SSC CGL 2024 PYQ — Question 54

The correct answer is option 1 i.e. $3\sqrt5\over5$.

$\sqrt{9sin^2 26°+9sin^2 64°+36\over 32-7cos^2 32°-7cos^2 58°}$

$=\sqrt{9sin^2 26°+9sin^2 (90°-26°)+36\over 32-7cos^2 (90°-58°)-7cos^2 58°}$

$=\sqrt{9sin^2 26°+9cos^2 26°+36\over 32-7sin^2 58°-7cos^2 58°}$

$=\sqrt{9(sin^2 26°+cos^2 26°)+36\over 32-7(sin^2 58°+cos^2 58°)}$

$=\sqrt{9+36\over 32-7}$   [∵ sin²θ + cos²θ =1]

$=\sqrt{45\over 25}$

= $3\sqrt5\over5$