1
JEE Main 2020 (Online) 2nd September Evening Slot
+4
-1
Let f : R $$\to$$ R be a function which satisfies
f(x + y) = f(x) + f(y) $$\forall$$ x, y $$\in$$ R. If f(1) = 2 and
g(n) = $$\sum\limits_{k = 1}^{\left( {n - 1} \right)} {f\left( k \right)}$$, n $$\in$$ N then the value of n, for which g(n) = 20, is :
A
20
B
9
C
5
D
4
2
JEE Main 2020 (Online) 9th January Evening Slot
+4
-1
Let a – 2b + c = 1.

If $$f(x)=\left| {\matrix{ {x + a} & {x + 2} & {x + 1} \cr {x + b} & {x + 3} & {x + 2} \cr {x + c} & {x + 4} & {x + 3} \cr } } \right|$$, then:
A
ƒ(50) = 1
B
ƒ(–50) = –1
C
ƒ(50) = –501
D
ƒ(–50) = 501
3
JEE Main 2020 (Online) 8th January Evening Slot
+4
-1
Let ƒ : (1, 3) $$\to$$ R be a function defined by
$$f(x) = {{x\left[ x \right]} \over {1 + {x^2}}}$$ , where [x] denotes the greatest integer $$\le$$ x. Then the range of ƒ is
A
$$\left( {{2 \over 5},{1 \over 2}} \right) \cup \left( {{3 \over 4},{4 \over 5}} \right]$$
B
$$\left( {{3 \over 5},{4 \over 5}} \right)$$
C
$$\left( {{2 \over 5},{4 \over 5}} \right]$$
D
$$\left( {{2 \over 5},{3 \over 5}} \right] \cup \left( {{3 \over 4},{4 \over 5}} \right)$$
4
JEE Main 2020 (Online) 8th January Morning Slot
+4
-1
The inverse function of

f(x) = $${{{8^{2x}} - {8^{ - 2x}}} \over {{8^{2x}} + {8^{ - 2x}}}}$$, x $$\in$$ (-1, 1), is :
A
$${1 \over 4}{\log _e}\left( {{{1 - x} \over {1 + x}}} \right)$$
B
$${1 \over 4}\left( {{{\log }_8}e} \right){\log _e}\left( {{{1 - x} \over {1 + x}}} \right)$$
C
$${1 \over 4}\left( {{{\log }_8}e} \right){\log _e}\left( {{{1 + x} \over {1 - x}}} \right)$$
D
$${1 \over 4}{\log _e}\left( {{{1 + x} \over {1 - x}}} \right)$$
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