वक्र y = 2x3 - 5x2 + x - 2 पर बिंदु (1, -1) पर अभिलंब की ढलान क्या है?

This question was previously asked in
AAI ATC Junior Executive Official Paper (Held On: 27 Dec, 2023 Shift 2)
View all AAI JE ATC Papers >
  1. \(\frac{1}{2}\)
  2. \(\frac{1}{3}\)
  3. -4
  4. -3

Answer (Detailed Solution Below)

Option 2 : \(\frac{1}{3}\)
Free
AAI ATC JE Physics Mock Test
11 K Users
15 Questions 15 Marks 15 Mins

Detailed Solution

Download Solution PDF

अवधारणा:

वक्र y = f(x) के स्पर्श रेखा की ढलान m = \(\rm dy\over dx\)

अभिलंब की ढलान = \(\rm -{1\over m}\) = \(\rm -{1\over {dy\over dx}}\)

गणना:

दिया गया वक्र y = 2x3 - 5x2 + x - 2

समीकरण को x के सापेक्ष अवकलन करने पर

\(\rm dy\over dx\) = 6x2 - 10x + 1

बिंदु (1, -1) पर ढलान

\(\rm dy\over dx\) x = 1 पर = 6(1)2 - 10(1) + 1

\(\rm dy\over dx\) = 6 - 10 + 1

\(\rm dy\over dx\) = -3

अभिलंब की ढलान (m') = \(\rm -{1\over {dy\over dx}}\)

m' = \(\boldsymbol{\rm -{1 \over -3}}\) = \(\boldsymbol{\rm {1 \over 3}}\)

बिंदु (1, -1) पर वक्र के अभिलंब की ढलान 1/3 है।

विकल्प 2 सही है। 
Latest AAI JE ATC Updates

Last updated on Jul 16, 2025

-> Predict Your Marks via AAI ATC Rank Predictor 2025 for free. 

-> AAI ATC answer key 2025 has been released on July 16, 2025 at the official website. 

-> Check the AAI ATC Exam Analysis 2025 for July 14, 2025 Exam. 

-> AAI ATC admit card 2025 has been released. 

The AAI ATC Exam 2025 will be conducted on July 14, 2025, for Junior Executive. 

-> AAI JE ATC recruitment 2025 application form has been released at the official website. The last date to apply for AAI ATC recruitment 2025 is May 24, 2025. 

-> AAI JE ATC 2025 notification is released on April 4, 2025, along with the details of application dates, eligibility, and selection process.

-> A total number of 309 vacancies are announced for the AAI JE ATC 2025 recruitment.

-> This exam is going to be conducted for the post of Junior Executive (Air Traffic Control) in the Airports Authority of India (AAI).

-> The Selection of the candidates is based on the Computer-Based Test, Voice Test and Test for consumption of Psychoactive Substances.

-> The AAI JE ATC Salary 2025 will be in the pay scale of Rs 40,000-3%-1,40,000 (E-1).

-> Candidates can check the AAI JE ATC Previous Year Papers to check the difficulty level of the exam.

-> Applicants can also attend the AAI JE ATC Test Series which helps in the preparation.

More Properties of Lines Questions

More Lines Questions

Get Free Access Now
Hot Links: teen patti gold real cash teen patti download teen patti joy official real cash teen patti teen patti dhani