English
Hindi

Question

Download Solution PDF

If  f(x) =, where [x] is the Greatest Integer but not larger than x, then  is

This question was previously asked in
NIMCET 2014 Official Paper
Download PDF Attempt in App
View all NIMCET Papers >
  1. -1
  2. 0
  3. 1
  4. Does not exist

Answer (Detailed Solution Below)

Option 4 : Does not exist
Free Tests
View all Free tests >
Free
NIMCET 2020 Official Paper
120 Qs. 480 Marks 120 Mins
Start Now

Detailed Solution

Download Solution PDF

Concept:

Greatest Integer Function:

Greatest Integer Function [x] indicates an integral part of the real number x which is a nearest and smaller integer to x. It is also known as floor of x

  • In general, If n≤ x ≤ n+1 Then [x] = n     (n ∈ Integer)
  • Means if x lies in [n, n+1) then the Greatest Integer Function of x will be n.

 

Calculation:

Given: 

f(x) =

f(x) =

So,  doesn't exists

Download Solution PDF
Latest NIMCET Updates

Last updated on Jun 12, 2025

->The NIMCET 2025 provisional answer key is out now. Candidates can log in to the official website to check their responses and submit objections, if any till June 13, 2025.

-> NIMCET exam was conducted on June 8, 2025.

-> NIMCET 2025 admit card was out on June 3, 2025.

-> NIMCET 2025 results will be declared on June 27, 2025. Candidates are advised to keep their login details ready to check their scrores as soon as the result is out.

-> Check NIMCET 2025 previous year papers to know the exam pattern and improve your preparation.

Exams Tests Super Practice

More Continuity of a function Questions

Q1.Let f : R → be a function given by \(f(x) = \left\lbrace \begin{matrix} \frac{1-\cos 2x}{x^2} & , & x < 0 \\\ α & , & x = 0 \\\ \frac{β \sqrt{1-\cos x}}{x} & , & x>0 \end{matrix} \right.\), where α, β ∈ R. If f is continuous at x = 0, then α2 + β2 is equal to: 
Q2.If the function f(x) = \(\left\{\begin{array}{c} \frac{72^x-9^x-8^x+1}{\sqrt{2}-\sqrt{1+\cos x}} , \quad x\ne0 \\ a \log _e 2 \log _e 3, \quad x= 0 \end{array}\right.\) is continuous at x = 0, then the value of a2 is equal to 
Q3.Let the function f(x) defined as \(f(x)=\frac{x-|x|}{x}\), then
Q4.If f(x) = \(\left\{\begin{array}{l}\rm mx+1, \text { if } x \leq \frac{\pi}{2} \\ \sin \rm x+n, \text { if } x>\frac{\pi}{2}\end{array}\right.\), is continuous at x = \(\frac{\pi}{2}\), then
Q5.If f(x) = x2 sin\(\rm \frac{1}{x}\), where x ≠ 0, then the value of the function f at x = 0, so that the function is continuous at x = 0, is
Q6.The function f(x) = e|x| is
Q7.The function f(x) = cot x is discontinuous on the set
Q8.If f(x) = 2x and g(x) = \(\rm \frac{x^2}{2}\) + 1, then which of the following can be a discontinuous function
Q9.The value of k which makes the function defined by f(x) = \(\left\{\begin{array}{ll}\sin \frac{1}{\rm x}, & \text { if } \rm x \neq 0 \\ \rm k, & \text { if } \rm x = 0\end{array}\right.\), continuous at x = 0 is
Q10.The function f(x) = |x| + |x – 1| is

More Limit and Continuity Questions

Q1.Consider the following statements :  I. f(x) is continuous at x = 0.  Il. f(x) is continuous at x = 1  Which of the statements given above is/are correct? 
Q2.What is f(0.999) + f(1.001) equal to
Q3.What is \(\rm \lim_{x\rightarrow \frac{\pi}{2}}(\sec \theta-\tan \theta)\) equal to? 
Q4.Which one of the following is correct regarding \(\rm \lim_{x\rightarrow 3}\frac{|x-3|}{x-3}\)?
Q5.\(\lim _{x \rightarrow 0} \frac{\int_0^{x^2}(\sin \sqrt{t}) d t}{x^3}\) is equal to : 
Q6.If f : R → R is a function defined by f(x) = [x – 1] cos ((2x – 1)/2)π, where [.] denotes the greatest integer function, then f is:
Q7.\(\lim _{n \rightarrow \infty}\left(\left(\frac{n}{n+1}\right)^α+\sin \frac{1}{n}\right)^n\) where α ∈ Q is equal to  
Q8.If \(\lim _{n \rightarrow \infty}\left(\sqrt{n^2-n-1}+n \alpha+\beta\right)=0\) then 8(α + β) is equal to
Q9.Let f : R → be a function given by \(f(x) = \left\lbrace \begin{matrix} \frac{1-\cos 2x}{x^2} & , & x < 0 \\\ α & , & x = 0 \\\ \frac{β \sqrt{1-\cos x}}{x} & , & x>0 \end{matrix} \right.\), where α, β ∈ R. If f is continuous at x = 0, then α2 + β2 is equal to: 
Q10.If the function \(\rm f(x)=\frac{\sin 3x+\alpha \sin x-\beta \cos 3x}{x^3}\) x ∈ R is continuous at x = 0, then f(0) is equal to : 
Suggested Test Series
View All >
NIMCET Previous Year Papers Mock Test
8 Total Tests with 1 Free Tests
Start Free Test

NIMCET Important Links

Eligibility CriteriaAdmit CardSyllabus and Exam PatternAnswer KeyCut OffBooks

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 gold old version happy teen patti teen patti 100 bonus teen patti mastar teen patti gold download