List of top Mathematics Questions asked in MHT CET

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

If \( \vec{a} = 2\hat{i} - \hat{j} + \hat{k} \) and \( \vec{b} = \hat{i} + 2\hat{j} - 3\hat{k} \), find the magnitude of \( \vec{a} \times \vec{b} \).

Find the area of the region bounded by the curve \(y^2 = 8x\) and the line \(x = 2\).

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

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

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 \( \sin^{-1}\left(\frac{1}{2}\right) + \cos^{-1}\left(\frac{1}{2}\right) \)?

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 \( x \)

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 \(y(0)=1\).

The equation \(x^2 - Ky^2 - 4x + 6y - 5 = 0\) represents a pair of straight lines. Find the point of intersection.

If \(y = f\left(\frac{3 + 2x}{3 - 2x}\right)\), where \(f(x) = \tan(\log x)\), and \(\frac{dy}{dx} = \frac{A}{B + Cx^2} \cdot \sec^2\left(\log \frac{3 + 2x}{3 - 2x}\right)\), then find \(A, B, C\).

Consider the following logical statements:
R: If \(p \rightarrow q\) is false, then \(p \vee q\) is false.
S: If \(p \leftrightarrow q\) is false, then \(p \vee q\) is false.
Evaluate the truth values of R and S.

What is the probability of an impossible event?

If $\frac{dy}{dx} = y + 5$ and $y(0) = 4$, then $y(\log 2)$ is equal to

Find the value of \( \tan(105^\circ) \) using compound angle identities.

The converse of the statement \( ((\sim p) \land q) \rightarrow r \) is:

If \(A\) is a \(3\times3\) matrix such that \(|A| = 4\) and \(B = \text{adj}\,A\), find the value of \(|B|\).

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 \( \vec{b} = \hat{i} + 2\hat{j} - 3\hat{k} \).