1
WB JEE 2023
MCQ (More than One Correct Answer)
+2
-0
Change Language

Which statement(s) is/are applicable above critical temperature?

A
A gas cannot be liquified.
B
Surface tension of a liquid is very high.
C
A liq. phase cannot be distinguished from a gas phase.
D
Density changes continuously with P or V.
2
WB JEE 2023
MCQ (More than One Correct Answer)
+2
-0
Change Language

Which of the following mixtures act(s) as buffer solution?

A
NaOH + CH$$_3$$COOH (1 : 1 mole ratio)
B
NH$$_4$$OH + HCl (2 : 1 mole ratio)
C
CH$$_3$$COOH + NaOH (2 : 1 mole ratio)
D
CH$$_3$$COOH + NaOH (1 : 2 mole ratio)
3
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 $${n \over {{a_1} + {a_2}\, + \,...\,{a_n}}}$$
4
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Suppose $$f:R \to R$$ be given by $$f(x) = \left\{ \matrix{ 1,\,\,\,\,\,\,\,\,\,\,\mathrm{if}\,x = 1 \hfill \cr {e^{({x^{10}} - 1)}} + {(x - 1)^2}\sin {1 \over {x - 1}},\,\mathrm{if}\,x \ne 1 \hfill \cr} \right.$$

then

A
f'(1) does not exist
B
f'(1) exists and is zero
C
f'(1) exist and is 9
D
f'(1) exists and is 10
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