Differential Calculus Book Back Questions

11th Standard

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Business Maths

Time : 00:45:00 Hrs
Total Marks : 30
    5 x 1 = 5
  1. If f(x) = x2 - x + 1, then f (x + 1) is

    (a)

    x2

    (b)

    x

    (c)

    1

    (d)

    x2 + x + 1

  2. The graph of the line y = 3 is

    (a)

    Parallel to x-axis

    (b)

    Parallel to y-axis

    (c)

    Passing through the origin

    (d)

    Perpendicular to x-axis

  3. 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)

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

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

    (a)

    (0, \(\infty \))

    (b)

    (0, \(\infty \))

    (c)

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

    (d)

    (1, \(\infty \))

  5. 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)

  6. 3 x 2 = 6
  7. Determine whether the following functions are odd or even?
    f(x) = x2-|x|

  8. If f(x) = 2x, show that f(x) . f(y) = f(x + y)

  9. Evaluate: \(\underset { x\rightarrow a }{ lim } \frac { { x }^{ \frac { 3 }{ 5 } }-{ a }^{ \frac { 3 }{ 5 } } }{ { x }^{ \frac { 1 }{ 5 } }-{ a }^{ \frac { 1 }{ 5 } } } \)

  10. 3 x 3 = 9
  11. Differentiate sin2 x with respect to x2.

  12. If \(\lim _{ x\leftarrow 2 }{ \frac { { x }^{ n }-2^{ n } }{ x-2 } =448 } \) ,then find the least positive integer n

  13. Draw the graph y = 9 - x2

  14. 2 x 5 = 10
  15. Draw the graph of the following function \(f(x)=\frac { |x| }{ x } \)

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

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