JEE Questions for Maths Applications Of Derivatives Quiz 2 - MCQExams.com

The point on the curve y = x3 at which the tangent to the curve is parallel to the X-axis is
  • (2, 2)
  • (3, 3)
  • (4, 4)
  • (0, 0)
The equation of normal to the curve x2y = x2 - 3x + 6 at the point with abscissa x = 3 is
  • 3x + 27y = 79
  • 27x - 3y = 79
  • 27x + 3y = 79
  • 3x - 27y = 79
The maximum area of the rectangle that can be inscribed in a circle of radius r is
  • πr2
  • r2
  • πr2/4
  • 2r2
The length of the subtangent to the curve x2 y2 = a4 at (-a, a) is
  • a/2
  • 2a
  • a
  • a/3
If the curves x2 = 9A(9 - y) and x2 = A(y +intersect; orthogonally, then the value of A is
  • 3
  • 4
  • 5
  • 7
  • 9
The greatest value of sin3 x + cos3 x is
  • 1
  • 2
  • √2
  • √3
The equation of the normal line to the curve y = x loge x parallel to 2x - 2y + 3 = 0 is
  • x + y = 3e-2
  • x - y = 6e-2
  • x - y = 3e-2
  • x - y = 6e2
A population p(t) of 1000 bacteria introduced into nutrient medium grows according to the relation p(t) = 1000 + (1000t/100 + t2). The maximum size of this bacterial population is
  • 1100
  • 1250
  • 1050
  • 5250
The points on the curve y = 2x2 - 6x - 4 at which the tangent is parallel to the X - axis is

  • Maths-Applications of Derivatives-9071.png
  • 2)
    Maths-Applications of Derivatives-9072.png

  • Maths-Applications of Derivatives-9073.png
  • (0, -4)

  • Maths-Applications of Derivatives-9074.png
If x = t2 and y = 2t, then equation of the normal at t = 1 is
  • x + y - 3 = 0
  • x + y - 1 = 0
  • x + y + 1 = 0
  • x + y + 3 = 0
If tangent to the curve x = at2, y = 2a is perpendicular to X - axis, then its point of contact is
  • (a, a)
  • (0, a)
  • (0, 0)
  • (a, 0)
The perimeter of a sector is a constant. If its area is to be maximum, then the sectorial angle is

  • Maths-Applications of Derivatives-9078.png
  • 2)
    Maths-Applications of Derivatives-9079.png

  • Maths-Applications of Derivatives-9080.png

  • Maths-Applications of Derivatives-9081.png
If ST and SN are the lengths of the subtangent and the subnormal at the point θ = π/2 on the curve x = a(θ + sin θ), y = a(1 - cos θ), a ≠ 1, then
  • ST = SN
  • ST = 2SN
  • ST2 = aSN3
  • ST3 = aSN
The length of the subtangent at any point (x1, y1) on the curve y = ax (a >is
  • 2 log a
  • 1/log a
  • log a

  • Maths-Applications of Derivatives-9084.png
The absolute maximum of x40 - x20 on the interval [0, 1] is
  • -1/4
  • 0
  • 1/4
  • 1/2
The point on the curve √x + √y = √a, the normal at which is parallel to the X - axis is
  • (0, 0)
  • (0, a)
  • (a, 0)
  • (a, a)
If f(x) = 1 + 2x2 + 22 x4 + ...+210 x20. Then, f(x) has
  • more than one minimum
  • exactly one minimum
  • at least one maximum
  • None of the above

Maths-Applications of Derivatives-9089.png
  • -1, 1
  • -2, 2
  • -3, 3
  • -4, 4
The equation of the tangent to the curve x = 2 cos3 θ and y = sin3θ at the point, θ = π/4 is
  • 2x + 3y = 3√2
  • 2x - 3y = 3√2
  • 3x + 2y = 3√2
  • 3x + 2y = 3√2
The minimum value of 4e2x + 9e-2x is
  • 11
  • 12
  • 10
  • 14
Let f '(x) be differentiable for all x. If f(= - 2 and f '(x) ≥ 2, ∀ x ϵ [1, 6], then
  • f(< 8
  • f(≥ 8
  • f(≥ 5
  • f(≤ 5
The value of c from the Lagrange's mean value theorem for which
Maths-Applications of Derivatives-9094.png
  • 5
  • 1
  • √15
  • None of these
What are the value of c for while Rolle's theorem for the functions f(x) = x3 - 3x2 + 2x in the interval [0, 2] is verified?
  • c = ± 1
  • c = 1 ± 1/ √3
  • c = ± 2
  • None of these
The function xx is increasing, when
  • x > 1/e
  • x < 1/e
  • x < 0
  • ∀ x
If f(x) = x3 and g(x) = x3 - 4x in -2 ≤ x ≤ 2, then consider the statements
I f(x) and g(x) satisfy mean value theorem.
II f(x) and g(x) both satisfy rolle's theorem.
of these Statements
  • I and II are correct
  • Only I is correct
  • None is correct
  • I and II are correct
The function f(x) = 2x3 - 15x2 + 36x + 6 is strictly decreasing in the interval
  • (2, 3)
  • (-∞, 2)
  • (3, 4)
  • (-∞,∪(4, ∞)
  • (-∞,∪ (3, ∞)
If f(x) be a differentiable function in [2, 7]. If f(= 3 and f '(x) ≤ 5 for all x in (2, 7), then the maximum possible value of f(x) at x = 7 is
  • 7
  • 15
  • 28
  • 14
If f(x) is differentiable and strictly increasing function, then the value of
Maths-Applications of Derivatives-9101.png
  • -1
  • 0
  • 1
  • 2
The function x - cot x
  • never decreases
  • always increases
  • always decreases
  • sometimes increases and sometimes decreases
If f is a real valued differentiable function, such that f(x) f ' (x) < 0 for all real x, then
  • f(x) must be an increasing function
  • f(x) must be decreasinf function
  • |f(x)| mus be increasing function
  • |f(x)| must be decreasing function
Rolle's theorem is applicable in the interval [-2, 2] for the function
  • f(x) = x2
  • f(x) = 4x4
  • f(x) = 2x3 + 3
  • f(x) = π|x|
Which of the following function is decreasing on (0, π/?
  • sin 2x
  • cos 3x
  • tan x
  • cos 2x
The value of c in mean value theorem for the function f(x) = 2x2 + 3x + 4 in the interval [1, 2] is
  • 1/2
  • 1/3
  • 3/2
  • 2/3
The function f(x) = [x(x - 2)]2 is increasing in the set
  • (-∞,∪ (2, ∞)
  • (-∞, 1)
  • (0,∪ (2, ∞)
  • (1, 2)
  • (0, 2)

Maths-Applications of Derivatives-9109.png
  • increasing when x > 0
  • strictly increasing when x > 0
  • strictly increasing at x = 0
  • not continuous at x = 0 and so it is not increasing when x > 0
The function f(x) = ax + b is strictly increasing for all real x, if
  • a > 0
  • a < 0
  • a = 0
  • a ≤ 0
If f(x) = kx - cos x is monotonically increasing for all x ϵ R, then
  • K > - 1
  • K < 1
  • K > 1
  • None of these
The value of c in (0,satisfying the mean value theorem for the function f(x) = x(x - 1)2, x ϵ [0, 2] is equal to
  • 3/4
  • 4/3
  • 1/3
  • 2/3
  • 5/3
In which of the following functions Rolle's theorem is applicable ?

  • Maths-Applications of Derivatives-9114.png
  • 2)
    Maths-Applications of Derivatives-9115.png

  • Maths-Applications of Derivatives-9116.png

  • Maths-Applications of Derivatives-9117.png
If the mean value theorem is f(b) - (b - a)f '(c). Then, for the function x2 - 2x + 3 in [1, 3/2], the value of c is
  • 6/5
  • 5/4
  • 4/3
  • 7/6
A function f is defined f(x) = ex sin x in [0, π]. Which of the following is not correct ?
  • f is continuous in [0, π]
  • f is differentiable in [0, π]
  • f(= f(π)
  • Rolle's theorem is not true in [0, π]
The function f(x) = (9 - x2)2 increases in
  • (-3,∪(3, ∞)
  • (-∞, -∪ (3, ∞)
  • (-∞, -∪ (0, 3)
  • (-3, 3)
  • (3, ∞)
If a < 0, the function (eax + e-ax) is a decreasing function for all values ofx, where
  • x < 0
  • x > 0
  • x < 1
  • x > 1
The function f defined by f(x) = x3 - 6x2 - 36x + 7 is increasing, if
  • x > 2 and also x > 6
  • x > 2 and also x < 6
  • x > -2 and also x < 6
  • x < - 2 and also x > 6
The function f(x) = x2 e-x increases in the interval
  • (0, 2)
  • (2, 3)
  • (3, 4)
  • (4, 5)
If f(x) = kx - sin x in monotonically increasing, then
  • k > 1
  • k > - 1
  • k < 1
  • k < - 1
If 2a + 3b + 6c = 0, then at least one root of the equation ax2 + bx + c = 0 lies in the interval
  • (0, 1)
  • (1, 2)
  • (2, 3)
  • (1, 3)
In the interval [0, 1], the function x2 - x + 1 is
  • increasing
  • decreasing
  • neither increasing nor decreasing
  • do not say anything

Maths-Applications of Derivatives-9128.png
  • (0, ∞)
  • (-∞, 0)
  • (-∞, ∞)
  • None of these
The function f(x) = 1 - x3
  • increases everwhere
  • decreases in (0, ∞ )
  • increases in (0, ∞)
  • None of the above
0:0:1


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