फलन f(x) = sin x के संबंध में निम्नलिखित कथनों पर विचार करें:

1. f(x) अंतराल (0, π) में बढ़ता है।

2. f(x) अंतराल में घटता है।

उपरोक्त कथनों में से कौन सा/से सही है/हैं?

This question was previously asked in
NDA (Held On: 18 Apr 2021) Maths Previous Year paper
View all NDA Papers >
  1. केवल 1
  2. केवल 2
  3. 1 और 2 दोनों
  4. न तो 1 और न ही 2

Answer (Detailed Solution Below)

Option 2 : केवल 2
Free
NDA 01/2025: English Subject Test
30 Qs. 120 Marks 30 Mins

Detailed Solution

Download Solution PDF

अवधारणा:

फलन f(x):

  •  f'(x) > 0 होने के x मानों के लिए बढ़ता है
  • f'(x) < 0 होने के x मानों के लिए घटता है

 

गणना:

दिया गया फलन f(x) = sin x है

∴ f'(x) = cos x

x ∈ (0, ), cos x > 0 और x ∈ ( , π), cos x <0 के लिए

∴ x ∈ (0, π) के लिए, f (x) अधिकतम तक बढ़ जाता है और फिर π पर घटाता है।

x ∈ , cos x < 0 के लिए 

∴ f(x) x ∈ के लिए कम हो जाती है

statement 2 is correct Only.

Latest NDA Updates

Last updated on Jul 7, 2025

->UPSC NDA Application Correction Window is open from 7th July to 9th July 2025.

->UPSC had extended the UPSC NDA 2 Registration Date till 20th June 2025.

-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.

->The NDA exam date 2025 has been announced. The written examination will be held on 14th September 2025.

-> The selection process for the NDA exam includes a Written Exam and SSB Interview.

-> Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100. 

-> Candidates must go through the NDA previous year question paper. Attempting the NDA mock test is also essential. 

More Applications of Derivatives Questions

More Differential Calculus Questions

Hot Links: online teen patti real money teen patti star teen patti neta