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SSC CHSL 2021 PYQ — Question 62

SSC CHSL - 6 Aug 2021 - Shift 1 • Quantitative Aptitude • Q62

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Evaluate the following expression. tan⁡260∘+cos⁡ec30∘sin⁡90∘+3sec⁡230∘4sin⁡245∘+sec⁡260∘−cot⁡230∘−5cos⁡290∘\frac{{{{\tan }^2}{{60}^ \circ } + \cos ec{{30}^ \circ }\sin {{90}^ \circ } + 3{{\sec }^2}{{30}^ \circ }}}{{4{{\sin }^2}{{45}^ \circ } + {{\sec }^2}{{60}^ \circ } - {{\cot }^2}{{30}^ \circ } - 5{{\cos }^2}{{90}^ \circ }}}

 

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 3.

tan⁡260∘+cosec 30∘sin⁡90∘+3sec⁡230∘4sin⁡245∘+sec⁡260∘−cot⁡230∘−5cos⁡290∘\frac{\tan^2 60^{\circ}+ cosec\: 30^{\circ}\sin 90^{\circ}+3 \sec^230^{\circ}}{4 \sin^2 45^{\circ}+ \sec^2 60^{\circ} - \cot^2 30^{\circ}-5 \cos^290^{\circ}}

⇒ (3+2×1+3×43)(4×12+4−3−5×0)\frac{(3 + 2 × 1 + 3 × \frac{4}{3})}{(4 × \frac{1}{2} + 4 - 3 - 5 × 0)}

⇒ 9/3

⇒ 3

 The required value of tan⁡260∘+cosec 30∘sin⁡90∘+3sec⁡230∘4sin⁡245∘+sec⁡260∘−cot⁡230∘−5cos⁡290∘\frac{\tan^2 60^{\circ}+ cosec\: 30^{\circ}\sin 90^{\circ}+3 \sec^230^{\circ}}{4 \sin^2 45^{\circ}+ \sec^2 60^{\circ} - \cot^2 30^{\circ}-5 \cos^290^{\circ}} is 3.