SATHEE: Application of Derivatives 4 Question 28

Application of Derivatives 4 Question 28

####29. If $p, q$ and $r$ are any real numbers, then

(a) $max (p, q) < max (p, q, r)$

$(1982, 1 M)$

(b) $min (p, q) = \frac{1}{2} (p + q - | p - q |)$

(d) None of the above

Objective Questions II

(One or more than one correct option)

$30. If f (x) = \begin{array}{ccc} \cos (2 x) & \cos (2 x) & \sin (2 x) \\ - \cos x & \cos x & - \sin x, then \\ \sin x & \sin x & \cos x \end{array}$

(2017 Adv.) (a) $f (x)$ attains its minimum at $x = 0$

(b) $f (x)$ attains its maximum at $x = 0$

(d) $f^{'} (x) = 0$ at exactly three points in $(- π, π)$

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Answer:

Correct Answer: 29. (a, b)

Solution:

Since, $max (p, q) = \begin{array}{ll} p, & if p > q \end{array}$

$q, if q > p$

$p$ , if $p$ is greatest.

and $max (p, q, r) = q$ , if $q$ is greatest.

$r$ , if $r$ is greatest.

$∴ max (p, q) < max (p, q, r)$ is false.

We know that, $| p - q | = \begin{array}{ll} p - q, & if p \geq q \\ q - p, & if p < q \end{array}$

$= \begin{array}{ll} q, & if p \geq q \\ p, & if p < q \end{array}$

$\Rightarrow \frac{1}{2} p + q - | p - q | = min (p, q)$ $\cos 2 x \cos 2 x \sin 2 x$

Application of Derivatives 4 Question 28

Objective Questions II

Answer:

Engineering Preparation

Medical Preparation

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Application of Derivatives 4 Question 28

Objective Questions II

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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