1
JEE Main 2020 (Online) 5th September Morning Slot
Numerical
+4
-0
Change Language
The natural number m, for which the coefficient of x in the binomial expansion of

$${\left( {{x^m} + {1 \over {{x^2}}}} \right)^{22}}$$ is 1540, is .............
Your input ____
2
JEE Main 2020 (Online) 5th September Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If $$\alpha $$ is positive root of the equation, p(x) = x2 - x - 2 = 0, then

$$\mathop {\lim }\limits_{x \to {\alpha ^ + }} {{\sqrt {1 - \cos \left( {p\left( x \right)} \right)} } \over {x + \alpha - 4}}$$ is equal to :
A
$${1 \over \sqrt2}$$
B
$${1 \over 2}$$
C
$${3 \over \sqrt2}$$
D
$${3 \over 2}$$
3
JEE Main 2020 (Online) 5th September Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If
$$\int {\left( {{e^{2x}} + 2{e^x} - {e^{ - x}} - 1} \right){e^{\left( {{e^x} + {e^{ - x}}} \right)}}dx} $$ = $$g\left( x \right){e^{\left( {{e^x} + {e^{ - x}}} \right)}} + c$$

where c is a constant of integration, then g(0) is equal to :
A
1
B
2
C
e
D
e2
4
JEE Main 2020 (Online) 5th September Morning Slot
Numerical
+4
-0
Change Language
Four fair dice are thrown independently 27 times. Then the expected number of times, at least two dice show up a three or a five, is _________.
Your input ____
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