1
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
2
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
3
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
4
AIEEE 2011
+4
-1
Let $R$ be the set of real numbers.

Statement I : $A=\{(x, y) \in R \times R: y-x$ is an integer $\}$ is an equivalence relation on $R$.

Statement II : $B=\{(x, y) \in R \times R: x=\alpha y$ for some rational number $\alpha\}$ is an equivalence relation on $R$.
A
Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
B
Statement I is true, Statement II is false.
C
Statement I is false, Statement II is true.
D
Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.
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