1
JEE Main 2020 (Online) 3rd September Evening Slot
+4
-1
Let R1 and R2 be two relation defined as follows :
R1 = {(a, b) $$\in$$ R2 : a2 + b2 $$\in$$ Q} and
R2 = {(a, b) $$\in$$ R2 : a2 + b2 $$\notin$$ Q},
where Q is the set of all rational numbers. Then :
A
Neither R1 nor R2 is transitive.
B
R2 is transitive but R1 is not transitive.
C
R1 and R2 are both transitive.
D
R1 is transitive but R2 is not transitive.
2
JEE Main 2020 (Online) 3rd September Morning Slot
+4
-1
Consider the two sets :
A = {m $$\in$$ R : both the roots of
x2 – (m + 1)x + m + 4 = 0 are real}
and B = [–3, 5).
Which of the following is not true?
A
A $$\cap$$ B = {–3}
B
B – A = (–3, 5)
C
A $$\cup$$ B = R
D
A - B = ($$-$$$$\propto$$, $$-$$3) $$\cup$$ (5, $$\propto$$)
3
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
4
JEE Main 2020 (Online) 2nd September Morning Slot
+4
-1
If R = {(x, y) : x, y $$\in$$ Z, x2 + 3y2 $$\le$$ 8} is a relation on the set of integers Z, then the domain of R–1 is :
A
{0, 1}
B
{–2, –1, 1, 2}
C
{–1, 0, 1}
D
{–2, –1, 0, 1, 2}
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