List of top Mathematics Questions on Area of the region bounded asked in CBSE CLASS XII

An ant is observed crawling on a sheet of paper along a straight line given by equation \( y = 2x - 4 \). Area of the surface covered by the ant bounded by y-axis, x-axis and \( x = 1 \) is :

The area of the shaded region of the circle given below is equal to :

Which of the following expressions will give the area of region bounded by the curve $y=x^2$ and line $y=16$?

Find the particular solution of the differential equation \( \left( x e^{\frac{y}{x}} + y \right) dx = x \, dy \), given that \( y = 1 \) when \( x = 1 \).

Find the particular solution of the differential equation \( \frac{dy}{dx} = y \cot 2x \), given that \( y\left(\frac{\pi}{4}\right) = 2 \).

Find \( \frac{dy}{dx} \), if \( y = (\cos x)^x + \cos^{-1}(\sqrt{x}) \) is given:

Find the principal value of \( \tan^{-1}(1) + \cos^{-1}\left(-\frac{1}{2}\right) + \sin^{-1}\left(-\frac{1}{\sqrt{2}}\right) \):

Express \( \tan^{-1} \left( \frac{\cos x}{1 - \sin x} \right) \), where \( -\frac{\pi}{2}<x<\frac{\pi}{2} \), in the simplest form.

Show that the function \( f(x) = \sin x + \cos x \) is strictly decreasing in the interval \( \left( \frac{\pi}{4}, \frac{5\pi}{4} \right) \).

The volume of a cube is increasing at the rate of \( 6 \, {cm}^3/{s} \). How fast is the surface area of the cube increasing, when the length of an edge is \( 8 \, {cm} \)?

If \[ \begin{bmatrix} a & c & 0 \\ b & d & 0 \\ 0 & 0 & 5 \end{bmatrix} \] is a scalar matrix, then the value of \( a + 2b + 3c + 4d \) is:

The function \( f(x) = kx - \sin x \) is strictly increasing for:

The function \( f(x) = |x| + |x - 2| \) is

Let \( \vec{a} \) be any vector such that \( |\vec{a}| = a \). The value of \( |\vec{a} \times \hat{i}|^2 + |\vec{a} \times \hat{j}|^2 + |\vec{a} \times \hat{k}|^2 \) is: