Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 8 - Maxima and Minima>Target Exercises>Q 10

EASY

JEE Advanced

IMPORTANT

Earn 100

If $x z = 1$ , where $x > 0$ , then the least value of $x + z$ is

50% studentsanswered this correctly

Important Questions on Maxima and Minima

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 8 - Maxima and Minima>Target Exercises>Q 11

The minimum value of

\log_{a} x + \log_{x} a, 0 < x < a,

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 8 - Maxima and Minima>Target Exercises>Q 12

The minimum value of

2 \log_{10} x - \log_{x} 0.01; x > 1

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 8 - Maxima and Minima>Target Exercises>Q 13

The function

f (x) = \int_{1}^{x} [2 (t - 1) {(t - 2)}^{3} + 3 {(t - 1)}^{2} {(t - 2)}^{2}] d t

has

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 8 - Maxima and Minima>Target Exercises>Q 14

For a function $y = f (x)$ , if $\frac{d y}{d x} = 0$ and $\frac{d^{2} y}{d x^{2}} = 0$ at a point $x = a$ , then

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 8 - Maxima and Minima>Target Exercises>Q 15

The fraction exceeding its

p^{th}

power by the greatest number possible, where

p \geq 2

, is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 8 - Maxima and Minima>Target Exercises>Q 16

If

y = x^{2} + a x + b

has a minimum at

x = 3

and the minimum value is

5,

then the values of

a

and

b

are

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 8 - Maxima and Minima>Target Exercises>Q 17

The greatest value of the function

f (x) = x e^{- x}

in

[0, \infty)

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 8 - Maxima and Minima>Target Exercises>Q 18

The least value of the function

f (x) = \cos^{- 1} x^{2}

in the interval

[- \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}]

is