### CAT Content

Instructions

For the following questions answer them individually

Question 11

Question 12

Question 13

## Letasolution y = y(x) of the differential equation$$x\sqrt{x^2 - 1} dy - y\sqrt{y^2 - 1}dx = 0$$ satisfy $$y(2) = \frac{2}{\sqrt{3}}$$STATEMENT-1: $$y(x) = \sec\left(\sec^{-1}x - \frac{\pi}{6}\right)$$STATEMENT-2: y(x) is given by $$\frac{1}{y} = \frac{2\sqrt{3}}{x} - \sqrt{1 - \frac{1}{x^2}}$$

Instructions

Consider the function $$f : (-\infty, \infty) \rightarrow (-\infty, \infty)$$ defined by
$$f(x) = \frac{x^2 - ax + 1}{x^2 + ax + 1}, 0 < a < 2$$.

Question 14

Question 15

Question 16

## Let$$g(x) = \int_{0}^{e^x}\frac{f'(1)}{1 + t^2} dt$$.Which of the following is true?

Instructions

Consider the lines
$$L_1:\frac{x+1}{3} = \frac{y+2}{1} = \frac{z+1}{2}$$
$$L_1:\frac{x-2}{1} = \frac{y+2}{2} = \frac{z-3}{3}$$

Question 17

Question 18

Question 19

## The distance of the point (1,1, 1) from the plane passing through the point (-1, -2, -1) and whose normalis perpendicularto both the lines $$L_1$$ and $$L_2$$ is

Instructions

For the following questions answer them individually

Question 20

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