JEE Questions for Maths Applications Of Derivatives Quiz 10 - MCQExams.com

The normal of the curve x = a (cos θ + θ sin θ), y = a (sin θ – θ cos θ) at any θ is such that
  • It makes a constant angle with x – axis
  • It passes through the origin
  • It is at a constant distance from the origin
  • None of the above
The slope of the tangent to the curve x = 3t2 + 1, y = t3 –1 at x = 1 is
  • 0
  • 1/2
  • ∞
  • –2
An equation of the tangent to curve y = x4 from the point (2,not on the curve is
  • y = 0
  • x = 0
  • x + y = 0
  • None of these

Maths-Applications of Derivatives-10012.png
  • x + 9y – 6 = 0
  • 9x – y – 6 = 0
  • 9x + y + 6 = 0
  • x + 9y + 6 = 0
  • 9x + y – 6 = 0
At what point on the curve x3 – 8a2y = 0, the slope of the normal is –2/3
  • (a, a)
  • (2a, –a)
  • (2a, a)
  • None of these
The tangent drawn at the point (0,on the curve y = e2x meets x – axis at the point

  • Maths-Applications of Derivatives-10015.png
  • 2)
    Maths-Applications of Derivatives-10016.png
  • (2,0)
  • (0,0)
The equation of the tangent to the curve (1 + x2)y = 2 – x, where it crosses the x – axis is

  • Maths-Applications of Derivatives-10018.png
  • 2)
    Maths-Applications of Derivatives-10019.png

  • Maths-Applications of Derivatives-10020.png

  • Maths-Applications of Derivatives-10021.png
The equation of the tangent to curve y = bex/a at the point where it crosses y – axis is

  • Maths-Applications of Derivatives-10023.png
  • 2)
    Maths-Applications of Derivatives-10024.png

  • Maths-Applications of Derivatives-10025.png

  • Maths-Applications of Derivatives-10026.png
Angle between the tangent to the curve y = x2 – 5x + 6 at the points (2,and (3,is

  • Maths-Applications of Derivatives-10028.png
  • 2)
    Maths-Applications of Derivatives-10029.png

  • Maths-Applications of Derivatives-10030.png

  • Maths-Applications of Derivatives-10031.png
For the curve xy = c2 the subnormal at any point varies as
  • x2
  • x3
  • y2
  • y3
The angle between the curves y = sin x and y = cos x is

  • Maths-Applications of Derivatives-10034.png
  • 2)
    Maths-Applications of Derivatives-10035.png

  • Maths-Applications of Derivatives-10036.png

  • Maths-Applications of Derivatives-10037.png
If a tangent to the curve y = 6x – x2 is parallel to the line 4x – 2y –1 = 0, then the point of tangency on the curve is
  • (2, 8)
  • (8, 2)
  • (6, 1)
  • (4, 2)
The normal to the curve x = a(1 + cos θ), y = a sin θ at ‘θ’ always passes through the fixed point
  • (a, a)
  • (0, a)
  • (0,
  • (a, 0)
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 abscissa of the point on the curve y = a(ex/a + e–x/a) where the tangent is parallel to the x - axis is
  • 0
  • a
  • 2a
  • –2a
If the line ax + by + c = 0 is normal to the curve xy = 1 then
  • a > 0, b < 0
  • a > 0, b > 0
  • a < 0, b < 0
  • Data is unsufficient
The equation of the tangent to the curve y = (1 + x)y + sin–1 (sin2 x) at x = 0 is
  • x + y = 1
  • x + y + 1 = 0
  • 2x – y + 1 = 0
  • x + 2y + 2 = 0

Maths-Applications of Derivatives-10045.png

  • Maths-Applications of Derivatives-10046.png
  • 2)
    Maths-Applications of Derivatives-10047.png

  • Maths-Applications of Derivatives-10048.png

  • Maths-Applications of Derivatives-10049.png
The equation of the curve with passes through the point (0,and the slope 3x2 + 2x + 5 at any point (x, y) is
  • y = 3x3 + 2x2 + 5x + 1
  • y = 2x3 + 3x2 + 5x + 1
  • y = x3 + x2 + 5x + 1
  • y = x3 + x2 + 5x –1
The length of the subtangent at ‘t’ on the curve x = a(t + sin t), y = a(1 – cos t) is

  • Maths-Applications of Derivatives-10052.png
  • 2)
    Maths-Applications of Derivatives-10053.png

  • Maths-Applications of Derivatives-10054.png

  • Maths-Applications of Derivatives-10055.png

Maths-Applications of Derivatives-10057.png
  • 0
  • ∞
  • -∞

  • Maths-Applications of Derivatives-10058.png

Maths-Applications of Derivatives-10060.png
  • 16
  • 12
  • 8
  • 4
  • 2
If the line ax + by + c = 0 is a tangent to the curve xy = 4, then
  • a < 0, b > 0
  • a ≤ 0, b > 0
  • a < 0, b < 0
  • a ≤ 0, b < 0
The equation of normal of x2 + y2 – 2x + 4y – 5 = 0 at (2,is
  • y = 3x – 5
  • 2y = 3x + 4
  • y = 3x + 4
  • y = x + 1

Maths-Applications of Derivatives-10069.png
  • (–∞, –1]
  • (–∞, 0]
  • [1, ∞)
  • (0, ∞)

Maths-Applications of Derivatives-10071.png
  • (–∞, 0]
  • [0, ∞)
  • R
  • None of these
In the interval [0, 1], the function x2 – x + 1 is
  • Increasing
  • Decreasing
  • Neither increasing or Decreasing
  • None of the above

Maths-Applications of Derivatives-10074.png
  • Increasing
  • Decreasing
  • Neither increasing nor decreasing
  • None of the above
The function sin x – cos x is in the interval

  • Maths-Applications of Derivatives-10076.png
  • 2)
    Maths-Applications of Derivatives-10077.png

  • Maths-Applications of Derivatives-10078.png
  • None of these
The function sin x – bx + c will be increasing in the interval (–∞, ∞), if
  • b ≤ 1
  • b ≤ 0
  • b < – 1
  • b ≥ 0
The function x4 – 4x is decreasing in the interval
  • [–1, 1]
  • (–∞, 1)
  • [1, +∞)
  • None of these

Maths-Applications of Derivatives-10082.png

  • Maths-Applications of Derivatives-10083.png
  • 2)
    Maths-Applications of Derivatives-10084.png

  • Maths-Applications of Derivatives-10085.png

  • Maths-Applications of Derivatives-10086.png

Maths-Applications of Derivatives-10088.png
  • x < 2 and also x > 6
  • x > 2 and also x < 6
  • x < –2 and also x < 6
  • x < –2 and also x > 6

Maths-Applications of Derivatives-10090.png
  • Decreasing
  • Increasing
  • Neither increasing or decreasing
  • None of the above
If f’(x) is zero in the interval (a, b) then in this interval it is
  • Increasing function
  • Decreasing function
  • Only for a > 0 and b > 0 is increasing function
  • None of the above

Maths-Applications of Derivatives-10092.png
  • Decreasing
  • Increasing
  • Neither increasing nor decreasing
  • Increasing for x > 0 and decreasing for x < 0

Maths-Applications of Derivatives-10094.png
  • (1, 2)
  • (3, 4)
  • R
  • No value of a

Maths-Applications of Derivatives-10096.png

  • Maths-Applications of Derivatives-10097.png
  • 2)
    Maths-Applications of Derivatives-10098.png

  • Maths-Applications of Derivatives-10099.png

  • Maths-Applications of Derivatives-10100.png
The range in which y = – x2 + 6x – 3 is increasing is
  • x < 3
  • x > 3
  • 7 < x < 8
  • 5 < x < 6

Maths-Applications of Derivatives-10103.png
  • 1 < x < 2
  • x > 2
  • x < 1
  • None of these

Maths-Applications of Derivatives-10105.png

  • Maths-Applications of Derivatives-10106.png
  • 2)
    Maths-Applications of Derivatives-10107.png

  • Maths-Applications of Derivatives-10108.png

  • Maths-Applications of Derivatives-10109.png

Maths-Applications of Derivatives-10111.png
  • k < 3
  • k ≤ 3
  • k > 3
  • None of these

Maths-Applications of Derivatives-10113.png
  • Even and is strictly increasing in (0, ∞)
  • Odd and is strictly decreasing in (–∞,∞)
  • Odd and is strictly increasing in (–∞,∞)
  • Neither even nor odd, but is strictly increasing in (–∞,∞)
The function f(x) = tan x – x
  • Always increases
  • Always decreases
  • Never decreases
  • Sometimes increases and sometimes decreases

Maths-Applications of Derivatives-10116.png
  • (0,∞)
  • (-∞,0)
  • (-∞,∞)
  • None of these

Maths-Applications of Derivatives-10118.png
  • k < 1
  • k > 1
  • k < 2
  • k > 2

Maths-Applications of Derivatives-10120.png

  • Maths-Applications of Derivatives-10121.png
  • 2)
    Maths-Applications of Derivatives-10122.png

  • Maths-Applications of Derivatives-10123.png

  • Maths-Applications of Derivatives-10124.png
The interval in which the function x3 increases less rapidly than 6x2 + 15x + 5, is
  • (–∞, –1)
  • (–5, 1)
  • (–1, 5)
  • (5, ∞)

Maths-Applications of Derivatives-10127.png
  • Increases in [0, ∞]
  • Decreases in [0, ∞]
  • Neither increases nor decreases in (0, ∞)
  • Increases in (–∞,∞)
  • 1 and 4 correct
The least value of k for which the function x2 + kx + 1 is an increasing function in the interval 1 < x < 2 is
  • –4
  • –3
  • –1
  • –2
0:0:1


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