The maximum value of sin x . cos x is
  • \(\frac{1}{4}\)
  • \(\frac{1}{2}\)
  • √2
  • 2√2
At x = \(\frac{5π}{6}\), f (x) = 2 sin 3x + 3 cos 3x is
  • maximum
  • minimum
  • zero
  • neither maximum nor minimum
Maximum slope of the curve y = -x³ + 3x² + 9x – 27 is
  • 0
  • 12
  • 16
  • 32
f(x) = x
  • x = e
  • x = \(\frac{1}{e}\)
  • x = 1
  • x = √e
The maximum value of (\(\frac{1}{x}\))is
  • e
  • e
  • (\(\frac{1}{e}\))
If the volume of a sphere is increasing at a constant rate, then the rate at which its radius is increasing is
  • a constant
  • proportional to the radius
  • inversely proportional to the radius
  • inversely proportional to the surface area
A particle is moving along the curve x = at² + bt + c. If ac = b², then particle would be moving with uniform
  • rotation
  • velocity
  • acceleration
  • retardation
The distance Y metres covered by a body in t seconds, is given by s = 3t² – 8t +The body will stop after
  • 1 s
  • \(\frac{3}{4}\) s
  • \(\frac{4}{3}\) s
  • 4 s
The position of a point in time Y is given by x = a + bt + ct², y = at + bt². Its acceleration at timet Y is
  • b – c
  • b + c
  • 2b – 2c
  • 2\(\sqrt{b^2+c^2}\)
The function f(x) = log (1 + x) – \(\frac{2x}{2+x}\) is increasing on
  • (-1, ∞)
  • (-∞, ∞)
f(x) = (\(\frac{e^{2x}-1}{e^{2x}+1}\)) is
  • an increasing function
  • a decreasing function
  • an even function
  • None of these
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
The function f(x) = cot x + x increases in the interval
  • (1, ∞)
  • (-1, ∞)
  • (0, ∞)
  • (-∞, ∞)
The function f(x) = \(\frac{x}{log x}\) increases on the interval
  • (0, ∞)
  • (0, e)
  • (e, ∞)
  • None of these
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
If f (x) = x³ – 6x² + 9x + 3 be a decreasing function, then x lies in
  • (-∞, -1) ∩ (3, ∞)
  • (1, 3)
  • (3, ∞)
  • None of these
The function f (x) = 1 – x³ – x
  • 1 < x < 5
  • x < 1
  • x > 1
  • all values of x
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
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
2x³ – 6x + 5 is an increasing function, if
  • 0 < x < 1
  • -1 < x < 1
  • x < -1 or x > 1
  • -1 < x < –\(\frac{1}{2}\)
0 h : 0 m : 1 s

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