, then the value of $\frac{\cos 3A}{\cos A} + 2$ is

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

Evaluate the integral: \(\int \frac{\sin x}{\sin 4x} \, dx\)