1
JEE Main 2021 (Online) 25th February Evening Shift
+4
-1
A function f(x) is given by $$f(x) = {{{5^x}} \over {{5^x} + 5}}$$, then the sum of the series $$f\left( {{1 \over {20}}} \right) + f\left( {{2 \over {20}}} \right) + f\left( {{3 \over {20}}} \right) + ....... + f\left( {{{39} \over {20}}} \right)$$ is equal to :
A
$${{{39} \over 2}}$$
B
$${{{19} \over 2}}$$
C
$${{{49} \over 2}}$$
D
$${{{29} \over 2}}$$
2
JEE Main 2021 (Online) 25th February Evening Shift
+4
-1
Let x denote the total number of one-one functions from a set A with 3 elements to a set B with 5 elements and y denote the total number of one-one functions form the set A to the set A $$\times$$ B. Then :
A
2y = 273x
B
y = 91x
C
2y = 91x
D
y = 273x
3
JEE Main 2021 (Online) 25th February Morning Shift
+4
-1
Let f, g : N $$\to$$ N such that f(n + 1) = f(n) + f(1) $$\forall$$ n$$\in$$N and g be any arbitrary function. Which of the following statements is NOT true?
A
If g is onto, then fog is one-one
B
f is one-one
C
If f is onto, then f(n) = n $$\forall$$n$$\in$$N
D
If fog is one-one, then g is one-one
4
JEE Main 2021 (Online) 24th February Morning Shift
+4
-1
Let f : R → R be defined as f (x) = 2x – 1 and g : R - {1} → R be defined as g(x) = $${{x - {1 \over 2}} \over {x - 1}}$$. Then the composition function f(g(x)) is :
A
one-one but not onto
B
onto but not one-one
C
both one-one and onto
D
neither one-one nor onto
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