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Q.

The shortest distance between the curve y= e x   and the line y=x is

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a

2  units   

b

1 2  units   

c

2units

d

1 2  units     

answer is D.

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Detailed Solution

We know the shortest and greatest distance between two 
Curves always lie along the common normal. Let the normal 
To the y= e x  at Q α, e α  meets the line y=x at P  .
Question Image 
dy dx = e x ∴−1= − 1 dy dx ⇒− e α =−1⇒α=0∴Q≡(0,1)  
∴ normal =y−1=−1(x−0)⇒x+y−1=0∴PQ= 1 4 + 1 4 ⇒ 1 2    

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