Match the statements of Column I with the values in Column II.| Column I | Column II…

MATHEMATICS · Subjective · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

Match the statements of Column I with the values in Column II.| Column I | Column II | |---|---| | (a) Number of values of

x\in\left(0,\frac{\pi}{2}\right)

at which

f(x)=\ln(\sin x)

is not monotonic | (p)

0

| | (b) If the greatest interval of decrease of

f(x)=x^3-3x+2

[a,b]

, then

a+b

| (q)

2

| | (c) Let

f(x)=\frac{x^2+2}{[x]}

1\leq x\leq3

, where

[\,\cdot\,]

denotes the greatest integer function. The least value of

f(x)

| (r)

-3

| | (d) The set of all values of

a

such that

f(x)=e^{2x}-(a+1)e^x+2x

is increasing for all

x\in\mathbb{R}

(-\infty,a]

. Then

a

| (s)

3