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If f(x+k) + f(x) = 0 AA x in R and k in ...

If `f(x+k) + f(x) = 0 AA x in R and k in R^(+)`, then the period of `f(x)` is

A

0

B

`(pi)/(2)`

C

2K

D

Does not exist

Text Solution

Verified by Experts

The correct Answer is:
C
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AAKASH SERIES-PERIODICITY AND EXTREME VALUES-Practice Sheet (Exericise-I) Level-I (Straight Objective Type Questions)
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  2. Period of cos x cos(60^(@) - x) cos (60^(@) + x) is

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  3. Period of sin(e^( tan x) + e^( cot x) ) is

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  4. The period of sin^4 x + cos^(4) x is

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  5. The period of sin^(3) x + cos^(3) x is

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  6. Period of 2 sin^(3) x - 3 cos^(3) x is

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  7. Period of cos (x+ (x)/(3) + (x)/(3^2) + …..) is

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  8. The period of tan(x+2x+3x.... nx) is

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  9. The period of ( tan theta -(1)/(3) tan^(3) theta ) ((1)/(3) - tan^(2) ...

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  10. The period of the function f(theta) = sin ((theta)/( 3)) + cos ((theta...

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  11. The period of f(x) = cos (x /3) + sin (x/2) is

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  12. Period of cos "" (3x)/(5) + 2 sin"" (2x)/( 7) - 5 cot 14 x is

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  13. The period of ( sin(2pix + a) )/( sin (2pix + b) ) is

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  14. If the period of (sin nx)/( sin"" (x)/(n) ) is 4pi then n=

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  15. Period of sin sqrt(x) + cos sqrt( x) =

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  16. Period of tan((3pix)/(4) ) - 2 sec ((pix)/( 3)) + 5 sin((2pix)/( 5)) i...

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  17. If f(x+k) + f(x) = 0 AA x in R and k in R^(+), then the period of f(x)...

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  18. If f(x) is an odd periodic function with period 2, then f(4)=

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  19. The period of the function f(x) = p|sin x| + p^(2)|cos x| + g(p) is (p...

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  20. The period of function f(x) = {x} + tan^(2) pi x+ | sin 3pix| is

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