List of top Mathematics Questions asked in MHT CET

If the slope of one of the two lines given by \(\frac{x^2}{a}+\frac{2xy}{h}+\frac{y^2}{b} = 0\) is twice that of the other, then \(h^2:ab =\) ...

The value of \(tan^{-1}(\sqrt{3})+sec^{-1}(-2)-sin^{-1}(-\frac{1}{2})\) is

If y = y(x) satisfies the differential equation \[ \left(\frac{2+\sin x}{1+y}\right)\frac{dy}{dx}=-\cos x \] and \( y(0)=2 \), then \( y\left(\frac{\pi}{2}\right) \) is equal to:

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:}

If \[ f(x)=\int \frac{x^2}{(1-x^2)(1+\sqrt{1-x^2})}\,dx \] and \( f(0)=2 \), then \( f\left(\frac12\right) \) is:

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 \(BC\).

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

If \( y = \cos^{-1} x \), find \( \frac{d^2y}{dx^2} \) in terms of \( y \).

Calculate the area of the region bounded by the curve \( y^2 = 4x \) and the line \( x = 3 \).

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

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 \(A, B, C\).

If \(n\) is an odd natural number and \[ I_n=\int_0^1 e^x(x-1)^n\,dx \] then \( I_n+nI_{n-1} \) is equal to:

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

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

Evaluate: \(\tan^{-1}(1) + \tan^{-1}(4) + \tan^{-1}(5) + \tan^{-1}\left(\frac{1}{4}\right) = \pi + \tan^{-1}\left(\frac{\alpha}{2}\right)\). Find the value of \(\alpha\).

Given \(\int_1^a (2x + 1) \, dx = 5\), find the sum of all values of \(a\).

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

In a certain culture of bacteria, the rate of increase is proportional to the number of bacteria present at that instant. It is found that there are 10,000 bacteria at the end of 3 hours and 40,000 bacteria at the end of 5 hours, then the number of bacteria present in the beginning are:

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

Find the area of the region bounded by the curve \(y^2 = 4x\) and the line \(x = 3\).

If a polygon has 54 diagonals, find the number of sides of the polygon.

Let \(f(x)\) be defined by: \[ f(x)= \begin{cases} \displaystyle \int_x^6 (|t-2|+3)\,dt, & x>4 2x+8, & x\le4 \end{cases} \] Then at \(x=4\), \(f(x)\) is:

\[ \int \frac{1}{x^{1/2}+x^{1/3}}\,dx \] is equal to:

If the statement \( (p \land q) \rightarrow (r \lor \neg s) \) is False (F), what are the truth values of \(p, q, r,\) and \(s\) respectively?

For \(n\in\mathbb{N}\), if \[ y=ax^{n+1}+bx^{-n}, \] then \[ x^2\frac{d^2y}{dx^2} \] is equal to: