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If f(x)={:{(x sin x", for " 0 lt x le pi...

If `f(x)={:{(x sin x", for " 0 lt x le pi/2),(pi/2 sin (pi+x)", for " pi/2 lt x lt pi):}`, then

A

`f(x)` is discontinuous at `x= pi/2`

B

`f(x)` is continuous at `x=pi/2`

C

`f(x)` is continuous at `x=0`

D

`f(x)` is discontinuous at `x=0`

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Verified by Experts

The correct Answer is:
A
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NIKITA PUBLICATION-CONTINUITY-MULTIPLE CHOICE QUESTIONS
  1. If f(x)={:{((sin 2x)/(sqrt(1-cos 2x))", for " 0 lt x lt pi/2),((cos x)...

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  2. If f(x)={:{(x-1", for " 1 le x lt 2),(2x+3", for " 2 le x le 3):}, the...

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  3. If f(x)={:{(x sin x", for " 0 lt x le pi/2),(pi/2 sin (pi+x)", for " p...

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  4. If f(x) is continuous at x=0, where f(x)={((sin x)/(x)+cos x", for " ...

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  5. If f(x)={:{(x+2", if " x le 4),(x+4", if " x gt 4):}, then

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  6. If f(x)={:{(2x", if " x lt 2),(2", if " x=2),(x^(2)", if " x gt2):}, t...

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  7. If f(x)={:{(x-1", for " 1 le x lt 2),(2", for " x=2),(2x-3", for " 2 l...

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  8. If f(x)={:{(x^(2)", for " x le 1),(x+3", for " x gt 1):}, then at x=1

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  9. If f(x)=sqrt(x-2), for 2 lt x lt 4, then f(x) is

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  10. If f(x)={:{(1-x", for " 0 lt x le 1), ( 1/2 ", for " x=0):}, then in [...

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  11. If f(x)={:{(3x+5", for " 0 le x lt 3),(2x+8", for " 3 le x lt 5),(x+13...

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  12. If f(x)={:{((sinx)/(x)", for " x lt 0),(x+1", for " x ge 0):}, then

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  13. If f(x)={((2x+5)/(x+1)", for " 0 le x lt 2),(4x-5", for " 2 le x le 4)...

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  14. If f(x)={:{((sin2x)/(sqrt(1-cos2x))", for " 0 lt x le pi/2),((cos x)/(...

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  15. If f(x)={:{(x", for " 0 le x lt 1),(2", for " x=1),(x+1", for " 1 lt x...

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  16. If f(x)=(x^(3)+3x+5)/(x^(3)-3x+2) in [0, 5], then f is

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  17. If f(x)=(x+1)/((x-2)(x-5)), then in [4, 6]

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  18. If f(x)=(x+1)/((x-2)(x-5)), then in [0, 1]

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  19. If f(x)={:{(x", for " x ge 0),(x^(2)", for " x lt 0):}, then f is

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  20. If f(x)={:{(x^(2)-4", for " 0 le x le 2),(2x+3", for " 2 lt x le 4),(x...

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