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JEE Advanced Level Test: Application of Derivative- 2 - Question 1

The value of ‘a’ for which x^{3} - 3x + a = 0 has two distinct roots in [0, 1] is given by

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JEE Advanced Level Test: Application of Derivative- 2 - Question 2

The value of ‘c’ in Lagrange’s mean value theorem for f (x) = x (x- 2)^{2} in [0, 1]

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JEE Advanced Level Test: Application of Derivative- 2 - Question 3

For the function f (x) = x^{3} - 6x^{2} + ax + b, if Roll’s theorem holds in [1, 3] with

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JEE Advanced Level Test: Application of Derivative- 2 - Question 4

Find Value of ‘c’ by using Rolle’s theorem for f (x) = log (x^{2} + 2) - log 3 on [-1,1]

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JEE Advanced Level Test: Application of Derivative- 2 - Question 5

The chord joining the points where x = p and x = q on the curve y = ax^{2} + bx + c is parallel to the tangent at the point on the curve whose abscissa is

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JEE Advanced Level Test: Application of Derivative- 2 - Question 6

The least value of k for which the function f(x) = x^{2} + kx + 1 is a increasing function in the interval 1 __<__ x __<__ 2

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JEE Advanced Level Test: Application of Derivative- 2 - Question 7

The interval in which f (x) = x^{3} - 3x^{2} - 9x + 20 is strictly decreasing

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JEE Advanced Level Test: Application of Derivative- 2 - Question 9

The number of stationary points of f (x) = sin x in [0,2π] are

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JEE Advanced Level Test: Application of Derivative- 2 - Question 10

Local minimum values of the function

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JEE Advanced Level Test: Application of Derivative- 2 - Question 11

If the function has maximum at x =-3, then the value of ‘a’ is

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JEE Advanced Level Test: Application of Derivative- 2 - Question 12

The point at which f (x) = (x- 1)^{4} assumes local maximum or local minimum value are

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JEE Advanced Level Test: Application of Derivative- 2 - Question 13

The global maximum and global minimum of f (x) = 2x^{3} - 9x^{2} + 12x + 6 in [0, 2]

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JEE Advanced Level Test: Application of Derivative- 2 - Question 16

If the percentage error in the surface area of sphere is k, then the percentage error in its volume is

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JEE Advanced Level Test: Application of Derivative- 2 - Question 17

If an error of is made in measuring the radius of a sphere then percentage error in its volume is

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JEE Advanced Level Test: Application of Derivative- 2 - Question 18

The height of a cylinder is equal to its radius. If an error of 1 % is made in its height. Then the percentage error in its volume is

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JEE Advanced Level Test: Application of Derivative- 2 - Question 19

The slope of the normal to the curve given by

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JEE Advanced Level Test: Application of Derivative- 2 - Question 20

The line is a tangent to the curve then n ∈

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JEE Advanced Level Test: Application of Derivative- 2 - Question 21

The points on the curve at which the tangent is perpendicular to x-axis are

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JEE Advanced Level Test: Application of Derivative- 2 - Question 22

The point on the curve at which the tangent drawn is

JEE Advanced Level Test: Application of Derivative- 2 - Question 23

The sum of the squares of the intercepts on the axes of the tangent at any point on the curve x ^{2/3} + y^{2/3}= a^{2/3} is

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JEE Advanced Level Test: Application of Derivative- 2 - Question 24

If the straight line x cos α + y sinα = p touches the curve at the point (a, b) on it, then

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JEE Advanced Level Test: Application of Derivative- 2 - Question 25

If the curves x = y² and xy = k cut each other orthogonally then k² =

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JEE Advanced Level Test: Application of Derivative- 2 - Question 26

The angle between the curves y = x³ and

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JEE Advanced Level Test: Application of Derivative- 2 - Question 27

If the curves ay + x² = 7 and x³ = y cut orthogonally at (1, 1) then a =

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JEE Advanced Level Test: Application of Derivative- 2 - Question 28

A particle moves along a line is given by then the distance travelled by the particle before it first comes to rest is

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JEE Advanced Level Test: Application of Derivative- 2 - Question 29

A particle is moving along a line such that s = 3t^{3} - 8t + 1. Find the time ‘t’ when the distance ‘S’ travelled by the particle increases.

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JEE Advanced Level Test: Application of Derivative- 2 - Question 30

A particle moves along a line by S = t^{3} - 9t^{2} + 24t the time when its velocity decreases.

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