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The value of `f(0),` so that the function `f(x)=((27-2x)^2-3)/(9-3(243+5x)^(1//5)-2)(x!=0)` is continuous, is given `2/3` (b) 6 (c) 2 (d) 4

A

`2//3`

B

6

C

2

D

4

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The correct Answer is:
C
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ML KHANNA-LIMITS, CONTINUITY AND DIFFERENTIABILITY -PROBLEM SET (2) (MULTIPLE CHOICE QUESTIONS)
  1. Let f(x) =(1- tanx)/(4x-pi), x ne pi/4, x in [0, pi/2]. If f(x) is con...

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  2. The value of f(0), so that the function f(x) = (sqrt(a^(2) -ax + x^(...

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  3. The value of f(0), so that the function f(x)=((27-2x)^2-3)/(9-3(243+5x...

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  4. f(x) ={{:((sqrt(1+px)- sqrt(1-px))/x, -1 le x lt 0),((2x+1)/(x-2), 0 l...

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  5. f(x) =(x-1)^(1/(2-x)) is not defined at x = 2. If f(x) is continuous,...

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  6. The function f(x) = {{:(x^(2)//a, 0 le x lt 1),(a, 1 le x lt sqrt(2)),...

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  7. If f(x) = x^(a) log x and f(0) = 0 then the value of alpha for which ...

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  8. The value of a for which the function f(x)=f(x)={((4^x-1)hat3)/(sin(x...

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  9. If f(x) =(e^(x)-1)^(4)/(sin(x^(2)/lambda^(2))log (1+x^(2)/2)), x ne 0 ...

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  10. Let f(x) = (x(1+ a cos x) - b sinx)/x^(3), x ne 0 f(0) = 1. If f(x) is...

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  11. f(x) = {{:((1- cos 4x)/x^(2), x lt 0),(=a, x =0),(=sqrt(x)/(sqrt(16+sq...

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  12. The function f(x) = {{:(x + asqrt(2) sin x, 0 le x lt pi//4),(2x cotx ...

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  13. In order that the function f(x) = (x+1)^(cot x) is continuous at x=0...

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  14. Function f(x) = (sin 2x)^(tan^(2)2x) is not defined at x=pi/4. If f(x...

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  15. Let f(x)=(tan(pi/4-x))/(cot2x),x!=pi/4 . The value which should be ass...

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  16. If f(x) = (2-(256 -7x)^(1//8))/((5x+32)^(1//5)-2), (x ne 2), then for ...

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  17. The value of lambda that makes the function f(x) = {{:((cos x)^(1//sin...

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  18. Let f''(x) be continuous at x = 0 and f''(0)=4, Then value of lim(x t...

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  19. If the function f(x) = {{:((1+ |sin x|^(a/(sin x))), -pi//6 lt x lt 0)...

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  20. Let f(x) = {{:(-2 sin x, x le -pi//2),(a sin x + b, -pi//2 lt x lt pi/...

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