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JEE Advanced Level Test: Monotonicity- 2 - JEE MCQ


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16 Questions MCQ Test Mathematics (Maths) Class 12 - JEE Advanced Level Test: Monotonicity- 2

JEE Advanced Level Test: Monotonicity- 2 for JEE 2024 is part of Mathematics (Maths) Class 12 preparation. The JEE Advanced Level Test: Monotonicity- 2 questions and answers have been prepared according to the JEE exam syllabus.The JEE Advanced Level Test: Monotonicity- 2 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for JEE Advanced Level Test: Monotonicity- 2 below.
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JEE Advanced Level Test: Monotonicity- 2 - Question 1

The values of p for which the function

f(x)=x5 – 3x + ln 5 decreases for all real x is

JEE Advanced Level Test: Monotonicity- 2 - Question 2

 For which values of `a' will the function

f(x) = x4 + ax3 +  + 1 will be concave upward along the entire real line

JEE Advanced Level Test: Monotonicity- 2 - Question 3

The function f(x) = x(x + 3) e–x/2 satisfies all the conditions of Rolle's theorem in [–3, 0]. The value of c which verifies Rolle's theorem, is

JEE Advanced Level Test: Monotonicity- 2 - Question 4

For what values of a does the curve

f(x) = x(a2 – 2a – 2) + cos x is always strictly monotonic  x ∈ R.

JEE Advanced Level Test: Monotonicity- 2 - Question 5

If the function f(x) = x3 – 6ax2 + 5x satisfies the conditions of Lagrange's mean theorem for the interval [1, 2] and the tangent to the curve y = f(x) at x = 7/4 is parallel to the chord joining the points of intersection of the curve with the ordinates x = 1 and x = 2. Then the value of a is

JEE Advanced Level Test: Monotonicity- 2 - Question 6

The function f(x) = tan-1 (sin x + cos x) is an increasing function in

JEE Advanced Level Test: Monotonicity- 2 - Question 7

A function y = f(x) has a second order derivative f" = 6(x – 1). If its graph passes through the point (2, 1) and at that point the tangent of the graph is y = 3x – 5, then the function is

JEE Advanced Level Test: Monotonicity- 2 - Question 8

 If f(x) = [a sin x + b cosx] / [c sin x + d cos x] is monotonically increasing, then

JEE Advanced Level Test: Monotonicity- 2 - Question 9

The equation xex = 2 has

JEE Advanced Level Test: Monotonicity- 2 - Question 10

If f(x) = 1 + x l and g(x) =  then for x ³ 0

JEE Advanced Level Test: Monotonicity- 2 - Question 11

The set of values of the parameter `a' for which the function; f(x) = 8ax – a sin 6x – 7x – sin 5x increases & has no critical points for all x Î R, is

JEE Advanced Level Test: Monotonicity- 2 - Question 12

f : [0, 4] → R is a differentiable function then for some a, b Î (0, 4), f2(4) – f2(0) equals

JEE Advanced Level Test: Monotonicity- 2 - Question 13

 If 0 < a < b <  and f(a, b) = , then

JEE Advanced Level Test: Monotonicity- 2 - Question 14

 Let f(x) = ax4 + bx3 + x2 + x – 1. If 9b2 < 24a, then number of real roots of f(x) = 0 are

JEE Advanced Level Test: Monotonicity- 2 - Question 15

If f(x) = (x – 1) (x – 2) (x – 3) (x – 4), then roots of f'(x) = 0 not lying in the interval

JEE Advanced Level Test: Monotonicity- 2 - Question 16

If f(x) = 1 + xm (x – 1)n, m, n ∈ N, then f'(x) = 0 has atleast one root in the interval

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