1
WB JEE 2011
MCQ (Single Correct Answer)
+1
-0.25

For the function $$f(x) = {e^{\cos x}}$$, Rolle's theorem is

A
applicable when $${\pi \over 2} \le x \le {{3\pi } \over 2}$$
B
applicable when $$0 \le x \le {\pi \over 2}$$
C
applicable when $$0 \le x \le \pi $$
D
applicable when $${\pi \over 4} \le x \le {\pi \over 2}$$
2
WB JEE 2011
MCQ (Single Correct Answer)
+1
-0.25

$$f(x) = \left\{ {\matrix{ {0,} & {x = 0} \cr {x - 3,} & {x > 0} \cr } } \right.$$

The function f(x) is

A
increasing when x $$\ge$$ 0
B
strictly increasing when x > 0
C
strictly increasing at x = 0
D
not continuous at x = 0 and so it is not increasing when x > 0
3
WB JEE 2011
MCQ (Single Correct Answer)
+1
-0.25

The function f(x) = ax + b is strictly increasing for all real x if

A
a > 0
B
a < 0
C
a = 0
D
a $$\le$$ 0
4
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

$$\mathop {\lim }\limits_{x \to \infty } \left\{ {x - \root n \of {(x - {a_1})(x - {a_2})\,...\,(x - {a_n})} } \right\}$$ where $${a_1},{a_2},\,...,\,{a_n}$$ are positive rational numbers. The limit

A
does not exist
B
is $${{{a_1} + {a_2}\, + \,...\,{a_n}} \over n}$$
C
is $$\root n \of {{a_1}{a_2}\,...\,{a_n}} $$
D
is $${n \over {{a_1} + {a_2}\, + \,...\,{a_n}}}$$
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