Jinesh Jain posted an Question
February 08, 2022 • 00:22 am 30 points
  • Mathematics (MA)

Let f: rr be defined by f(x)=f]. 9. 14. let f:0,1> r be the points of discontinuity of f are the continuous (a.) only the integral points tunction defined by f(

Let f: RR be defined by f(x)=F]. 9. 14. Let f:0,1> R be The points of discontinuity of f are the continuous (a.) Only the integral points Tunction defined by f(x) =)-2) x-3)(x-4) .Then the maximal subset of R on which b.) All rational numbers (c.) {tn :n is a non-negative integer} f has a continuous extension is (d.) All real numbers (a.)-,3) 10. A monotonic function (a.) Is always continuous (b.)-,3)u(4,o) (b.) Is continuous only if it intermediate value property (c.) R\{3,4 (d.) R (c.) Can be nowhere continuous (d.) Can be discontinuous at finitely many 15. The Continuous function f:R>R points defined by f(x) = (+1)is Which one of the following functions has exactly two points of discontinuity? 11. (a.) Onto but not one-one (b.) One-one but not onto (a.) fG)=if x>0 (a.) f(x)=o if xs0 (c.) Both one-one and onto (d.) Neither one-one nor onto 1 if 0Sxsl (b.) fx)0 otherwise 16. Let f:R >R be a continuous function. If fOCN, then xif 0srsl (c.) fx)10 otherwise (a.) f(R) =N (b.) f(R)CN but f need not be constant (d.) f(x)= 1if r is rational 0 if xis irational (C.) f is unbounded 12 Let f:a, b R be a continuous function (d.) f is a constant function and let f (a) < f(b). Then by intermediate Let f:la,b]> R be a monotonic function. 17. value theorem Then (a.) fla, b]) =[f (a). ftb)] (a.) f is continuous (b.) s(la. b]) =[sla). f(b)] (b.) f is discontinuous at at most two points (c.) f([a, b) c[s(a), f (b)] (c.) f is discontinuous at at finitely many (d.) f([a, b]) + [f (a). f (b)] points 13. (d.) f is discontinuous at at most countable Consider the function f:R R defined if x is rational, points Let S by f(x)= 2x-1, if x is irrational Let f: 0 10) >[0,10 be a continuous 18. be the set of points where f is continuous. Then mapping. Then (a.) f need not have any fixed point (a.) S = {1} (b.) f has at least 10 fixed points b.) S = {-1} (c.) f has at least 9 fixed points (c.) S=1,1} (d.) f has at least one fixed point (d.) S = o IIT Khas, Near I.LT., New Delhi-110016, Ph.: (011)-26537527, Cell: 9999183434 & 9899161734, 8588844789 udomy com: Website: www.dipsacademv.com 178

1 Answer(s) Answer Now
  • Anonymous User Best Answer

    9. f(x)=[x] is discontinue at x=n for all n€Z so f(x)=[x²] is discontinue at x²=n=> x=±√n for all n€N 10 monotonic fun always continus 11 b f is discontinus at 0,1 bcz f(0+)=1 f(0-)=0 and f(1+)=0 f(1-)=1


    sir, will you please send the solutions of question no. 12, 14, 15, 16, 17, 18


Do You Want Better RANK in Your Exam?

Start Your Preparations with Eduncle’s FREE Study Material

  • Updated Syllabus, Paper Pattern & Full Exam Details
  • Sample Theory of Most Important Topic
  • Model Test Paper with Detailed Solutions
  • Last 5 Years Question Papers & Answers