JEE PYQ: Application Of Derivatives Question 25
Question 25 - 2020 (02 Sep Shift 1)
If the tangent to the curve $y = x + \sin y$ at a point $(a, b)$ is parallel to the line joining $\left(0, \frac{3}{2}\right)$ and $\left(\frac{1}{2}, 2\right)$, then:
(1) $b = a$
(2) $|b - a| = 1$
(3) $|a + b| = 1$
(4) $b = \frac{\pi}{2} + a$
Show Answer
Answer: (2)
Solution
$\frac{dy}{dx} = \frac{1}{1-\cos y}$. Slope of line $= \frac{2-3/2}{1/2-0} = 1$. So $\frac{1}{1-\cos b} = 1 \Rightarrow \cos b = 0 \Rightarrow b = \frac{\pi}{2}$. Then $a = b - \sin b = \frac{\pi}{2} - 1$. $|b - a| = 1$.
BETA
