Differential Calculus Model Questions

11th Standard

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Business Maths

Time : 01:00:00 Hrs
Total Marks : 50
    5 x 1 = 5
  1. The graph of y = 2x2 is passing through

    (a)

    (0,0)

    (b)

    (2,1)

    (c)

    (2,0)

    (d)

    (0,2)

  2. Which one of the following functions has the property f (x) = \(f\left( \frac { 1 }{ x } \right) \)

    (a)

    \(f\left( x \right) =\frac { { x }^{ 2 }-1 }{ x } \)

    (b)

    \(f\left( x \right) =\frac { 1-{ x }^{ 2 } }{ x } \)

    (c)

    f(x) = x

    (d)

    \(f\left( x \right) =\frac { { x }^{ 2 }+1 }{ x } \)

  3. The range of f(x) = |x|, for all \(x\epsilon R\), is

    (a)

    (0, \(\infty \))

    (b)

    (0, \(\infty \))

    (c)

    (-\(\infty \)\(\infty \))

    (d)

    (1, \(\infty \))

  4. A function f(x) is continuous at x = a if \(\lim _{ x\rightarrow a }{ f\left( x \right) } \) is equal to

    (a)

    f(-a)

    (b)

    f\((\frac{1}{a})\)

    (c)

    2f(a)

    (d)

    f(a)

  5. If y = log x then y2 =

    (a)

    \(\frac{1}{x}\)

    (b)

    \(-\frac{1}{x^2}\)

    (c)

    \(-\frac{2}{x^2}\)

    (d)

    e2

  6. 5 x 2 = 10
  7. If \(f(x)=\frac { x+1 }{ x-1 } \) ,then prove that f(f(x))=x

  8. For \(f(x)=\frac { x-1 }{ 3x+1 } \) ,write the expression of \(f\left( \frac { 1 }{ x } \right) \) and \(\frac { 1 }{ f(x) } \)

  9. Find the derivative of the following functions from first principles log (x+1)

  10. Differentiate \({ x }^{ \frac { 2 }{ 3 } }\) from first principles

  11. Find \(\frac { dy }{ dx } \) if x2 + xy + y2 = 100

  12. 5 x 3 = 15
  13. Find  \(\frac{dy}{dx}\)   of the following functions: x = a (θ - sin θ),y = a(1- cosθ)

  14. Differentiate sin3 x with respect to cos3x.

  15. If ey (x + 1) = 1, show that \(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } ={ \left( \frac { dy }{ dx } \right) }^{ 2 }\)

  16. Evaluate \(\underset { x\rightarrow -3 }{ lim } \frac { { x }^{ 3 }+27 }{ { x }^{ 5 }+243 } \)

  17. Evaluate \(\underset { x\rightarrow 0 }{ lim } \frac { 2sinx-sin2x }{ { x }^{ 3 } } \)

  18. 4 x 5 = 20
  19. Draw the graph of the following function f(x)=e-2x

  20. Differentiate: \(\frac { sinx+cosx }{ sinx-cosx } \)with respect to 'x'

  21. Find the derivate of (x3-27)from first principles.

  22. Darw the graph of f(x) = logax; x > 0, a > 0 and \(a\ne 1\).

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