1
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.
2
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
3
JEE Main 2015 (Offline)
+4
-1
Let A and B be two sets containing four and two elements respectively. Then, the number of subsets of the set A $\times$ B , each having atleast three elements are
A
219
B
256
C
275
D
510
4
AIEEE 2012
+4
-1
Let X = {1, 2, 3, 4, 5}. The number of different ordered pairs (Y, Z) that can be formed such that Y $$\subseteq$$ X, Z $$\subseteq$$ X and Y $$\cap$$ Z is empty, is :
A
35
B
25
C
53
D
52
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