List of top Mathematics Questions asked in MHT CET

The area of the region bounded by the y-axis, y = cos x, y = sin x, when 0 ≤ x ≤\(\frac {π}{4}\), is

The general solution of the differential equation x2 + y2 – 2xy \(\frac {dy}{dx}\) = 0 is (where C is a constant of integration.)

The function f(x) = 2x3 – 9x2 + 12x +29 is monotonically increasing in the interval.

The equation of the line perpendicular to 2x – 3y + 5 = 0 and making an intercept 3 with positive Y-axis is

Argument of \(\frac {1-i√3}{1+i√3}\) is

Probability of getting odd numbers in first 100 numbers.

If \( f(x)=\dfrac{4x+7}{7x-4} \), then the value of \[ f\{f[f(2)]\} \] is
If \[ A = \begin{bmatrix} 2 & 3 \\ 1 & 2 \end{bmatrix}, \quad B = \begin{bmatrix} 1 & 0 \\ 3 & 1 \end{bmatrix}, \] then find \((AB)^{-1}\).
The value of \( m \) if the vectors \[ \mathbf{A} = i - j - 6k, \quad \mathbf{B} = i - 3j + 4k, \quad \mathbf{C} = 2i - 5j + mk \] are coplanar, is
The equation of a plane containing the lines \( \vec{r} = (i + 2j - 4k) + \lambda (2i + 3j + 6k) \) and \( \vec{r} = (i + 3j + 4k) + \mu (i + j - k) \) is
For \( f(x) = [x] \), where \( [x] \) is the greatest integer function, which of the following is true, for every \( x \in \mathbb{R} \)?
If \( ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 \) represents a joint equation of directrices of the hyperbola \( 16x^2 - 9y^2 = 144 \), then \( g + f - c = \)
The joint equation of two lines through the origin, each of which makes an angle of \(30^\circ\) with the line \(x + y = 0\), is
If \( \vec{a} = \hat{i} + 5\hat{k}, \, \vec{b} = 2\hat{i} + 3\hat{k}, \, \vec{c} = 4\hat{i} - \hat{j} + 2\hat{k}, \, \vec{d} = \hat{i} - \hat{j} \), then \( (\vec{c} - \vec{a}) \cdot (\vec{b} \times \vec{d}) = \)
The polar co-ordinates of the point whose cartesian co-ordinates are \( (-2, -2) \), are given by
$\cosec 2\theta-\cot 2\theta=$
If \(A(3,2,-1)\) and \(B(1,4,3)\), then the equation of the plane which bisects the segment \(AB\) perpendicularly is
The perimeter of the triangle whose vertices have the position vectors \( \hat{i} + \hat{j} + \hat{k} \), \( 5\hat{i} + 3\hat{j} - 3\hat{k} \), and \( 2\hat{i} + 5\hat{j} + 9\hat{k} \) is
Evaluate the integral \( \int_0^5 \frac{dx}{x^2 + 2x + 10} \)
For every value of \( x \), the function \( f(x) = \frac{1}{a^x}, a>0 \) is
In \( \triangle ABC \), if \( \frac{\cos A}{a} = \frac{\cos B}{b} = \frac{\cos C}{c} \) with usual notations, then the triangle is:
The derivative of $\cot^{-1}x$ with respect to $\log(1+x^2)$ is
If the symbolic form of the switching circuit is \( \sim p \vee ( p \wedge \sim q) \vee q \), then the current flows through the circuit only if:
The eccentricity of the hyperbola \( 16x^2 - 3y^2 - 32x - 12y - 44 = 0 \) is
Evaluate: \[ \frac{\cos 12^\circ - \sin 12^\circ}{\cos 12^\circ + \sin 12^\circ} + \frac{\sin 147^\circ}{\cos 147^\circ} \]