JEE Advanced Level Test: Monotonicity- 2 - JEE MCQ

For what values of a does the curve

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

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

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

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

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

The equation xe^x = 2 has

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

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

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

 If 0 < a < b <  and f(a, b) = , then

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

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

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