JEE Advanced · 2012 · 08 Apr 2012 · Paper 1 · Area Under Curves

Consider the curve ${\mathrm{C}}_1$ given by

and the curve ${\mathrm{C}}_2$ given by

L …

Consider the ellipses given by

If $\alpha$ is the area of the common region that lies inside both the given ellipses, then the value of $\cot \alpha$ is ____.

Let $\mathbb{R}$ denote the set of all real numbers. Then the area of the region

is

Let $S$ denote the locus of the mid-points of those chords of the parabola $y^2=x$, such that the area of the region enclosed between the parabola and the chord is $\frac{4}{3}$. Let $R$ denote the region lying in the first quadrant, enclosed by the parabola $y^2=x$ …

Let $S=\{(x,y)\in \mathbb{R}\times \mathbb{R}:x\ge 0,y\ge 0,y^2\le 4x,y^2\le 12-2x$ and $3y+\sqrt{8}x\le 5\sqrt{8}\}$. If the area of the region $S$ is $\alpha \sqrt{2}$, then $\alpha$ is equal to

Let $\mathrm{f}:[0,1]\to [0,1]$ be the function defined by $\mathrm{f}(\mathrm{x})=\frac{{\mathrm{x}}^3}{3}-{\mathrm{x}}^2+\frac{5}{9}\mathrm{x}+\frac{17}{36}$. Consider the square region $\mathrm{S}=[0,1]\times [0,1]$. Let …