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If for a continuous function `f,f(0)=f(1)=0,f^(prime)(1)=2a n dy(x)=f(e^x)e^(f(x))` , then `y^(prime)(0)` is equal to a. 1 b. 2 c. 0 d. none of these

A

1

B

2

C

0

D

none of these

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ML KHANNA-LIMITS, CONTINUITY AND DIFFERENTIABILITY -PROBLEM SET (2) (MULTIPLE CHOICE QUESTIONS)
  1. The derivative of f(x) =|x| at x = 0 is:

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  2. For a differentiable function f, the value of lim(h to 0) ([f(x+h)]^(2...

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  3. If for a continuous function f,f(0)=f(1)=0,f^(prime)(1)=2a n dy(x)=f(e...

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  4. The function f(x) = e^(|x|) is

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  5. Let f(x) be defined as f(x) = {{:(sin 2x, 0 lt x lt pi/6),(px + q, p...

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  6. Let f(x) = {{:(-1/|x|, "for " |x| ge 1),(ax^(2)-b, "for " |x| lt 1):},...

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  7. The derivative of f(x) =|x|^(3) at x=0 is:

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  8. If y=|tan (pi/4-x)|, then (dy)/(dx) at x=pi/4 is

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  9. Which of the following functions is differentiable at x = 0 ?

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  10. f(x)=||x|-1| is not differentiable at

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  11. The number of points at which the function f(x) =|x-0.5|+|x-1| + tan x...

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  12. Consider, f(x) = {{:(x^(2)/(|x|), x ne 0),(0, x =0):}

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  13. The function f(x) = (x^(2)-1)|x^(2) -3x+2| + cos(|x|) is not differen...

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  14. Consider the following statements S and R: S: Both sin x and cos x a...

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  15. If f(x) =x^(2) + x^(2)/(1+x^(2)) + x^(2)/(1+x^(2))^(2) + …… + x^(2)/(1...

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  16. Let f(x) be a function satisfying f(x+y)=f(x)+f(y) and f(x)=x g(x)"For...

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  17. Let f(x + y)=f(x)+f (y) and f(x) = x^2 g(x) for all x, y in R, where g...

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  18. A differentiable function f (x) satisfies the condition f(x+y) =f(x) +...

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  19. Let f(x + y) = f(x) f (y) for all x and y. Suppose that f(3) = 3 and f...

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  20. Let f(x+y)=f(x) f(y) and f(x)=1+(sin 2x)g(x) where g(x) is continuous....

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