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Class XII Maths Application of Derivatives Quiz 1

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Question 1

If f(x) = e^x and g(x) = e^-x for all x belonging to [a,b], then using Cauchy’s mean value theorem, the value of c is:

Question 2

Four points A, B, C and D lie in order on the parabola y = x² + x + 1. The coordinates of A, B and D are known as A (-2,3), B (-1, 1) and D (2,7). The coordinates of C for which the area of the quadrilateral ABCD is maximum.

Question 3

A ladder 26 m long is kept at an angle to reach a vertical height of 24 m from the horizontal ground. If the ladder slips at the rate of 8 m/sec horizontally. Find the rate of slip of ladder in vertical direction when it begins to slip.

Question 4

A ladder of ‘h’ cm length rests against a vertical wall and floor. The end touching the floor moves with v cm/s. Then what will be the rate of the movement of the upper end, when the lower end is t cm away from the vertical wall:

Question 5

Let f : [–1, 2] → R be differentiable such that 0 ≤ f '(t) ≤ 1 for t ∈ [–1, 0] and –1 ≤ f '(t) ≤ 0 for t ∈ [0, 2]. Then

Question 6

Rolle’s Theorem holds for the function f(x) = x³ + bx² + cx, 1 ≤ x ≤ 2 at the point $Description: Description: D:\GradeStack Courses\JEE Mains (Sent by Ravi)\JEE Mains Full Test\AIEEE-Full-Test-4-New_files\image313.png$ the value of b and c are

Question 7

X: Tangents can never be equation wise equal to normal
Y: Tangents of two different curves would imply that the curve have same equation
Z: If we have a semi – circle then all points exterior to the circle will have 2 tangents originating from them

Question 8

Assertion: The equation of the tangent to a circle

= 0
Reason: The equation of the normal of the above mentioned circle is y = x

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Jul 24JEE & BITSAT