Question

Match List - I with List - II and select the correct answer using the code given below the lists:

List - I (Function)	List - II (Maximum value)
A. $\sin x+\cos x$	1. $\sqrt{10}$
B. $3\sin x+4\cos x$	2. $\sqrt{2}$
C. $2\sin x+\cos x$	3. $5$
D. $\sin x+3\cos x$	4. $\sqrt{5}$

• A. $A-2,B-3,C-1,D-4$
• B. $A-2,B-3,C-4,D-1$
• C. $A-3,B-2,C-1,D-4$
• D. $A-3,B-2,C-4,D-1$

Answer 1

Answer: (B)

$A-2,B-3,C-4,D-1$

Max value of $a\sin x+b\cos x=\sqrt{a^2+b^2}$

For $\sin x+\cos x$ max value=$\sqrt{2}$

For $3\sin x+4\cos x$max value=$\sqrt{3^2+4^2}=5$

For $2\sin x+\cos x$max value=$\sqrt{2^2+1^2}=\sqrt{5}$

For $\sin x+3\cos x$ max value=$\sqrt{1^2+3^2}=\sqrt{10}$

So correct answer will be option D