List of top Mathematics Questions asked in MHT CET

If \( A = \begin{bmatrix} 4 & 5 2 & 1 \end{bmatrix} \), find \( A^{-1} \).

If $A = \begin{bmatrix} \sin \alpha & -\cos \alpha\\ \cos \alpha & \sin \alpha \end{bmatrix}$ and $\alpha \in (\frac{\pi}{2}, \frac{3\pi}{2})$. If $A + A^T = I$, then $\alpha =$}

If $\sin x \cos x = \frac{1}{4}$, then the general solution is:

If $A = \begin{bmatrix} \sin \alpha & -\cos \alpha \\ \cos \alpha & \sin \alpha \end{bmatrix}$ and $\alpha \in (\frac{\pi}{2}, \frac{3\pi}{2})$, if $A + A^T = I$, then $\alpha =$}

The parametric equations of the circle $x^2 + y^2 - 4x - 6y - 12 = 0$ are:

Four persons can hit a target correctly with probabilities $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}$ and $\frac{1}{5}$ respectively. If all hit at the target independently, then the probability that the target would be hit, is:

If $n \in \mathbb{Z}$, then the expression $\frac{2^n}{(1-i)^{2n}} + \frac{(1+i)^{2n}}{2^n}$ is equal to:

If $x = a \sin t - b \cos t$ and $y = a \cos t + b \sin t$, and it is given that $\frac{d^2y}{dx^2} = 0$, then:

The value of $\int \frac{x^2 - 1}{(x^4 + 3x^2 + 1) \tan^{-1}(x + \frac{1}{x})} dx$ is:

The range of the function $y = \log(\sin x)$ where $\sin x > 0$ is:

The value of $\int_{0}^{4} \sqrt{\frac{4-x}{4+x}} dx$ is:

In $\triangle ABC$, $(b-c)^2 \cos^2 \frac{A}{2} + (b+c)^2 \sin^2 \frac{A}{2} =$

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

Evaluate the definite integral: \( \displaystyle \int_{3}^{5} |x-4|\,dx \).

Find the value of \(k\) if the function \(f(x) = \dfrac{k\sin x}{x}\) is continuous at \(x = 0\) and \(f(0)=3\).

The probability of a shooter hitting a target is \( \frac{3}{4} \). Find the probability of hitting the target exactly 4 times in 5 shots.

If \(\cos 4x = \cos 3x\), find the general solution for \(x\).

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

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 \(x = 2\).

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

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

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 \( x+y+z=9 \).