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If f(x)=x^(2)-3x, then the points at whi...

If `f(x)=x^(2)-3x`, then the points at which `f(x)=f'(x)` are

A

both positive integers

B

both negative integers

C

both irrational

D

one rational and another irrational

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The correct Answer is:
C
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SURA PUBLICATION-DIFFERENTIAL CALCUS - DIFFERENTIABILITY AND METHODS OF DIFFERENTIATION-EXERCISE 10.5
  1. If y=f(x^(2)+2) " and " f'(3)=5, " then " (dy)/(dx) at x=1 is

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  2. If y=1/4u^(4) " and " u=2/3x^(3)+5, " then " (dy)/(dx) is

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  3. If f(x)=x^(2)-3x, then the points at which f(x)=f'(x) are

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  4. If y=1/(a-z), " then " (dz)/(dy) is

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  5. If y=cos(sinx^(2)), " then " (dy)/(dx) " at " x=sqrt(pi/2) is

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  6. If y=mx+c " and " f(0)=f'(0)=1, " then " f(2) is

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  7. If f(x)=xtan^(-1)x, then f'(1) is

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  8. d/dx(e^(x+5logx))

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  9. If the derivative of (ax-5)e^(3x) at x=0 is -13, then the value of a i...

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  10. x=(1-t^(2))/(1+t^(2)), y=(2t)/(1+t^(2)) " then " (dy)/(dx) is

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  11. If x=asintheta " and " y=bcostheta, " then " (d^(2)y)/(dx^(2)) is

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  12. The differential coefficient of log(10)x with respect to log(x)10 is

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  13. If f(x)=x+2, " then " f'(f(x)) at x=4 is

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  14. If y=(1-x)^(2)/x^(2), " then " (dy)/(dx)= is

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  15. If pv = 81, then (dp)/(dv) at v=9 is

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  16. If f(x) = {{:(x-5, "if" , x le 1),(4x^2-9, "if", 1 lt x lt 2),(3x+4 ,"...

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  17. It is given that f'(a) exists,then lim(xrarra)(xf(a) - af(x))/(x - a) ...

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  18. If f(x) = {{:(x+1, "when" , x lt 2),(2x-1, "when" ,x ge 2):}, then f'(...

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  19. If g(x) = (x^(2)+2x+3), f(x) and f(0)=5 and lim(xrarr0)(f(x)-5)/x = 4 ...

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  20. If f(x)={{:(x+2, -1 lt x lt 3), (5, x=3), (8-x, x gt 3):}, then at x=3...

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