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Class XII Maths Application of Derivatives Quiz 2

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Question 1

Find the equation of the normal for a circle of radius 8 and centre at (8,0) at the origin

Question 2

If the function f (x) = 2x³ − 9ax² + 12a² x + 1, where a > 0, attains its maximum and minimum at p and q respectively such that p² = q, then a equals

Question 3

The value of α for which the sum of the square of the roots of the x² –(a – 2)x – a – 1 = 0 assume the least value is

Question 4

Suppose the cubic x³ – px + q has three distinct real roots where p > 0 and q > 0. Then which one of the following holds?

Question 5

A boy falling from rest under gravity passes a certain point P. It was at a distance of 400 m from P, 4s prior to passing through P. If g = 10 m/s², then the height above the point P from where the body began to fall is

Question 6

A spherical iron ball 10 cm in radius is coated with a layer of ice of uniform thickness than melts at a rate of 50 cm³/min. When the thickness of ice is 5 cm, then the rate at which the thickness of ice decreases, is

Question 7

If the function f(x) = 2x² + 3x + 5 satisfies LMVT at x = 2 on the closed interval [1, a] then the value of ‘a’ is equal to-

Question 8

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

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Apr 20JEE & BITSAT