Match List-I with List-II and select the correct answer using the code given below. A B C D
List-I
List-II
a) Equation of tangent to the curve $y = b e^{- x / a}$ at $x = 0$

1) $x - 2 y = 2$

b) Equation of tangent to the curve $y = x^{2} + 1$ at $(1, 2)$
2) $y = 2 x$
c) Equation of normal to the curve $y = 2 x - x^{2}$ at $(2, 0)$

3) $x - y = π$

d) Equation of normal to the curve $y = sin x$ at $x = π$
4) $\frac{x}{a} + \frac{y}{b} = 1$

4 1 2 3

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4 2 1 3

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1 2 3 4

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1 4 3 2

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Solution

The correct option is B 4 2 1 3
(A) $y^{'} = \frac{- b}{a} e^{- x / a}$
$m = - \frac{b}{a}$
$(y - b) = \frac{- b}{a} (x - 0)$
$\frac{x}{a} + \frac{y}{b} = 1$
(B) $y^{'} = 2 x$
$y^{'} |_{x = 1} = 2$
$(y - 2) = 2 (x - 1)$
$y = 2 x$
(C) $y^{'} = 2 - 2 x$
$y^{'} |_{x = 2} = - 2$
Slope of normal $= \frac{1}{2}$
$(y - 0) = \frac{1}{2} (x - 2)$
$2 y = x - 2$
(D) $y^{'} = cos x$
$y^{'} |_{x = π} = - 1$
Slope of normal =1
$(y - 0) = 1 (x - π)$
$x - y = π$

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List-I	List-II
a) Equation of tangent to the curve $y = b e^{- x / a}$ at $x = 0$	1) $x - 2 y = 2$
b) Equation of tangent to the curve $y = x^{2} + 1$ at $(1, 2)$	2) $y = 2 x$
c) Equation of normal to the curve $y = 2 x - x^{2}$ at $(2, 0)$	3) $x - y = π$
d) Equation of normal to the curve $y = sin x$ at $x = π$	4) $\frac{x}{a} + \frac{y}{b} = 1$