Let \( f: R \rightarrow R \) defined by \( f(x)=\cos \pi[x] \), where \( [x] \) denotes the grea....

Channel:
Subscribers:
447,000
Published on ● Video Link: https://www.youtube.com/watch?v=ZbECUqQ8k_o



Duration: 2:06
0 views
0


Let \( f: R \rightarrow R \) defined by \( f(x)=\cos \pi[x] \), where \( [x] \) denotes the greatest integer function less than or equal to \( x \).
Statement-1: \( f(x) \) is a periodic function. because
Statement-2: \( [x] \) is aperiodic function.
(A) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.
(B) Statement-1 is true, statement-2 is true and statement-2 is not the correct explanation for statement-1.
(C) Statement-1 is true, statement-2 is false.
(D) Statement-1 is false, statement-2 is true.


πŸ“²PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live




Other Videos By PW Solutions


2024-01-21The value of \( \cos \left[\cos ^{-1}\left(-\frac{\sqrt{3}}{2}\right)+\frac{\pi}{6}\right] \) is....
2024-01-21If \( f(x)+f\left(\frac{1}{1-x}\right)=\frac{(1-x)}{(1+x)} \) for \( x \in R-\{-1,1\} \) then th....
2024-01-21Range of \( f(x)=\sin ^{-1} x+\tan ^{-1} x+\sec ^{-1} x \) is....
2024-01-21If \( \mathrm{f}^{2}(\mathrm{x}) \cdot \mathrm{f}\left(\frac{1-\mathrm{x}}{1+\mathrm{x}}\right)=....
2024-01-21The solution of the equation \( \sin ^{-1}\left(\tan \frac{\pi}{4}\right)-\sin ^{-1}\left(\sqrt{....
2024-01-21Domain of \( f(x)=\cos ^{-1} x+\cot ^{-1} x+\operatorname{cosec}^{-1} x \) is....
2024-01-21The domain of definition of \( f(x)=\sin ^{-1}(|x-1|-2) \) is:....
2024-01-21Let \( f(x)=\cos \left(\frac{\pi}{\sqrt{3}} \sin x+\sqrt{\frac{2}{3}} \pi \cos x\right) \). Whic....
2024-01-212-Bromopentane is heated with \( \mathrm{KOH} \) in alcoholic and aqueous medium respectively. F....
2024-01-21Let \( f(x) \) and \( g(x) \) be two real polynomials of degree 2 and 1 respectively. If \( f(g(....
2024-01-21Let \( f: R \rightarrow R \) defined by \( f(x)=\cos \pi[x] \), where \( [x] \) denotes the grea....
2024-01-21Let \( g: R \rightarrow R \) defined by \( g(x)=\left\{e^{x}\right\} \), where \( \{x\} \) denot....
2024-01-21Let \( f(x)=x^{4}+a x^{3}+b x^{2}+c x+d \) where \( a, b, c, d \), \( \in \mathrm{R} \) if \( \m....
2024-01-21If \( g(x)=\frac{9^{x}}{9^{x}+3} \), then the value of \[ \mathrm{g}\left(\frac{1}{50}\right)+\m....
2024-01-21Statement-1: The number of solutions of \( 2^{\cos x}= \) \( |\sin x| \) in \( x \in[0,2 \pi] \)....
2024-01-21The maximum number of isomers (including stereoisomers) that are possible on mono- chlorination ....
2024-01-21If \( \mathrm{f}(\mathrm{x})+2 f\left(\frac{1}{x}\right)=3 \mathrm{x}, \mathrm{x} \neq 0 \) and ....
2024-01-21Consider the following: 1. If \( \mathrm{R}=\{(\mathrm{a}, \mathrm{b}) \in \mathrm{N} \times \ma....
2024-01-21Let \( f(x)=\ln \left(\frac{3+a \sin x}{b+5 \sin x}\right) \) is odd function then number of pos....
2024-01-21The function \( f: \mathbb{R} \rightarrow\left[-\frac{1}{2}, \frac{1}{2}\right] \) defined as \(....
2024-01-21Let \( \mathrm{N} \) be the set of natural numbers greater than 100. Define the relation \( \mat....