If sec\(^2\) \(\theta\) + tan\(^2\) \(\theta\) = 3, then the angle \(\theta\) is equal to
30o
45o
60o
90o
105o
Correct answer is B
sec\(^2\) \(\theta\) + tan\(^2\) \(\theta\) = 3
Where 1 + tan\(^2\) \(\theta\) = sec\(^2\) \(\theta\)
1 + tan\(^2\) \(\theta\) + tan\(^2\) \(\theta\) = 3
2 tan\(^2\) \(\theta\) = 2
tan\(^2\) \(\theta\) = 1
tan\(\theta\) = √1
where √1 = 1
tan\(\theta\) = 1
And tan 45° = 1
∴ \(\theta\) = 45°
1, 1.8 and 1.5
1.8, 1.5 and 1
1.8, 1 and 1.5
1.51, 1 and 1.8
1.5, 1.8 and 1
Correct answer is B
By re-arranging the goals in ascending order 0. 0. 0. 0. 0, 1. 1. 1. 1. 1. 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 5.
Mean = \(\frac{36}{20}\) = 1.8
Median = \(\frac{1 + 2}{2}\)
= \(\frac{3}{2}\)
= 1.5
Mode = 1
= 1.8, 1.5 and 1
A regular hexagon is constructed inside a circle of diameter 12cm. The area of the hexagon is
36\(\pi\)cm2
54\(\sqrt{3}\)cm2
\(\sqrt{3}\)cm2
\(\frac{1}{x - 1}\)
Correct answer is B
Sum of interior angle of hexagon = [2(6) - 4]90°
= 720°
sum of central angle = 360°
Each central angle = \(\frac{360}{6}\)
= 60°
Area of Hexagon = \(\frac{1}{2}\) x 6 x 6 sin 60°
\(\frac{36 \times 6\sqrt{3}}{2 \times 2}\)
= \(54 \sqrt{3}\)cm2
12cm
6cm
6\(\sqrt{2}\)cm
12\(\sqrt{2}\)cm
Correct answer is C
\(\frac{6}{\sin 30}\) = \(\frac{x}{\sin 135}\)
\(\frac{6}{\sin 30}\) = \(\frac{x}{\sin 45}\)
x = \(\frac{6 \times \sin 45}{\sin 30}\)
= \(6 \sqrt{2}\)cm
An arithmetic progression has first term 11 and fourth term 32. The sum of the first nine terms is
351
531
135
153
Correct answer is A
1st term a = 11, 4th term = 32
nth term = a + (n - 1)d
4th term = 11 = (4 - 1)d
= 11 + 3d
= 32
3d = 21
d = 7
sn = n(2a + (n - 1)d)
sn = \(\frac{9}{2}\)(2 \times 11) + (9 - 1)7
\(\frac{9}{2}\)(22 + 56) = \(\frac{9}{2}\) x 78
= 351