Let $$\mathrm{ABCD}$$ be a quadrilateral with area 18 , with side $$\mathrm{A B}$$ parallel to the side $$\mathrm{C D}$$ and $$\mathrm{A B}=2 \mathrm{CD}$$. Let $$\mathrm{AD}$$ be perpendicular to $$\mathrm{AB}$$ and $$\mathrm{CD}$$. If a circle is drawn inside the quadrilateral ABCD touching all the sides, then its radius is :

Let $$f(x)=\frac{x}{\left(1+x^{n}\right)^{1 / n}}$$ for $$n \geq 2$$ and $$g(x)=\underbrace{(f o f o \ldots . o f)}_{f \text { occurs } n \text { times }}(x)$$. Then $$\int x^{n-2} g(x) d x$$ equals :

The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN is :

Consider the planes $$3 x-6 y-2 z=15$$ and $$2 x+y-2 z=5$$.

STATEMENT - 1 : The parametric equations of the line of intersection of the given planes are $$x=3+14 t, y=1+2 t, z=15 t$$

STATEMENT - 2 : The vectors $$14 \hat{i}+2 \hat{j}+15 \hat{k}$$ is parallel to the line of intersection of the given planes.