If cos θ = √32 and θ is less than 90o. Calculate cot(90−θ)sin2θ
4√3
4√3
√32
1√3
2√3
Correct answer is A
cot(90−θ)sin2θ
cot(90−θ)=tanθ
∴
\tan \theta = \frac{\sqrt{3}}{3}
\sin \theta = \frac{1}{2} \implies \sin^{2} \theta = \frac{1}{4}
\frac{\cot(90 - \theta)}{\sin^{2} \theta} = \frac{\sqrt{3}}{3}\div\frac{1}{4}
= \frac{4}{\sqrt{3}}
Find the area of a regular hexagon inscribed in a circle of radius 8cm
16\sqrt{3} cm3
96\sqrt{3} cm3
192\sqrt{3} cm3
16\sqrt{3} cm2
33cm2
Correct answer is B
Area of a regular hexagon = 8 x 8 x sin 60o
= 32 x \frac{\sqrt{3}}{2}
Area = 16\sqrt{3} x 6 = 96 \sqrt{3}cm2
\frac{7}{10}
\frac{3}{5}
\frac{4}{5}
\frac{3}{10}
Correct answer is B
Simple Space: (1, 2, 3, 4, 5, 6, 7, 8, 9, 10 = 10)
Prime: (2, 3, 5, 7)
multiples of 3: (3, 6, 9)
Prime or multiples of 3: (2, 3, 5, 6, 7, 9 = 6)
Probability = \frac{6}{10}
= \frac{3}{5}
Without using table, calculate the value of 1 + sec2 30o
2\frac{1}{3}
\frac{2}{15}
\frac{5}{3}
3\frac{1}{2}
Correct answer is A
1 + sec2 30o = sec 30o
= \frac{2}{\sqrt{3}}
\frac{(2)^2}{3}
= \frac{4}{3}
1 + sec2 30o = sec 30o
= 1 + \frac{4}{3}
= 2\frac{1}{3}
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