Question

Arrange the following equations in decreasing order of their number of solutions in $[0,2\pi ]$
I) $3{\sin }^2\theta +4{\cos }^2\theta =5$
II) $4{\sin }^2\theta +3{\cos }^2\theta =\frac{7}{2}$
III)$3{\sin }^2\theta +4{\cos }^2\theta =4$

• A. II,III,I
• B. I, II, III
• C. III, I, II
• D. III, II,I

Answer 1

Answer: (A)

II,III,I

I) gives $co{s}^2\theta =2$ so no solution
II) gives $si{n}^2\theta =\frac{1}{2}$ so $4$ solutions
III) gives $si{n}^2\theta =0$ so 3 solutions