English
Hindi

Question

Download Solution PDF

Every Cauchy sequence is

This question was previously asked in
UP TGT Mathematics 2016 Official Paper
Download PDF Attempt in App
View all UP TGT Papers >
  1. Unbounded
  2. Bounded
  3. Infinite
  4. None of these

Answer (Detailed Solution Below)

Option 2 : Bounded
Free Tests
View all Free tests >
Free
UP TGT Arts Full Test 1
125 Qs. 500 Marks 120 Mins
Start Now

Detailed Solution

Download Solution PDF

Basic properties of Cauchy sequences:

(i) Every convergent sequence is a Cauchy sequence,

(ii) Every Cauchy sequence of real (or complex) numbers is bounded,

(iii) If in a metric space, a Cauchy sequence possessing a convergent subsequence with limit is itself convergent and has the same limit.

∴ Every Cauchy sequence is bounded

Download Solution PDF
Latest UP TGT Updates

Last updated on May 6, 2025

-> The UP TGT Exam for Advt. No. 01/2022 will be held on 21st & 22nd July 2025.

-> The UP TGT Notification (2022) was released for 3539 vacancies.

-> The UP TGT 2025 Notification is expected to be released soon. Over 38000 vacancies are expected to be announced for the recruitment of Teachers in Uttar Pradesh. 

-> Prepare for the exam using UP TGT Previous Year Papers.

Exams Tests Super Practice

More Cauchy's Equation Questions

Q1.While numerically solving the differential equation \(\frac{dy}{dx} + 2xy^2 = 0, \) y(0) = 1 using Euler’s predictor corrector (improved Euler-Cauchy) method with a step size of 0.2, the value of y after the first step is
Q2.Every Cauchy sequence is
Q3.Cauchy’s linear differential equation \({x^n}\frac{{{d^n}y}}{{d{x^n}}} + {a_1}{x^{n - 1}}\frac{{{d^{n - 1}}}}{{d{x^{n - 1}}}} + \ldots + {a_n}y = f\left( x \right)\) can be reduced to a linear differential equation with constant coefficient by using substitution
Q4.The solution of the differential equation \({x^2}\frac{{{d^2}y}}{{d{x^2}}} - x\frac{{dy}}{{dx}} + y = \log x\) is
Q5.Consider the homogeneous ordinary differential equation  \({x^2}\frac{{{d^2}y}}{{d{x^2}}} - 3x\frac{{dy}}{{dx}} + 3y = 0,\)   x > 0 with y(x) as a general solution. Given that  y(1) = 1 and y(2) = 14 the value of y(1.5), rounded off to two decimal places, is ______.

More Differential Equations Questions

Q1.The partial differential equation obtained by eliminating φ from : φ(x + y + z, x2 + y2 − z2) = 0 is : 
Q2.The general solution of the differential equation \(\frac{d y}{d x}=e^{x-y}+x^{2} e^{-y} \) is
Q3.The solution of the differential equation \(\rm \frac{d^3y}{dx^3}-5.5\frac{d^2y}{dx^2}+9.5\frac{dy}{dx}-5y=0\) is expressed as 𝑦 = 𝐢1𝑒2.5π‘₯ + 𝐢2𝑒𝛼π‘₯ + 𝐢3𝑒𝛽π‘₯ , where 𝐢1, 𝐢2, 𝐢3, 𝛼, and 𝛽 are constants, with α and β being distinct and not equal to 2.5. Which of the following options is correct for the values of 𝛼 and 𝛽?
Q4.Differential equation of the family of curves given by x2 + y2 = 2ax is ________
Q5.Consider the differential equation   \(\rm \frac{dy}{dx}+y ln(y)=0\) If 𝑦(0) = 𝑒, then 𝑦(1) is ________ 
Q6.A differential equation is given as x (t + 2) + 3x (t + 1) + 2x (t) =0; x(0) = 0, x(1) = 1. The solution of this equation will be: 
Q7.If \(\lambda=\frac{[1+(dy/dx)^2]^3}{(d^2y/dx^2)^{2/3}}\), then the degree and order of the above differential equation are respectively
Q8.For the function z = tan-1 \(\frac{y}{x}\) consider the following statements : \({S_1} \equiv x\frac{{\partial z}}{{\partial x}} + y\frac{{\partial z}}{{\partial y}} = 0\) \({S_2} \equiv {x^2}\frac{{{\partial ^2}z}}{{\partial {x^2}}} + 2xy\frac{{{\partial ^2}z}}{{\partial x\partial y}} + {y^2}\frac{{{\partial ^2}z}}{{\partial {y^2}}} = 0\) \({S_3} \equiv \frac{{{\partial ^2}z}}{{\partial {x^2}}} + \frac{{{\partial ^2}z}}{{\partial {y^2}}} = 0\) Which of the following is true?
Q9.If z = f(x + ay) + Ο• (x - ay), then
Q10.The particular integral of difference equation yn+2 - 2yn+1 + yn = n22n is
Suggested Test Series
View All >
UP TGT Mock Test Series 2025
444 Total Tests with 6 Free Tests
Start Free Test
Pedagogy for All Teaching Exams (Paper 1 & 2) - Let's Crack TET!
345 Total Tests with   3 Free Tests
Start Free Test

UP TGT Important Links

Syllabus and Exam PatternEligibility CriteriaAdmit CardAnswer KeyAnswer KeyCut Off

More Engineering Mathematics Questions

Q1.If L = {1, 2, 3, 4, 6, 9, 36} is the lattice find the number of complements 9 is having in the below given Hasse diagram?
Q2.Which of the following statements is/are TRUE for undirected graphs?
Q3.\(\iint \frac{x y}{\sqrt{1-y^{2}}} d x d y\) Over the positive quadrant of the circle x2 + y2 = 1 is __________.
Q4.The real root of the equation x3 − x − 5 = 0 lying between 1 and 2 after first iteration by Newton-Raphson method is ________, if initial approximation is taken as x0 = 2 ∈ [1, 2] : 
Q5.Let X be uniform random variable on [0, 4] and Y be uniform random variable on [0, 1]. If X and Y are independent, then P(max {X, Y} > 3) is equal to : 
Q6.If R and D are the radius and diameter of the graph K4,7, then the ordered pair (R, D) is equal to : 
Q7.The largest number of faces in a simple connected maximal planar graph with 100 vertices is :
Q8.If for the matrix A, A3 = I then A−1 = __________. 
Q9.Energy of power signal is : 
Q10.With usual notations, the properties of maxima and minima under various conditions are __________. I II (P) Maxima (i) r t− s2 = 0 (Q) Minima (ii) rt − s2 < 0 (R) Saddle Point (iii) rt − s2 > 0, r > 0 (S)  Case of failure (iv) rt − s2 > 0, r < 0
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 Β© 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Hot Links： teen patti gold online teen patti download teen patti real money app teen patti master old version teen patti real cash