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

In the interval $$( - 2\pi ,0)$$, the function $$f(x) = \sin \left( {{1 \over {{x^3}}}} \right)$$.

A
never changes sign.
B
changes sign only once.
C
changes sign more than once but finitely many times.
D
changes sign infinitely many times.
2
WB JEE 2023
MCQ (Single Correct Answer)
+2
-0.5
Change Language

The average ordinate of $$y = \sin x$$ over $$[0,\pi ]$$ is :

A
$${2 \over \pi }$$
B
$${3 \over \pi }$$
C
$${4 \over \pi }$$
D
$$\pi $$
3
WB JEE 2023
MCQ (Single Correct Answer)
+2
-0.5
Change Language

The portion of the tangent to the curve $${x^{{2 \over 3}}} + {y^{{2 \over 3}}} = {a^{{2 \over 3}}},a > 0$$ at any point of it, intercepted between the axes

A
varies as abscissa
B
varies as ordinate
C
is constant
D
varies as the product of abscissa and ordinate
4
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
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