The sides of an equilateral triangle are increasing at the rate of 2cm/sec. The rate at which the are increases, when side is 10 cm is
  • 10 cm²/s
  • √3 cm²/s
  • 10√3 cm²/s
  • \(\frac{10}{3}\) cm²/s
A ladder, 5 meter long, standing oh a horizontal floor, leans against a vertical wall. If the top of the ladder slides downwards at the rate of 10 cm/sec, then the rate at which the angle between the floor and the ladder is decreasing when lower end of ladder is 2 metres from the wall is
  • \(\frac{1}{10}\) radian/sec
  • \(\frac{1}{20}\) radian/sec
  • 20 radiah/sec
  • 10 radiah/sec
The curve y – x
  • a vertical tangent (parallel to y-axis)
  • a horizontal tangent (parallel to x-axis)
  • an oblique tangent
  • no tangent
The equation of normal to the curve 3x² – y² = 8 which is parallel to the line ,x + 3y = 8 is
  • 3x – y = 8
  • 3x + y + 8 = 0
  • x + 3y ± 8 = 0
  • x + 3y = 0
If the curve ay + x² = 7 and x³ = y, cut orthogonally at (1, 1) then the value of a is
  • 1
  • 0
  • -6
  • 6
If y = x
  • 0.32
  • 0.032
  • 5.68
  • 5.968
The equation of tangent to the curve y (1 + x²) = 2 – x, w here it crosses x-axis is:
  • x + 5y = 2
  • x – 5y = 2
  • 5x – y = 2
  • 5x + y = 2
The points at which the tangents to the curve y = x² – 12x +18 are parallel to x-axis are
  • (2, – 2), (- 2, -34)
  • (2, 34), (- 2, 0)
  • (0, 34), (-2, 0)
  • (2, 2),(-2, 34).
The tangent to the curve y = e
  • (0, 1)
  • (-\(\frac{1}{2}\), 0)
  • (2, 0)
  • (0, 2)
The slope of tangent to the curve x = t² + 3t – 8, y = 2t² – 2t – 5 at the point (2, -1) is
  • \(\frac{22}{7}\)
  • \(\frac{6}{7}\)
  • \(\frac{-6}{7}\)
  • -6
The two curves; x³ – 3xy² + 2 = 0 and 3x²y – y³ – 2 = 0 intersect at an angle of
  • \(\frac{π}{4}\)
  • \(\frac{π}{3}\)
  • \(\frac{π}{2}\)
  • \(\frac{π}{6}\)
The interval on which the function f (x) = 2x³ + 9x² + 12x – 1 is decreasing is
  • [-1, ∞]
  • [-2, -1]
  • [-∞, -2]
  • [-1, 1]
Let the f: R → R be defined by f (x) = 2x + cos x, then f
  • has a minimum at x = 3t
  • has a maximum, at x = 0
  • is a decreasing function
  • is an increasing function
y = x (x – 3)² decreases for the values of x given by
  • 1 < x < 3
  • x < 0
  • x > 0
  • 0 < x <\(\frac{3}{2}\)
The function f(x) = 4 sin³ x – 6 sin²x + 12 sin x + 100 is strictly
  • increasing in (π, \(\frac{3π}{2}\))
  • decreasing in (\(\frac{π}{2}\), π)
  • decreasing in [\(\frac{-π}{2}\),\(\frac{π}{2}\)]
  • decreasing in [0, \(\frac{π}{2}\)]
Which of the following functions is decreasing on(0, \(\frac{π}{2}\))?
  • sin 2x
  • tan x
  • cos x
  • cos 3x
The function f(x) = tan x – x
  • always increases
  • always decreases
  • sometimes increases and sometimes decreases
  • never increases
If x is real, the minimum value of x² – 8x + 17 is
  • -1
  • 0
  • 1
  • 2
The smallest value of the polynomial x³ – 18x² + 96x in [0, 9] is
  • 126
  • 0
  • 135
  • 160
The function f(x) = 2x³ – 3x² – 12x + 4 has
  • two points of local maximum
  • two points of local minimum
  • one maxima and one minima
  • no maxima or minima
0 h : 0 m : 1 s

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