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Q. The equation of the tangent to the curve $y=x+\frac{4}{x^{2}},$ that is parallel to the x-axis, is :-
(1) y = 0 (2) y = 1 (3) y = 2 (4) y = 3

**[AIEEE-2010]**Ans. (4)

Q. The intercepts on x-axis made by tangents to the curve, $\mathrm{y}=\int_{0}^{\mathrm{x}}|\mathrm{t}| \mathrm{dt}, \mathrm{x} \in \mathrm{R}$ which are parallel to the line y = 2x, are equal to
$(1) \pm 1$ $(2) \pm 2$ (3) $\pm 3$ (4) $\pm 4$

**[JEE-MAIN 2013]**Ans. (1)

Q. The normal to the curve, $x^{2}+2 x y-3 y^{2}=0,$ at $(1,1):$
(1)meets the curve again in the third quadrant
(2) meets the curve again in the fourth quadrant
(3) does not meet the curve again
(4) meets the curve again in the second quadrant

**[JEE-MAIN 2015]**Ans. (2)

Q. Consider $f(x)=\tan ^{-1}(\sqrt{\frac{1+\sin x}{1-\sin x}}), x \in\left(0, \frac{\pi}{2}\right) .$ A normal to $y=f(x)$ at $x=\frac{\pi}{6}$ also passes through the point :
( 1)$\left(\frac{\pi}{4}, 0\right)$b
(2) (0, 0)
(3) $\left(0, \frac{2 \pi}{3}\right)$
(4) $\left(\frac{\pi}{6}, 0\right)$

**[JEE-MAIN 2016]**Ans. (3)

Q. If the curves $\mathrm{y}^{2}=6 \mathrm{x}, 9 \mathrm{x}^{2}+\mathrm{by}^{2}=16$ intersect each other at right angles, then the value of $\mathrm{b}$ is :
(1) $\frac{7}{2}$ (2) 4 (3) $\frac{9}{2}$ (4) 6

**[JEE-MAIN 2016]**Ans. (3)