Class JEE Mathematics Sets, Relations, and Functions Q #1068
KNOWLEDGE BASED
APPLY
4 Marks 2016 JEE Main 2016 (Online) 10th April Morning Slot MCQ SINGLE
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 $Q - P \neq \phi$
(B) $Q \nsubseteq P$
(C) $P \nsubseteq Q$
(D) $P = Q$
Prev Next
Correct Answer: D
Explanation
Given, for set P:
$sin\theta - cos\theta = \sqrt{2}cos\theta$
$sin\theta = (\sqrt{2} + 1)cos\theta$
$cos\theta = (\sqrt{2} - 1)sin\theta$ ... (1)

Given, for set Q:
$sin\theta + cos\theta = \sqrt{2}sin\theta$
$cos\theta = (\sqrt{2} - 1)sin\theta$ ... (2)

From (1) and (2), P = Q

More from this Chapter

NUMERICAL
Let $A=\{1,2,3,4\}$ and $\mathrm{R}$ be a relation on the set $A \times A$ defined by $R=\{((a, b),(c, d)): 2 a+3 b=4 c+5 d\}$. Then the number of elements in $\mathrm{R}$ is ____________.
MCQ_SINGLE
Let $Z$ be the set of integers. If $A = {x \in Z : 2(x + 2) (x^2 - 5x + 6) = 1}$ and $B = {x \in Z : -3 < 2x - 1 < 9}$, then the number of subsets of the set $A \times B$, is
MCQ_SINGLE
Let $R = \{(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)\}$ be a relation on the set $A = \{3, 6, 9, 12\}$. The relation is :
MCQ_SINGLE
The number of non-empty equivalence relations on the set ${1, 2, 3}$ is :
NUMERICAL
The number of elements in the set $\left\{n \in \mathbb{N}: 10 \leq n \leq 100\right.$ and $3^{n}-3$ is a multiple of 7$\}$ is ___________.
View All Questions