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For the following questions answer them individually
Let ABCD be a quadrilateral with area 18, with side AB parallel to the side CD and AB =2CD. Let AD be perpendicular to AB and CD. If a circle is drawn inside the quadrilateral ABCD touchingall the sides, then its radius is
Lat $$f(x) = \frac{x}{\left(1 + x^n\right)^{\frac{1}{n}}}$$ for $$n \geq 2$$ and $$g(x) = \underbrace{(f\circ f \circ ... \circ f)(x)}_{f occurs n times}$$. Then $$\int x^{n-2}g(x)dx$$ 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 $$3x - 6y - 2z = 15$$ and $$2x + y - 2z = 5$$.
STATEMENT-1: The parametric equations of the line of intersection of the given planes are $$x = 3 + 14t, y = 1 + 2t, z = 15t.
because
STATEMENT-2: The vector $$14\hat{i} + 2 \hat{j} + 15 \hat{k}$$ is parallel to the line ofintersection of given planes.
STATEMENT-1: The curve $$y = \frac{-x^2}{2} + x + 1$$ is symmetric with respect to the line x = 1.
because
STATEMENT-2: A parabola is symmetric aboutits axis.
Let $$f(x) = 2 + \cos x$$ for all real x.
STATEMENT-1: For each real t, there exists a point c in $$[t, t + \pi]$$ such that $$f'(c) = 0.$$
because
STATEMENT-2: $$f(t) = f(t + 2\pi)$$ for each real t.
Lines $$L_1 : y - x = 0$$ and $$L_2 : 2x + y = 0$$ intersect the line $$L_3 : y + 2 = 0$$ at P and Q, respectively. The bisector of the acute angle between $$L_1$$ and $$L_2$$ intersects $$L_3$$ at R.
STATEMENT-1: The ratio PR : RQ equals $$2\sqrt{2} : \sqrt{5}.$$
because
STATEMENT-2: In any triangle, bisector of an angle divides the triangle into two similar triangles.
