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

MCQ_SINGLE
Let $S = \mathbb{N} \cup \{0\}$. Define a relation R from S to $\mathbb{R}$ by: $R = \{(x, y) : \log_e y = x \log_e (\frac{2}{5}), x \in S, y \in \mathbb{R}\}$. Then, the sum of all the elements in the range of $R$ is equal to:
NUMERICAL
Let A = {n $\in$ N : H.C.F. (n, 45) = 1} and Let B = {2k : k $\in$ {1, 2, ......., 100}}. Then the sum of all the elements of A $\cap$ B is ____________.
NUMERICAL
The sum of all the elements of the set $\{ \alpha \in \{ 1,2,.....,100\} :HCF(\alpha ,24) = 1\} $ is __________.
MCQ_SINGLE
Let $S = {1, 2, 3, … , 100}$. The number of non-empty subsets A of S such that the product of elements in A is even is :
NUMERICAL
For $n \geq 2$, let $S_n$ denote the set of all subsets of $\{1,2, \ldots, n\}$ with no two consecutive numbers. For example $\{1,3,5\} \in S_6$, but $\{1,2,4\} \notin S_6$. Then $n\left(S_5\right)$ is equal to ________
View All Questions