JEE Questions for Maths Applications Of Derivatives Quiz 3 - MCQExams.com


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  • 0
  • 2)
    Maths-Applications of Derivatives-9132.png

  • Maths-Applications of Derivatives-9133.png
  • None of these

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  • Maths-Applications of Derivatives-9136.png
  • 2)
    Maths-Applications of Derivatives-9137.png

  • Maths-Applications of Derivatives-9138.png

  • Maths-Applications of Derivatives-9139.png

  • Maths-Applications of Derivatives-9140.png
If f be continuous on [1, 5] and differentiable (1, 5). If f(= - 3 and f ' (x) ≥ 9, ∀ x ϵ (1, 5), then
  • f(≥ 33
  • f(≥ 36
  • f( ≤ 36
  • f(≥ 9
  • f(≤ 9
If f(x) = x2 - 2x + 4 on [1, 5], then the value of a constant c such that
Maths-Applications of Derivatives-9143.png
  • 0
  • 1
  • 2
  • 3
The function f(x) = 2x3 - 3x2 + 90x + 174 is the interval
  • 1/2 < x < 1
  • 1/2 < x < 2
  • 3 < x < 59/4
  • - ∞ < x < ∞
In the mean value theorem f(b) - f(a) = (b - a)f ' (c), if a - 4b = 9 and f(x) = √x, then the value of c is
  • 8.00
  • 5.25
  • 4.00
  • 6.25
A stone is dropped into a quiet lake and waves move in circles at the speed of 5 cm/s. At that instant, when the radius of circular wave is 8 cm, how far is the enclosed area increasing?
  • 6π cm2 / s
  • 8π cm2 / s
  • 8/3 cm2 / s
  • 80π cm2 / s
The radius of a cylinder is increasing at the rate of 5 cm/min, so that its volume is constant. When its radius is 5 cm and height is 3 cm, then the rate of decreasing of its height is
  • 6 cm/min
  • 3 cm/min
  • 5 cm/min
  • 2 cm/min

Maths-Applications of Derivatives-9149.png
  • 1/x
  • x
  • x2
  • 1/x2
A sphere increases its volume at the rate of π cm3/s. The rate at which its surface area increases, when the radius is 1 cm is
  • 2π sq cm/s
  • π sq cm/s
  • 3π/2 sq cm/s
  • π/2 sq cm/s
The total revenue (in Rupees) received from the sale of x units of a product is given by R(x) = 13x2 + 26x + 15. Then, the marginal revenue (in Rupees) when x = 15, is
  • 116
  • 126
  • 136
  • 416
  • 146
The distance travelled by a bus in t sec after the breakes are applied is 1 + 2t - 2t2 metres. The distance travelled by the bus before it stops is equal to
  • 0.5 m
  • 1 m
  • 1.5 m
  • 2.5 m
An edge of a variable cube is increasing at the rate of 10 cm/s. How fast the volume of the cube will increase, when the edge is 5 cm long ?
  • 750 cm3 / s
  • 75 cm3 / s
  • 150 cm3 / s
  • 25 cm3 / s
If the error committed in measuring the radius of the circle is 0.05%, then the corresponding error in calculating the area is
  • 0.05%
  • 0.0025%
  • 0.25%
  • 0.1%
  • 0.2%
A stone is thrown vertically upwards from the top of a tower 64 m high according to the law s = 48t - 16t2 . The greatest height attained by the stone ground is
  • 36 m
  • 32 m
  • 100 m
  • 64 m
If there is 2% error in measuring the radius of sphere, then .... will be the percentage error in the surface area.
  • 3%
  • 1%
  • 4%
  • 2%
A spherical balloon is expanding. If the radius is increasing at the rate of 2 cm/min, then the rate at which the volume increases (in cm3 / min), when the radius is 5 cm, is
  • 10 π
  • 100 π
  • 200 π
  • 50 π
If gas is being pumped into a spherical balloon at the rate of 30 ft 3/min. Then, the rate at which the radius increases, when it reaches the value 15 ft is
  • 1/15π ft/min
  • 1/30π ft/min
  • 1/20 ft/min
  • 1/25 ft/min
If a particle moves along a straight line with the law of motion given by s2 = at 2 + 2bt + c. Then, the acceleration varies, are
  • 1/s3
  • 1/s
  • 1/s4
  • 1/s2
OB and OC are two roads enclosing an angle of 120°. X and Y start from 0 at the same time. X travels along OB with a speed of 4 km/h and Y travels along OC with a speed of 3 km/h. The rate at which the shortest distance between X and Y is increasing after 1 h is
Maths-Applications of Derivatives-9161.png
  • √37 km/h
  • 37 km/h
  • 13 km/h
  • √13 km/h
A particle moves along a straight line according to the law s = 16— 2t + 3t3 , where s metres is the distance of the particle from a fixed point at the end of t sec. The acceleration of the particle at the end of 2 s is
  • 36 m/s2
  • 34 m/s2
  • 36 m
  • None of these
The radius of a circle is increasing at the rate of 0.1 cm/s. When the radius of the circle is 5 cm, the rate of change of its area is
  • -π cm2/s
  • 10π cm2/s
  • 0.1π cm2/s
  • 5π cm2/s
  • π cm2/s
A spherical balloon is being inflated at the rate of 35 cc/min. The rate of increase of the surface area of the balloon, when its diameter is 14 cm, is
  • 7 sq cm/min
  • 10 sq cm/min
  • 17.5 sq cm/min
  • 28 sq cm/min
A spherical iron ball 10 cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of 50 cm2/min. When the thickness of ice is 15 cm, then the rate at which the thickness of ice decreases, is
  • 5/6π cm/min
  • 1/54π cm/min
  • 1/18π cm/min
  • 1/36π cm/min
A ladder 10 m long rests against a vertical wall with the lower end on the horizontal ground. The lower end of the ladder is pulled along the ground away from the wall at the rate of 3 cm/s. The height of the upper end while it is descending at the rate of 4 cm/s, is
  • 4√3 m
  • 5√3 m
  • 5√2 m
  • 8 m
  • 6 m
A right circular cylinder which is open at the top and has a given surface area, will have the greatest volume, if its height h and radius r are related by
  • 2h = r
  • h = 4r
  • h = 2r
  • h = r
If f = - 1 and x = 2 are extreme points of f (x) = α log |x| + βx2 + x, then

  • Maths-Applications of Derivatives-9169.png
  • 2)
    Maths-Applications of Derivatives-9170.png

  • Maths-Applications of Derivatives-9171.png

  • Maths-Applications of Derivatives-9172.png
The greatest and least value of (sin-1 x)2 + (cos-1 x)2 are respectively

  • Maths-Applications of Derivatives-9174.png
  • 2)
    Maths-Applications of Derivatives-9175.png

  • Maths-Applications of Derivatives-9176.png

  • Maths-Applications of Derivatives-9177.png

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  • e
  • 1/e
  • e2
  • e3
The slope of the tangent of the curve y2 exy = 9e-3 x2 at (-1,is
  • -15/2
  • -9/2
  • 15
  • 15/2
  • 9/2
The slope of the normal of the curve
Maths-Applications of Derivatives-9182.png
  • 1/4
  • - (1/4)
  • 4
  • -4
  • 0
The point of the parabola y2 = 64x which is nearest to the line 4x + 3y + 35 = 0 has coordinates
  • (9, -24)
  • (1, 81)
  • (4, -16)
  • (-9, -24 )
If x is real, then the minimum value of
Maths-Applications of Derivatives-9190.png
  • 3
  • 1/3
  • 1/2
  • 2
The condition that f(x) = ax3 + bx2 + cx + d has no extreme value is
  • b2 > 3ac
  • b2 = 4ac
  • b2 = 3ac
  • b2 < 3ac
Find the slope of the normal to the curve 4x3 - 3xy2 + 6x2 - 5xy - 8y2 + 9x + 14 = 0 at the point (-2, 3)
  • ∞
  • 1
  • 9/2
  • 2/9
Let f : [0,1] → R(the set of all real numbers) be a function. Suppose the function f is twice differentiable,
f(= f(= 0 and satisfies f ''(x) - 2f '(x) + f(x) ≥ ex, x ϵ [0,1].
A line L : y = mx + 3 meets Y - axis at E(0,the arc of the parabola y2 = 16x, 0 ≤ y ≤ 6 at the point F(xo , yo). The tangent to the parabola at F(x0, yo) interest the Y - axis at G(0, y1). The slope m of the line L is chosen such that the area of ∆EFG has a local maximum
Maths-Applications of Derivatives-9194.png
  • A = 4, B = 1, C = 2, D = 3
  • A = 3, B = 4, C = 1, D = 2
  • A = 1, B = 3, C = 2, D = 4
  • A = 1, B = 3, C = 4, D = 2
A rectangular sheet of fixed perimeter with sides having their lengths in the ratio 8 : 15 is converted into an open rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squares is 100, the resulting box has maximum volume. The lengths of the sides of the rectangular sheet are
  • 24
  • 32
  • 45
  • 60
The function f(x) = 2|x| + |x + 2|-1||x - 2|x|| has a local minimum or a local maximum at
  • -2
  • -2/3
  • 2
  • 2/3
The intercepts on X - axis made by tangents to the curve,
Maths-Applications of Derivatives-9198.png
  • ± 1
  • ± 2
  • ± 3
  • ± 4
The equation of the tangent to the curve y = e|x| at the point, where the curve cuts the line x = 1 is
  • e(x + y) = 1
  • y = ex = 1
  • x + y = e
  • None of these
If at each point of the curve y = x3 - ax2 + x + 1 tangent is inclined at an acute angle with the positive direction of the X-axis, then
  • a ≤ √3
  • a > 0
  • - √3 ≤ a ≤ √3
  • None of these
The difference between the greatest and the least value of the function
Maths-Applications of Derivatives-9202.png

  • Maths-Applications of Derivatives-9203.png
  • 2)
    Maths-Applications of Derivatives-9204.png

  • Maths-Applications of Derivatives-9205.png
  • None of these
The maximum value of xe-x is
  • e
  • 1/e
  • -e
  • -1/e

Maths-Applications of Derivatives-9208.png
  • local maximum π and 2π
  • local minimum at π and local maximum at 2π
  • local maximum at π and local minimum at 2π
  • local maximum at π and 2π

Maths-Applications of Derivatives-9210.png
  • Statement I is correct, Statement II is correct
  • Statement I is correct, statement II is correct; statement II is correct explanation for Statement I
  • Statement I is correct, statement II is correct; Statement II is not a correct explanation for Statement i.
  • statement I is correct, statement II is incorrect
The point (0,is closer to the curve x2 = 2y at
  • (2√2, 0)
  • (0, 0)
  • (2, 2)
  • None of these
The point on the curve y = x3 at which tangent is parallel to the point (1,is
  • (0, 0)
  • (1, - 1)
  • (-1, 1)
  • (-1, -1)

Maths-Applications of Derivatives-9214.png
  • ab
  • abe2
  • abe
  • ab/e
The maximum value of f(x) = 2 sin x + cos 2x, 0 ≤ x ≤ π/2 occurs at x is
  • 0
  • π/6
  • π/2
  • None of these

Maths-Applications of Derivatives-9217.png
  • -1
  • does not exist
  • 0
  • 1
0:0:1


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