English
Hindi

Question

Download Solution PDF

/dx is equal to:

This question was previously asked in
ISRO Scientist Electronics 2024 Official Paper
Attempt in App
View all ISRO Scientist Papers >
  1. sin(x)
  2. ex
  3. cos(x)
  4. tan(x)

Answer (Detailed Solution Below)

Option 3 : cos(x)
Free Tests
View all Free tests >
Free
ISRO Scientist/Engineer Fluid Mechanics Mock Test
20 Qs. 20 Marks 25 Mins
Start Now

Detailed Solution

Download Solution PDF

Concept:

The given function is a power series:

This is the Taylor (Maclaurin) series expansion of .

Calculation:

Differentiate both sides with respect to :

This new series is the Maclaurin expansion of .

Download Solution PDF
Latest ISRO Scientist Updates

Last updated on Jun 24, 2025

-> ISRO Scientist Engineering apply online 2025 link has been activated (ISRO:ICRB:03(CEPO):2025).

-> A total of 39 vacancies are announced for the ISRO recruitment in Civil, RAC and other disciplines

-> ISRO Scientist Engineering recruitment 2025 notification has been released for 320 vacancies. The last date to fill ISRO application form is June 16 (Advt No. ISRO:ICRB:02(EMC):2025).

-> ISRO Scientist Engineer recruitment 2025 for 31 vacancies has been released. 

->ISRO Scientist recruitment 2025 notification has been released. 

->The last date to apply for ISRO scientist recruitment 2025 is May 30 ( Advt.No. ISRO:ICRB:01:(EMC):2025). 

->Candidates with BE/BTech degree in the respective discipline can only apply for ISRO Scientist recruitment 2025. 

-> Candidates can refer ISRO Scientist previous year paper to prepare for the exam. 

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

More Analysis Questions

Q1.What is the cardinality of the set of real solutions of ex + x = 1?
Q2.Let u = u(x, t) be the solution of the following initial value problem  \(\rm \left\{\begin{matrix}u_t+2024u_x=0,&x ∈ R, t>0\\\ u(x, 0)=u_0(x), &x ∈ R\end{matrix}\right.\) where u0 : ℝ → ℝ s an arbitrary C1 function. Consider the following statements:  S1 : If At = {x ∈ ℝ : u(x, t) < 1} and |At| denotes the Lebesgue measure of A, for every t ≥ 0, then |At| = |A0|, ∀t > 0 S2 : If u0 is Lebesgue integrable, then for every t > 0, the function x → u(x, t) is Lebesgue integrable. 
Q3.Let (an)n≥1 be a bounded sequence in ℝ. Which of the following statements is FALSE? 
Q4.Consider the set A = {x ∈ ℚ : 0 < (√2 - 1)x < √2 + 1} as a subset of ℝ. Which of the following statements is true?
Q5.For each n ≥ 1 define fn : ℝ → ℝ by \(\rm f_n(x)=\frac{x^2}{√{x^2+\frac{1}{n}}}, \) x ∈ ℝ where √ denotes the non-negative square root. Wherever \(\rm \lim_{n \rightarrow \infty}f_n(x)\) exists, denote it by f(x). Which of the following statements is true? 
Q6.Let \(\rm S =\left\{x \in R:x >1 \ and \ \frac{1-x^4}{1-x^3}>22\right\}\) Which of the following is true about S? 
Q7.Let C be the collection of all sets S such that the power set of S is countably infinite. Which of the following statements is true? 
Q8.Let 𝑐00 = {(𝑥1, 𝑥2, 𝑥3, … ) ∶ 𝑥𝑖 ∈ ℝ, 𝑖 ∈ ℕ, 𝑥𝑖 ≠ 0 only for finitely many indices 𝑖}. For (𝑥1, 𝑥2, 𝑥3, … ) ∈ 𝑐00, let ‖(𝑥1, 𝑥2, 𝑥3, … )‖∞ = sup{|𝑥𝑖 | ∶ 𝑖 ∈ ℕ}. Define 𝐹, 𝐺 ∶ (𝑐00, ‖⋅‖∞) → (𝑐00, ‖⋅‖∞) by 𝐹((𝑥1, 𝑥2, … , 𝑥𝑛, … )) = \(\rm \left((1+x)_{x_1}, (2+\frac{1}{2})x_2,..., (n+\frac{1}{n})x_n,...\right)\) 𝐺((𝑥1, 𝑥2, … , 𝑥𝑛, … )) = \(\rm \left(\frac{x_1}{1+1},\frac{x_2}{2+\frac{1}{2}},..., \frac{x_n}{n+\frac{1}{n}},..\right)\) for all (𝑥1, 𝑥2, … , 𝑥𝑛, … ) ∈ 𝑐00. Then
Q9.Let ℓ2 = {(𝑥1, 𝑥2, 𝑥3, … ) ∶ 𝑥𝑛 ∈ ℝ for all 𝑛 ∈ ℕ and \(\rm \Sigma_{n=1}^\infty x_n^2<\infty \}\) For a sequence (𝑥1, 𝑥2, 𝑥3, … ) ∈ ℓ2 , define ‖(𝑥1, 𝑥2, 𝑥3, … )‖2 = \(\rm (\Sigma_{n=1}^\infty x_n^2)^{\frac{1}{2}}\) Let 𝑆 ∶ (ℓ2 , ‖⋅‖2) → (ℓ2 , ‖⋅‖2) and 𝑇 ∶ (ℓ2 , ‖⋅‖2) → (ℓ2 , ‖⋅‖2) be defined by 𝑆(𝑥1, 𝑥2, 𝑥3, … ) = (𝑦1, 𝑦2, 𝑦3, … ), where 𝑦𝑛 = \(\rm \left\{\begin{matrix}0,&n=1\\\ x_{n-1},& n\ge2\end{matrix}\right.\) 𝑇(𝑥1, 𝑥2, 𝑥3, … ) = (𝑦1, 𝑦2, 𝑦3, … ), where 𝑦𝑛 = \(\rm \left\{\begin{matrix}0,&n\ is\ odd\\\ x_{n},& n\ is\ even\end{matrix}\right.\) Then
Suggested Test Series
View All >
ISRO Scientist Mock Test 2025
119 Total Tests with 3 Free Tests
Start Free Test
ISRO Scientist Electronics Mock Test
58 Total Tests with   1 Free Tests
Start Free Test

More Mathematical Science Questions

Q1.What is the cardinality of the set of real solutions of ex + x = 1?
Q2.Let A be a 10 x 10 real matrix. Assume that the rank of A is 7. Which of the following statements is necessarily true? 
Q3.Let a point P be chosen at random on the line segment AB of length α. Let Z1 and Z2 denote the lengths of line segments AP and BP respectively. Then the value of E(|Z1 - Z2|) Is 
Q4.Consider the contour γ given by \(\rm \gamma (\theta)=\left\{\begin{matrix}e^{2i \theta}&for\ \theta \in [0, \pi /2]\\\ 1+2e^{2i\theta}&for\ \theta \in [\pi/2, 3\pi/2]\\\ e^{2i\theta}&for\ \theta \in [3\pi/2, 2\pi]\end{matrix}\right.\) Then what is the value of \(\rm \int_{\gamma}\frac{dz}{z(z-2)}\)?
Q5.Let X1....X10 be a random sample from a distribution with the probability density function \(\rm f(x|θ)=\left\{\begin{matrix}θ x^{θ-1}, & if \:0<x<1\\\ 0, & otherwise,\end{matrix}\right.\) where θ > 0 Is an unknown parameter. The prior distribution of θ is given by   \(\rm \pi (θ)=\left\{\begin{matrix}θ e^{-θ}, & if\ θ>0\\\ 0, & otherwise,\end{matrix}\right.\) The Bayes estimator of θ under squared error loss is  
Q6.For a quadratic form f(x, y, z) ∈ ℝ[x, y z], we say that (a, b, c) ∈ ℝ3 is a zero of f if f(a, b, c) = 0. Which of the following quadratic forms has at least one zero different from (0, 0, 0)? 
Q7.Let A : ℝm → ℝn be a non-zero linear transformation. Which of the following statements is true? 
Q8.Let X1, X2 be a random sample from a population having probability density function f ∈ { f0, f1} where  \(\rm f_0(x)=\left\{\begin{matrix}\frac{1}{2}& if\ 0\le x\le 2\\\ 0&otherwise\end{matrix}\right.\ and \ \rm f_1(x)=\left\{\begin{matrix}\frac{1}{4}& if\ 0\le x\le 4\\\ 0&otherwise\end{matrix}\right.\) For testing the null hypothesis H0 : f = f0 against the alternate hypothesis H1 : f = f1, the power of a most powerful test of size α = 0.05 is equal to  
Q9.Let V be the real vector space of 2 x 2 matrices with entries in ℝ. Let T : V → V denote the linear transformation defined by T(B) = AB for all B ∈ V, where \(\rm A=\begin{pmatrix}2&0\\\ 0&1\end{pmatrix}\). What is the characteristic polynomial of T? 
Q10.The expected number of distinct units in a simple random sample of 3 units drawn with replacement from a population of 100 units is  
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 teen patti game - 3patti poker teen patti club teen patti master gold apk