1
JEE Main 2020 (Online) 6th September Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
$$\mathop {\lim }\limits_{x \to 1} \left( {{{\int\limits_0^{{{\left( {x - 1} \right)}^2}} {t\cos \left( {{t^2}} \right)dt} } \over {\left( {x - 1} \right)\sin \left( {x - 1} \right)}}} \right)$$
A
is equal to 0
B
is equal to $${1 \over 2}$$
C
does not exist
D
is equal to $$ - {1 \over 2}$$
2
JEE Main 2020 (Online) 6th September Morning Slot
Numerical
+4
-0
Change Language
Set A has m elements and set B has n elements. If the total number of subsets of A is 112 more than the total number of subsets of B, then the value of m.n is ______.
Your input ____
3
JEE Main 2020 (Online) 6th September Morning Slot
Numerical
+4
-0
Change Language
Let f : R $$ \to $$ R be defined as
$$f\left( x \right) = \left\{ {\matrix{ {{x^5}\sin \left( {{1 \over x}} \right) + 5{x^2},} & {x < 0} \cr {0,} & {x = 0} \cr {{x^5}\cos \left( {{1 \over x}} \right) + \lambda {x^2},} & {x > 0} \cr } } \right.$$

The value of $$\lambda $$ for which f ''(0) exists, is _______.
Your input ____
4
JEE Main 2020 (Online) 6th September Morning Slot
Numerical
+4
-0
Change Language
If $$\overrightarrow a $$ and $$\overrightarrow b $$ are unit vectors, then the greatest value of

$$\sqrt 3 \left| {\overrightarrow a + \overrightarrow b } \right| + \left| {\overrightarrow a - \overrightarrow b } \right|$$ is_____.
Your input ____
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