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If f(x)={(mx+1" , if "xle(pi)/(2)),...

If `f(x)={(mx+1" , if "xle(pi)/(2)),(sinx+n" , if "xgt(pi)/(2)):}`, is continuous at x=`(pi)/(2)`, then

A

`m=1,n=0`

B

`m=(npi)/(2)+1`

C

`n=(mpi)/(2)`

D

`m=n=(pi)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
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ACCURATE PUBLICATION-CONTINUITY-QUESTIONS CARRYING 1 MARKS (MCQ.s (TYPE-I))
  1. If f(x)={(kx+2" , "xle5),(3x-4" , "xgt5):} is continuous at ...

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  2. If f(x)= {(mx+1,,x,le,5),(3x-5,,x,>,5):} is continuous, then the value...

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  3. If f(x)= {(mx-1,,x,le,5),(3x-5,,x,>,0):} is continuous, then the value...

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  4. If f(x)= {(kx^2,,x,<,2),(3,,x,ge,2):} is continuous at x = 2, then the...

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  5. If f(x) ={(kx^2),(3):}, ((x <3),(x ge3)) and f is continuous at x = 3 ...

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  6. f(x) = {((sin x)/(x),,x,ne,0),(k-1,,x,=,0):} is continuous at x = 0, t...

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  7. If function defined by : f(x)= {((sin3x)/(2x),,x,ne,0),(k+1,,x,=,0):} ...

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  8. If function defined by : f(x)= {((sin3x)/(4x),,x,ne,0),(k+1,,x,=,0):} ...

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  9. If f(x) = {((sin 5x)/(2x),,x,ne,0),(k,,x,=,0):} is continuous at x = 0...

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  10. The function f(x) = {{:(("sin x")/(x)+ cos x ,if x != 0),(k , if x = 0...

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  11. The function f(x) = [x], where [x] denotes the greatest integer functi...

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  12. The number of points at which the function f(x)=(1)/(x-[x]) is not con...

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  13. The function given by f(x)=tax x is discontinuous on the set

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  14. The function f(x)=|x|+|x-1| is

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  15. The value of 'k' which makes the function defined by : f(x) = {:{(sin(...

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  16. If (x)=2x and g(x)=(x^(2))/(2)+1, then which of the following can be a...

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  17. The function f(x)=(4-x^(2))/(4x-x^(3)) is

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  18. The function f(x)=cotx is discontinuous on the set

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  19. If f(x)=x^(2)"sin"(1)/(x), where xne0 then the value of the function f...

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  20. If f(x)={(mx+1" , if "xle(pi)/(2)),(sinx+n" , if "xgt(pi)/(2...

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