1
JEE Main 2018 (Online) 16th April Morning Slot
+4
-1
Let N denote the set of all natural numbers. Define two binary relations on N as R = {(x, y) $$\in$$ N $$\times$$ N : 2x + y = 10} and R2 = {(x, y) $$\in$$ N $$\times$$ N : x + 2y = 10}. Then :
A
Range of R1 is {2, 4, 8).
B
Range of R2 is {1, 2, 3, 4}.
C
Both R1 and R2 are symmetric relations.
D
Both R1 and R2 are transitive relations.
2
JEE Main 2018 (Offline)
+4
-1
Two sets A and B are as under :

A = {($$a$$, b) $$\in$$ R $$\times$$ R : |$$a$$ - 5| < 1 and |b - 5| < 1};

B = {($$a$$, b) $$\in$$ R $$\times$$ R : 4($$a$$ - 6)2 + 9(b - 5)2 $$\le$$ 36 };

Then
A
neither A $$\subset$$ B nor B $$\subset$$ A
B
B $$\subset$$ A
C
A $$\subset$$ B
D
A $$\cap$$ B = $$\phi$$ ( an empty set )
3
JEE Main 2018 (Online) 15th April Morning Slot
+4
-1
Consider the following two binary relations on the set A = {a, b, c} :
R1 = {(c, a), (b, b), (a, c), (c, c), (b, c), (a, a)} and
R2 = {(a, b), (b, a), (c, c), (c, a), (a, a), (b, b), (a, c)}.
Then :
A
both R1 and R2 are not symmetric.
B
R1 is not symmetric but it is transitive.
C
R2 is symmetric but it is not transitive.
D
both R1 and R2 are transitive.
4
JEE Main 2016 (Online) 10th April Morning Slot
+4
-1
Let P = {$$\theta$$ : sin$$\theta$$ $$-$$ cos$$\theta$$ = $$\sqrt 2 \,\cos \theta$$}

and Q = {$$\theta$$ : sin$$\theta$$ + cos$$\theta$$ = $$\sqrt 2 \,\sin \theta$$} be two sets. Then
A
P $$\subset$$ Q and Q $$-$$ P $$\ne$$ $$\phi$$
B
Q $$\not\subset$$ P
C
P $$\not\subset$$ Q
D
P = Q
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