The integer n for which \[\underset{x\to 0}{\mathop{\lim }}\,\,\frac{(\cos x-1)\,(\cos x-{{e}^{x}})}{{{x}^{n}}}\] is a finite non-zero number is [IIT Screening 2002]

The integer n for which \[\underset{x\to 0}{\mathop{\lim }}\,\,\frac{(

1.	The integer n for which \[\underset{x\to 0}{\mathop{\lim }}\,\,\frac{(\cos x-1)\,(\cos x-{{e}^{x}})}{{{x}^{n}}}\] is a finite non-zero number is [IIT Screening 2002]
A.	1
B.	2
C.	3
D.	4
Answer» D. 4

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The integer n for which \[\underset{x\to 0}{\mathop{\lim }}\,\,\frac{(\cos x-1)\,(\cos x-{{e}^{x}})}{{{x}^{n}}}\] is a finite non-zero number is [IIT Screening 2002]

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