List of top Mathematics Questions asked in MHT CET

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.

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?

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

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

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

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

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

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 \(x=0\).

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

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."