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1
JEE Main 2021 (Online) 16th March Morning Shift
+4
-1
The range of a$$\in$$R for which the

function f(x) = (4a $$-$$ 3)(x + loge 5) + 2(a $$-$$ 7) cot$$\left( {{x \over 2}} \right)$$ sin2$$\left( {{x \over 2}} \right)$$, x $$\ne$$ 2n$$\pi$$, n$$\in$$N has critical points, is :
A
[1, $$\infty$$)
B
($$-$$3, 1)
C
$$\left[ { - {4 \over 3},2} \right]$$
D
($$-$$$$\infty$$, $$-$$1]
2
JEE Main 2021 (Online) 26th February Evening Shift
+4
-1
Let $$A = \{ 1,2,3,....,10\}$$ and $$f:A \to A$$ be defined as

$$f(k) = \left\{ {\matrix{ {k + 1} & {if\,k\,is\,odd} \cr k & {if\,k\,is\,even} \cr } } \right.$$

Then the number of possible functions $$g:A \to A$$ such that $$gof = f$$ is :
A
55
B
105
C
5!
D
10C5
3
JEE Main 2021 (Online) 26th February Morning Shift
+4
-1
Let R = {(P, Q) | P and Q are at the same distance from the origin} be a relation, then the equivalence class of (1, $$-$$1) is the set :
A
$$S = \{ (x,y)|{x^2} + {y^2} = \sqrt 2 \}$$
B
$$S = \{ (x,y)|{x^2} + {y^2} = 2\}$$
C
$$S = \{ (x,y)|{x^2} + {y^2} = 1\}$$
D
$$S = \{ (x,y)|{x^2} + {y^2} = 4\}$$
4
JEE Main 2021 (Online) 25th February Evening Shift
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 :
$${{{39} \over 2}}$$
$${{{19} \over 2}}$$
$${{{49} \over 2}}$$
$${{{29} \over 2}}$$