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###### Jinesh Jain posted an Question
February 08, 2022 • 00:39 am 30 points
• IIT JAM
• Mathematics (MA)

# 9. let f:r r be a continuous function with 13. let s(x)= sin x-x+ and period p>0. then g(r) = s)dt is a g(x) = cosx-1+for xe r. which of the (a.) constant funct

9. Let f:R R be a continuous function with 13. Let S(x)= sin x-x+ and period p>0. Then g(r) = s)dt is a g(x) = cosx-1+for xe R. Which of the (a.) Constant function following statements are correct? (b.) Continuous function (a.) f(x)20 for all x>0 (c.) Continuous function but not (b.) 8 is an increasing function on 0, differentiable (d.) Neither continuous nor differentiable (c.)g is an decreasing function on |0, o 10. Let f:(-1,1) > R be the function defined by (d.) f is a decreasing function on [0, then f(x) =e"l*) 14. 14. Let I=[0,1CR For xe R let p(r) = dist(x,1) =inf {r-y: ye I}. Then (a.) f is decreasing in (-1,0) (a.) o(x) is discontinuous somewhere on R (b.) f is increasing in (0,1) (b.) olx) is continuous on R but not (c.) f(x) =1 has two solutions in (-1,1) continuously differentiable exactly at x =0 (d.) f(x)=1 has no solutions in (-1,1) (c.) olr) is continuous on R but not 11. Let f be a twice differentiable function on continuously differentiable exactly at x= 0 and x=1 R.Given that f"(x)>0 for all xe R, (a.) f(x) =0 has exactly two solution on R (d.) o(x) is differentiable on R . (b.) f(x) =0 has a positive solution if 15. Consider the function f(0) =0 and f'(0) =0 S)= cos(x-5|) + sin (x-3|)+|x+10-(+4) At which Of the following point is f not (c.) f(x) =0 has no positive solution if differentiable? f (0) =0 and f'(0) >>0 (a.) x = 5 (d.) f(x) =0 has no positive solution if (b.) x=3 s(0) = 0 and f'(0) <0 (c.)x=-10 12. Suppose f:R>R is a differentiable (d.) x= 0 function. Then which of the following statements are necessarily true? 16. Define f: R- > Rby if x<0, Then which of the (a.) If f'a) Sr-1 for all xe R (d.) f(0) does not exist (d.) None of these 28A/11, (First Floor) Jia Sarai, Hauz Khas, Near L.L.T., New Delhi-110016, Ph.: (011)-26537527, Cell: 9999183434 & 9899161734, 8588R4478g 103

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