JEE Questions for Maths Applications Of Derivatives Quiz 8 - MCQExams.com

For all x ∈ (0,:
  • ex < 1 + x
  • loge (1+x) < x
  • sin x > x
  • loge x > x
If the normal to the curve y = f(x) of the point (3,makes an angle 3π/4 with the positive axis, then : f\'(= :
  • –1
  • 2)
    Maths-Applications of Derivatives-9725.png

  • Maths-Applications of Derivatives-9726.png
  • 1

Maths-Applications of Derivatives-9728.png
  • (-∞,-2)
  • (-2,-1)
  • (1,2)
  • (2,∞)
Let f(x) = | x | for 0 < | x | ≤ 2
= 1 for x = 0
then x = 0 has :
  • a local maximum
  • no local maximum
  • a local minimum
  • no extremum

Maths-Applications of Derivatives-9731.png

  • Maths-Applications of Derivatives-9732.png
  • 2)
    Maths-Applications of Derivatives-9733.png

  • Maths-Applications of Derivatives-9734.png

  • Maths-Applications of Derivatives-9735.png

Maths-Applications of Derivatives-9737.png
  • 4
  • 2
  • 1
  • –4

Maths-Applications of Derivatives-9739.png

  • Maths-Applications of Derivatives-9740.png
  • 2)
    Maths-Applications of Derivatives-9741.png

  • Maths-Applications of Derivatives-9742.png

  • Maths-Applications of Derivatives-9743.png

Maths-Applications of Derivatives-9745.png
  • 1
  • 0
  • 9
  • 18

Maths-Applications of Derivatives-9747.png

  • Maths-Applications of Derivatives-9748.png
  • 2)
    Maths-Applications of Derivatives-9749.png
  • 0
  • 1

Maths-Applications of Derivatives-9751.png
  • 5
  • 10
  • 0
  • 15

Maths-Applications of Derivatives-9753.png
  • 0
  • 1
  • –1
  • 2

Maths-Applications of Derivatives-9755.png

  • Maths-Applications of Derivatives-9756.png
  • 2)
    Maths-Applications of Derivatives-9757.png

  • Maths-Applications of Derivatives-9758.png

  • Maths-Applications of Derivatives-9759.png

Maths-Applications of Derivatives-9761.png
  • Even function
  • Odd function
  • Not define
  • Increasing Function

Maths-Applications of Derivatives-9762.png
  • 1.2
  • 1.4
  • 1.6
  • 1.8

Maths-Applications of Derivatives-9764.png

  • Maths-Applications of Derivatives-9765.png
  • 2)
    Maths-Applications of Derivatives-9766.png

  • Maths-Applications of Derivatives-9767.png

  • Maths-Applications of Derivatives-9768.png

Maths-Applications of Derivatives-9770.png
  • 22
  • 11
  • 0
  • 5

Maths-Applications of Derivatives-9772.png
  • 1
  • 2

  • Maths-Applications of Derivatives-9773.png

  • Maths-Applications of Derivatives-9774.png

Maths-Applications of Derivatives-9776.png
  • 2
  • 2)
    Maths-Applications of Derivatives-9777.png

  • Maths-Applications of Derivatives-9778.png

  • Maths-Applications of Derivatives-9779.png

Maths-Applications of Derivatives-9781.png

  • Maths-Applications of Derivatives-9782.png
  • 2)
    Maths-Applications of Derivatives-9783.png

  • Maths-Applications of Derivatives-9784.png
  • None of these

Maths-Applications of Derivatives-9786.png

  • Maths-Applications of Derivatives-9787.png
  • 2)
    Maths-Applications of Derivatives-9788.png

  • Maths-Applications of Derivatives-9789.png

  • Maths-Applications of Derivatives-9790.png

Maths-Applications of Derivatives-9792.png

  • Maths-Applications of Derivatives-9793.png
  • 2)
    Maths-Applications of Derivatives-9794.png

  • Maths-Applications of Derivatives-9795.png

  • Maths-Applications of Derivatives-9796.png

Maths-Applications of Derivatives-9798.png
  • 7
  • 13
  • 20
  • 0

Maths-Applications of Derivatives-9800.png

  • Maths-Applications of Derivatives-9801.png
  • 2)
    Maths-Applications of Derivatives-9802.png

  • Maths-Applications of Derivatives-9803.png

  • Maths-Applications of Derivatives-9804.png

Maths-Applications of Derivatives-9806.png
  • 1
  • 2
  • 3
  • 4

Maths-Applications of Derivatives-9808.png

  • Maths-Applications of Derivatives-9809.png
  • 2)
    Maths-Applications of Derivatives-9810.png

  • Maths-Applications of Derivatives-9811.png

  • Maths-Applications of Derivatives-9812.png
Two measarment of a cylinder are varying in such a way that the volume is kept constant. If the rates of change of the radius (r) and high (h) are equal in magnitute but opposite is sign then
  • r = 2h
  • h = 2r
  • h = r
  • h = 4r

Maths-Applications of Derivatives-9815.png
  • 2
  • 1
  • 3
  • –3
At any point of a curve (sub tangent) (sub normal) is equal to the square of the
  • Slope of the tangent at the point
  • Slope of the normal at the point
  • Abscissa of the point
  • Ordinate of the point

Maths-Applications of Derivatives-9817.png

  • Maths-Applications of Derivatives-9818.png
  • 2)
    Maths-Applications of Derivatives-9819.png

  • Maths-Applications of Derivatives-9820.png

  • Maths-Applications of Derivatives-9821.png

Maths-Applications of Derivatives-9823.png
  • At most one root
  • No root
  • Exactly one root exist
  • At least one root

Maths-Applications of Derivatives-9825.png

  • Maths-Applications of Derivatives-9826.png
  • 2)
    Maths-Applications of Derivatives-9827.png

  • Maths-Applications of Derivatives-9828.png

  • Maths-Applications of Derivatives-9829.png

Maths-Applications of Derivatives-9831.png

  • Maths-Applications of Derivatives-9832.png
  • 2)
    Maths-Applications of Derivatives-9833.png

  • Maths-Applications of Derivatives-9834.png

  • Maths-Applications of Derivatives-9835.png

Maths-Applications of Derivatives-9837.png

  • Maths-Applications of Derivatives-9838.png
  • 2)
    Maths-Applications of Derivatives-9839.png

  • Maths-Applications of Derivatives-9840.png
  • Not defined

Maths-Applications of Derivatives-9842.png

  • Maths-Applications of Derivatives-9843.png
  • 2)
    Maths-Applications of Derivatives-9844.png

  • Maths-Applications of Derivatives-9845.png

  • Maths-Applications of Derivatives-9846.png
A stone is falling freely and describes a distance s in t seconds given by equation s = 1/2 gt2. The acceleration of the stone is
  • Uniform
  • Zero
  • Non – uniform
  • Indeterminate
The equation of motion of a particle is given by s = 2t3 – 9t2 + 12t + 1, where s and t are measured in cm and sec. The time when the particle stops momentarily is
  • 1sec
  • 2 sec
  • 1, 2 sec
  • None of the above
If a spherical Balloon has a variable diameter 3x + 9/2, then the rate of charge of its volume with respect to x is

  • Maths-Applications of Derivatives-9850.png
  • 2)
    Maths-Applications of Derivatives-9851.png

  • Maths-Applications of Derivatives-9852.png
  • None of these
The velocity of a particle at time t is given by the relation v = 6t – t2/6. The distance travelled in 3 seconds is, if s = 0 at t = 0

  • Maths-Applications of Derivatives-9854.png
  • 2)
    Maths-Applications of Derivatives-9855.png

  • Maths-Applications of Derivatives-9856.png

  • Maths-Applications of Derivatives-9857.png
The equation of motion of a car is s = t2 – 2t, where is measured in hours and s in kilometres. When the distance travelled by a car is 15 km, the velocity of the car is
  • 2 km/h
  • 4 km/h
  • 3 km/h
  • 8 km/h
A stone moving vertically upwards has its equation of motion s = 490t – 4.9 t2. The maximum height reached by the stone is
  • 12250
  • 1225
  • 36750
  • None of these
The law of motion in a straight line s = 1/2 vt, then acceleration is
  • Constant
  • Proportional to t
  • Proportional to v
  • Proportional to s
A point moves in a straight line during time t = 0 to t = 3 according to the law s = 15 t – 2t2. The average velocity is
  • 3
  • 9
  • 15
  • 27

Maths-Applications of Derivatives-9863.png
  • proportional to t
  • Proportional to s
  • s
  • Constant
The equation of motion of a stone, thrown vertically upwards is s = ut – 6.3t2, where the units of s and t are cm and sec. if the stone reaches a maximum height in 3 sec, then u =
  • 18.9 cm/sec
  • 12.6 cm/sec
  • 37.8 cm/sec
  • None of these
A particle moves in a straight line so that its velocity at any point is given v2 = a + bx, where a, b ≠ 0 are constants. The acceleration is
  • Zero
  • Uniform
  • Non - uniform
  • Indeterminate

Maths-Applications of Derivatives-9867.png

  • Maths-Applications of Derivatives-9868.png
  • 2)
    Maths-Applications of Derivatives-9869.png

  • Maths-Applications of Derivatives-9870.png
  • None of these
The equation of motion of a stone thrown vertically upwards from the surface of a planet is given by s = 10 t – 3t2, and the units of s and t are cm and sec respectively. The stone will return to the surface of the planet after

  • Maths-Applications of Derivatives-9872.png
  • 2)
    Maths-Applications of Derivatives-9873.png

  • Maths-Applications of Derivatives-9874.png

  • Maths-Applications of Derivatives-9875.png
A body moves according to the formula v = 1 + t2 where v is the velocity at time t. The acceleration after 3 sec will be (v in cm/sec)
  • 24 cm/sec2
  • 12 cm/sec2
  • 6 cm/sec2
  • None of these
The length of the side of a square sheet of metal is increasing at the rate of 4 cm/sec. The rate at which the area of the sheet is increasing when the length of its side is 2cm, is
  • 16 cm2/sec
  • 8 cm2/sec
  • 32 cm2/sec
  • None of these
The equations of motion of two stones thrown vertically simultaneously are s = 19.6t – 4.9t2 and s = 9.8t – 4.9 t2 respectively and the maximum height attained by the first one is h. When the height of the first stone is maximum, the height of the second stone will be
  • h/3
  • 2h
  • h
  • 0
0:0:1


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