1
WB JEE 2023
MCQ (Single Correct Answer)
+2
-0.5
Change Language

If the volume of the parallelopiped with $$\overrightarrow a \times \overrightarrow b ,\overrightarrow b \times \overrightarrow c $$ and $$\overrightarrow c \times \overrightarrow a $$ as conterminous edges is 9 cu. units, then the volume of the parallelopiped with $$(\overrightarrow a \times \overrightarrow b ) \times (\overrightarrow b \times \overrightarrow c ),(\overrightarrow b \times \overrightarrow c ) \times (\overrightarrow c \times \overrightarrow a )$$, and $$(\overrightarrow c \times \overrightarrow a ) \times (\overrightarrow a \times \overrightarrow b )$$ as conterminous edges is

A
9 cu. units
B
729 cu. units
C
81 cu. units
D
243 cu. units
2
WB JEE 2023
MCQ (Single Correct Answer)
+2
-0.5
Change Language

Given $$f(x) = {e^{\sin x}} + {e^{\cos x}}$$. The global maximum value of $$f(x)$$

A
does not exist.
B
exists at a point in $$\left( {0,{\pi \over 2}} \right)$$ and its value is $$2{e^{{1 \over {\sqrt 2 }}}}$$.
C
exists at infinitely many points.
D
exists at $$x=0$$ only.
3
WB JEE 2023
MCQ (Single Correct Answer)
+2
-0.5
Change Language

Consider a quadratic equation $$a{x^2} + 2bx + c = 0$$ where a, b, c are positive real numbers. If the equation has no real root, then which of the following is true?

A
a, b, c cannot be in A.P. or H.P. but can be in G.P.
B
a, b, c cannot be in G.P. or H.P. but can be in A.P.
C
a, b, c cannot be in A.P. or G.P. but can be in H.P.
D
a, b, c cannot be in A.P., G.P. or H.P.
4
WB JEE 2023
MCQ (Single Correct Answer)
+2
-0.5
Change Language

Let $${a_1},{a_2},{a_3},\,...,\,{a_n}$$ be positive real numbers. Then the minimum value of $${{{a_1}} \over {{a_2}}} + {{{a_2}} \over {{a_3}}}\, + \,...\, + \,{{{a_n}} \over {{a_1}}}$$ is

A
1
B
n
C
nC2
D
2
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