Match List I with List II
| LIST I | LIST II | ||
| A. | sin 2 x | I. | decreases from 1 to 0 in $\left(0, \frac{\pi}{2}\right)$ |
| B. | tan x | II. | decreases if $x \in \left(0, \frac{\pi}{6}\right)$ |
| C. | cos x | III. | increases from 0 to 1 in $\left(0, \frac{\pi}{4}\right)$ |
| D. | cos 3 x | IV. | is an increasing function in each quadrant |
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → A-III, B-IV, C-I, D-II
(A) $y=\sin 2x$
$y'=2\cos 2x=0$
$x=\frac{π}{4}$
so $\sin 2x$ increases from 0 → 1 in $(0,\frac{π}{4})$ (III)
(B) $y=\tan x$
$y'=\sec^2x=0⇒x=\frac{π}{2}$
but $\sec^2x≥0$ always of $\tan x$ increasing in each quadrant (IV)
(C) $y=\cos x$
$y'=-\sin x=0⇒x=0,π,2π,....$
$⇒\cos x$ is decreasing from 1 to 0 in $(0,\frac{π}{6})$ (I)
(D) $y=\cos 3x$
= $\cos z$ decreasing in $z∈(0,\frac{π}{2})$
$⇒x∈(0,\frac{π}{6})$ (II)