CBSE  /  Class 12  /  Maths  /  Application of Derivatives

  • 1. 
    f(x) = (\(\frac{e^{2x}-1}{e^{2x}+1}\)) is

  • an increasing function
  • a decreasing function
  • an even function
  • None of these

  • 2. 
    If f (x) = \(\frac{x}{sin x}\) and g (x) = \(\frac{x}{tan x}\), 0 < x ≤ 1, then in the interval

  • both f (x) and g (x) are increasing functions
  • both f (x) and g (x) are decreasing functions
  • f(x) is an increasing function
  • g (x) is an increasing function

  • 3. 
    The function f(x) = cot x + x increases in the interval

  • (1, ∞)
  • (-1, ∞)
  • (0, ∞)
  • (-∞, ∞)

  • 4. 
    The function f(x) = \(\frac{x}{log x}\) increases on the interval

  • (0, ∞)
  • (0, e)
  • (e, ∞)
  • None of these

  • 5. 
    The value of b for which the function f (x) = sin x – bx + c is decreasing for x ∈ R is given by

  • b < 1
  • b ≥ 1
  • b > 1
  • b ≤ 1

  • 6. 
    If f (x) = x³ – 6x² + 9x + 3 be a decreasing function, then x lies in

  • (-∞, -1) ∩ (3, ∞)
  • (1, 3)
  • (3, ∞)
  • None of these

  • 7. 
    The function f (x) = 1 – x³ – x

  • 1 < x < 5
  • x < 1
  • x > 1
  • all values of x

  • 8. 
    Function, f (x) = \(\frac{λ sin x+ 6 cos x}{2 sin x + 3 cos x}\) is monotonic increasing, if

  • λ > 1
  • λ < 1
  • λ < 4
  • λ > 4

  • 9. 
    The length of the longest interval, in which the function 3 sin x – 4 sin³ x is increasing is

  • \(\frac{π}{3}\)
  • \(\frac{π}{2}\)
  • \(\frac{3π}{2}\)
  • π

  • 10. 
    2x³ – 6x + 5 is an increasing function, if

  • 0 < x < 1
  • -1 < x < 1
  • x < -1 or x > 1
  • -1 < x < –\(\frac{1}{2}\)
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