Match the items of List-I to the items of Lis | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) . The period of $\sin^2 x$ is $\pi$. Thus,$A-V$.$B$. The maximum value of $a \cos 	heta + b \sin 	heta$ is $\sqrt{a^2+b^2}$. Here,$\frac{\pi}{3}

Vedclass · Accepted Answer

$A-V, B-I, C-II, D-III$

Vedclass · Answer

(A) . The period of $\sin^2 x$ is $\pi$. Thus,$A-V$.$B$. The maximum value of $a \cos 	heta + b \sin 	heta$ is $\sqrt{a^2+b^2}$. Here,$\frac{\pi}{3} \sqrt{(\sqrt{3})^2+(1)^2} = \frac{\pi}{3} 	imes 2 = \frac{2\pi}{3}$. Thus,$B-I$.$C$. The period of $\sin \frac{x}{3}$ is $\frac{2\pi}{1/3} = 6\pi$ and the period of $\cos \frac{x}{2}$ is $\frac{2\pi}{1/2} = 4\pi$. The period of the sum is the $LCM(6\pi, 4\pi) = 12\pi$. Thus,$C-II$.$D$. For $y=|\sin x|$ and $y=1$,we have $|\sin x|=1$,so $\sin x = \pm 1$. In the interval $(0, \pi)$,$\sin x = 1$ at $x = \frac{\pi}{2}$. Thus,$D-III$.Therefore,the correct match is $A-V, B-I, C-II, D-III$.

List-$I$	List-$II$
$A$. The period of $\sin^2 x$ is	$I$. $\frac{2\pi}{3}$
$B$. Maximum value of $\frac{\pi}{3}(\sqrt{3}\cos 3x + \sin 3x)$	$II$. $12\pi$
$C$. The period of $\sin \frac{x}{3} + \cos \frac{x}{2}$ is	$III$. $\frac{\pi}{2}$
$D$. Intersection points of $y=\|\sin x\|$ and $y=1$ in $(0, \pi)$	$IV$. $\frac{3\pi}{2}$
	$V$. $\pi$

Similar Questions

If $A + B = 225^\circ$,then $\frac{\cot A}{1 + \cot A} \cdot \frac{\cot B}{1 + \cot B} = $

The smallest positive value of $x$ (in degrees) for which $\tan(x+100^{\circ}) = \tan(x+50^{\circ}) \tan(x) \tan(x-50^{\circ})$ is (in $^{\circ}$)

If $(\alpha+\beta)$ is not a multiple of $\frac{\pi}{2}$ and $3 \sin (\alpha-\beta)=5 \cos (\alpha+\beta)$,then $\tan \left(\frac{\pi}{4}+\alpha\right)+4 \tan \left(\frac{\pi}{4}+\beta\right)=$

If $0 < x, y < \pi$ and $\cos x + \cos y - \cos(x + y) = \frac{3}{2}$,then $\sin x + \cos y$ is equal to ...... .

If $x = \log \left[ \cot \left( \frac{\pi}{4} + \theta \right) \right]$, then the value of $\sinh x$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module