1
JEE Main 2022 (Online) 27th June Morning Shift
Numerical
+4
-1
Change Language

Let f : R $$\to$$ R be a function defined by $$f(x) = {{2{e^{2x}}} \over {{e^{2x}} + e}}$$. Then $$f\left( {{1 \over {100}}} \right) + f\left( {{2 \over {100}}} \right) + f\left( {{3 \over {100}}} \right) + \,\,\,.....\,\,\, + \,\,\,f\left( {{{99} \over {100}}} \right)$$ is equal to ______________.

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2
JEE Main 2022 (Online) 27th June Morning Shift
Numerical
+4
-1
Change Language

If the sum of all the roots of the equation

$${e^{2x}} - 11{e^x} - 45{e^{ - x}} + {{81} \over 2} = 0$$ is $${\log _e}p$$, then p is equal to ____________.

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3
JEE Main 2022 (Online) 27th June Morning Shift
Numerical
+4
-1
Change Language

The number of ways, 16 identical cubes, of which 11 are blue and rest are red, can be placed in a row so that between any two red cubes there should be at least 2 blue cubes, is _____________.

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4
JEE Main 2022 (Online) 27th June Morning Shift
Numerical
+4
-1
Change Language

If the coefficient of x10 in the binomial expansion of $${\left( {{{\sqrt x } \over {{5^{{1 \over 4}}}}} + {{\sqrt 5 } \over {{x^{{1 \over 3}}}}}} \right)^{60}}$$ is $${5^k}\,.\,l$$, where l, k $$\in$$ N and l is co-prime to 5, then k is equal to _____________.

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