1
WB JEE 2021
MCQ (More than One Correct Answer)
+2
-0
Change Language
$$\mathop {\lim }\limits_{n \to \infty } \left\{ {{{\sqrt n } \over {\sqrt {{n^3}} }} + {{\sqrt n } \over {\sqrt {{{(n + 4)}^3}} }} + {{\sqrt n } \over {\sqrt {{{(n + 8)}^3}} }} + .... + {{\sqrt n } \over {\sqrt {{{[n + 4(n - 1)]}^3}} }}} \right\}$$ is
A
$${{5 - \sqrt 5 } \over {10}}$$
B
$${{5 + \sqrt 5 } \over {10}}$$
C
$${{2 + \sqrt 3 } \over {2}}$$
D
$${{2 - \sqrt 3 } \over {2}}$$
2
WB JEE 2021
MCQ (More than One Correct Answer)
+2
-0
Change Language
Let $$f(x) = \left\{ {\matrix{ {0,} & {if} & { - 1 \le x \le 0} \cr {1,} & {if} & {x = 0} \cr {2,} & {if} & {0 < x \le 1} \cr } } \right.$$ and let $$F(x) = \int\limits_{ - 1}^x {f(t)dt} $$, $$-$$1 $$\le$$ x $$\le$$ 1, then
A
F is continuous function in [$$-$$1, 1]
B
F is discontinuous function in [$$-$$1, 1]
C
F'(x) exists at x = 0
D
F'(x) does not exist at x = 0
3
WB JEE 2021
MCQ (More than One Correct Answer)
+2
-0
Change Language
The greatest and least value of $$f(x) = {\tan ^{ - 1}} - {1 \over 2}\,ln \,x\,on\,\left[ {{1 \over {\sqrt 3 }},\sqrt 3 } \right]$$ are
A
$${f_{\min }} = \sqrt 3 - 1$$
B
$${f_{\max }} = {\pi \over 6} + {1 \over 4}\ln 3$$
C
$${f_{\min }} = {\pi \over 3} - {1 \over 4}\ln 3$$
D
$${f_{\max }} = {\pi \over {12}} + \ln 5$$
4
WB JEE 2021
MCQ (More than One Correct Answer)
+2
-0
Change Language
Let f and g be periodic functions with the periods T1 and T2 respectively. Then f + g is
A
periodic with period T1 + T2
B
non periodic
C
periodic with the period T1
D
periodic when T1 = T2
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