KVPY Sample Paper KVPY Stream-SX Model Paper-29

The tangent to the curve, \[y=x{{e}^{{{x}^{2}}}}\] passing, through the point \[(1,e)\] also passes through the point:

A) \[(2,3e)\]

B) \[\left( \frac{4}{3},2e \right)\]

C) \[\left( \frac{5}{3},2e \right)\]

D) \[(3,6e)\]

Correct Answer: B

Solution :

\[y=x{{e}^{{{x}^{2}}}}\]

\[(1,e)\]lies on this

Now, \[\frac{dy}{dx}=x{{e}^{{{x}^{2}}}}.2x+{{e}^{{{x}^{2}}}}.1\]

Put \[x=1\]

\[m=2e+e=3e\]

Equation of tangent at \[(1,e)\]

\[y-e=3e(x-1)\]

\[y-e=3ex-3e\]

\[y=3ex-2e\]

\[\left( \frac{4}{3},2e \right)\]satisfies it

\[\therefore \]Answer is B.