English
Hindi
Telugu

Question

Download Solution PDF

If  and , then  is:

This question was previously asked in
AAI ATC Junior Executive 21 Feb 2023 Shift 2 Official Paper
Download PDF Attempt in App
View all AAI JE ATC Papers >
  4. 1

Answer (Detailed Solution Below)

Option 2 :
Free Tests
View all Free tests >
Free
AAI ATC JE Physics Mock Test
15 Qs. 15 Marks 15 Mins
Start Now

Detailed Solution

Download Solution PDF

Given:

 and 

Concept:

Use formula 

And 

Calculation:

 and 

Differentiate both equation with respect to t .

 and 

 and 

Now , we know that 

Then 

Now multiply by t in numerator and denominator both on the right hand then

Hence the option (2) is correct.

Download Solution PDF
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.

‹‹ Previous Ques
Next Ques ››
Exams Tests Super Practice

More Evaluation of derivatives Questions

Q1.If log 2 = 0.2614, log 3 = 0.3521, log 6 = ?
Q2.If \(y(\alpha)=\sqrt{2\left(\frac{\tan \alpha+\cot \alpha}{1+\tan ^2 \alpha}\right)+\frac{1}{\sin ^2 \alpha}}\) where \(\alpha \in\left(\frac{3 \pi}{4}, \pi\right)\), then \(\frac{d y}{d \alpha}\ \rm at\ \alpha=\frac{5 \pi}{6}\) is
Q3.If f(a + b + 1 – x) = f(x) ∀x, where a and b are fixed positive real numbers, then \(\rm \frac{1}{(a+b)} \int_a^b x(f(x)+f(x+1)) d x\) is equal to
Q4.If \(\rm y=x^{\sec^2x}\times\frac{1}{x^{\tan^2x}}\), then \(\rm \frac{dy}{dx}=?\)
Q5.If y = u2 + log u and u = ex, then find \(\rm \frac{dy}{dx}:\)
Q6.If \(x=a\left(t+\frac{1}{t}\right)\) and \(y=a\left(t-\frac{1}{t}\right)\), then \(\frac{d x}{d y}\) is:
Q7.The derivative of \(\tan ^{-1}\left(\frac{\sqrt{1+x^2}-1}{x}\right)\) with respect to tan-1x is:
Q8.If \(y=x+\frac{x^{3}}{3}+\frac{x^{5}}{5}+\cdots\), then \(\frac{d y}{d x}\) is equal to
Q9.Find the derivative of sin−1x with respect to x assuming it to exist.
Q10.If \(\rm\frac{e^x}{1−x}\) = B0 + B1x + B2x2 + ……. + Bnxn + ……, then the value of (Bn − Bn−1) is

More Differential Calculus Questions

Q1.What is g’(0) equal to? 
Q2.What is h’(0) equal to? 
Q3.What is the least value of f(x)? 
Q4.What is the greatest value of f(x)? 
Q5.What is the maximum value of a cos x + b sin x + c? 
Q6.What is the minimum value of the function f(x) = log10(x2 + 2x + 11)? 
Q7.If log 2 = 0.2614, log 3 = 0.3521, log 6 = ?
Q8.The growth model for a population is Nt = N0ert where Nt is the population at time t, N0 is the initial population and r is the per capita growth rate. How long does it take for the population numbers to double?
Q9.Suppose that the growth rate of the number of individuals (N) in a population in an environment with a carrying capacity K is modelled as \(\frac{d N}{d t}=r N \frac{K-N}{K}\) where r is the per capita growth rate and t is time; r and K are positive constants. At which of the following values of N will the population growth rate be the maximum?
Q10.The population P = P(t) at time ‘t’ of a certain species follows the differential equation dP/dt = 0.5P – 450. If P(0) = 850, then the time at which population becomes zero is:
Suggested Test Series
View All >
AAI ATC Junior Executive 2025 Mock Test Series
467 Total Tests with 3 Free Tests
Start Free Test
AAI Junior Executive (Common Cadre) Mock Test 2023
113 Total Tests with   1 Free Tests
Start Free Test

More Mathematics Questions

Q1.If cosec θ + cot θ = p, then \(\rm\frac{p^2-1}{p^2+1}\) equal:
Q2.In a binomial distribution, if the mean is 6 and the standard deviation is √2, then what are the values of the parameters n and p respectively?
Q3.Three perfect dice D1, D2 and D3 and are rolled. Let x, represent the numbers on D1, D2 and D3 respectively. What is the number of possible outcomes such that x < y < z?
Q4.Three perfect dice are rolled. Under the condition that no two show the same face, what is the probability that one of the faces shown is an ace (one)?
Q5.The occurrence of a disease in an industry is such that the workers have 20% chance of suffering from it. What is the probability that out of 6 workers chosen at random, 4 or more will suffer from the disease?
Q6.Two perfect dice are thrown. What C is the probability that the sum of the numbers on the faces is neither 9 nor 10?
Q7.Urn A contains 2 white and 2 black balls while urn B contains 3 white and 2 black balls. One ball is transferred from urn A to urn B and then a ball is drawn out of urn B. What is the probability that the ball is white?
Q8.A fair coin is tossed till two heads occur in succession. What is the probability that the number of tosses required is less than 6?  
Q9.The mean of the series x1, x2...xn is x̅ If xn is replaced by k, then what is the new mean?
Q10.Let \(\rm \Sigma_{i=1}^9x_i^2=885\) If M is the mean and σ is the standard deviation of  x1, x2, x3.....x9 then what is the value of M2 + σ2?
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
support@testbook.com
Toll Free:1800 833 0800
Office Hours: 10 AM to 7 PM (all 7 days)
Company
About usCareers We are hiringTeach Online on TestbookPartnersMediaSitemap
Products
Test SeriesTestbook PassOnline CoursesOnline VideosPracticeBlogRefer & EarnBooks
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Hot Links： teen patti glory all teen patti game teen patti master gold apk