111)

Solve the following equation.
2√3 sin² θ + cos θ – √3 = 0 where θ is an acute angle.

SSC CHSL 2021

A)

60°

B)

15°

C)

30°

D)

45°

112)

If \(\rm \sec\left(90^{\circ}-\frac{3θ}{2}\right)=\sqrt2\) , 0° < θ < 90°, then the value of 2sinθ + 4cos2θ will be:

SSC CHSL 2021

A)

3

B)

4

C)

2

D)

6

113)

If \( \rm \frac{\sin θ+\cos θ}{\sin θ-\cos θ}=3\), then the value of sin⁴ θ - cos⁴ θ is equal to:

SSC CHSL 2021

A)

\(\frac{4}{5}\)

B)

\(\frac{3}{5}\)

C)

\(\frac{1}{5}\)

D)

\(\frac{2}{5}\)

114)

If \(cosθ = \frac{4x}{1 + 4x^2}\), then what is the value of sin θ ?

SSC CHSL 2021

A)

\(\frac{1 - 4x^2}{4x}\)

B)

\(\frac{1 - 4x^2}{1+4x^2}\)

C)

\(\frac{1 + 4x^2}{1-4x^2}\)

D)

\(\frac{1 + 4x^2}{4x^2}\)

115)

If (sin A - cos A) = 0, then what is the value of cot A?

SSC CHSL 2021

A)

1

B)

π/4

C)

0

D)

π/6

116)

If \(cosecθ = \frac{41}{9}\) and θ is an acute angle, then the value of 5 tan θ will be:

SSC CHSL 2021

A)

\(\frac{7}{8}\)

B)

\(\frac{9}{8}\)

C)

\(\frac{11}{8}\)

D)

\(\frac{13}{4}\)

117)

Solve the following equation and find the value of θ.
3cot θ + tan θ - 2√3 = 0, 0 < θ < 90°

SSC CHSL 2021

A)

45°

B)

15°

C)

60°

D)

30°

118)

In Δ ABC, ∠A = 90°, AB = 20 cm and BC = 29 cm. What is the value of (sinB – cotC)?

SSC CHSL 2021

A)

\(- \frac{9}{{29}}\)

B)

\(\frac{9}{{29}}\)

C)

\(- \frac{189}{{580}}\)

D)

\(\frac{189}{{580}}\)

119)

If 2cos²θ = 3 (1 – sinθ), 0° < θ < 90°, then what is the value of (tan2θ + cosec3θ - sec2θ)

SSC CHSL 2021

A)

\(\sqrt 3 + 1\)

B)

\(\frac{{1 - \sqrt 3 }}{{\sqrt 3 }}\)

C)

\(\sqrt 3 - 1\)

D)

\(\frac{{1 + \sqrt 3 }}{{\sqrt 3 }}\)

120)

If tan x = cot (48° + 2x), and 0° < x < 90°, then what is the value of x?

SSC CHSL 2021

A)

12°

B)

14°

C)

16°

D)

21°