1)

If \(cosec θ =  \frac{\sqrt 5}{2}\) , then what will be the value of (sec θ + tan θ - cot θ sin θ) ?

SSC CHSL 2021

A)

\(2 + \frac{4\sqrt 5}{5}\)

B)

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

C)

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

D)

2 + √5

2)

If \(8sin^2θ + 2cosθ  = 5\), 0° < θ < 90°, then the value of \(tan^2θ + sec^2θ - sin^2θ\)  will be:

SSC CHSL 2021

A)

\(\frac{153}{72}\)

B)

\(\frac{431}{144}\)

C)

\(\frac{305}{144}\)

D)

\(\frac{23}{9}\)

3)

If 3cot²x - 7cosec²x + 7 = 0, then the value of x(0 ≤ x ≤ 90°) is:

SSC CHSL 2021

A)

30°

B)

0°

C)

90°

D)

60°

4)

What is the value of sin² 60° + tan² 45° + sec² 45° - cosec² 30° ?

SSC CHSL 2021

A)

4

B)

\(\frac{1}{4}\)

C)

\(-\frac{1}{4}\)

D)

-4

5)

If 2 tanx + 3 cotx = 5, then the value of 4 tan²x + 9 cot²x is:

SSC CHSL 2021

A)

11

B)

15

C)

17

D)

13

6)

2 cos θ + sec θ - 2√2 = 0, where θ is an acute angle. Find the value of θ. 

SSC CHSL 2021

A)

45°

B)

30°

C)

60°

D)

15°

7)

In ΔABC, if ∠B = 90°, AB = 21 cm and BC = 20 cm, then \(\rm \frac{1 \space +\space sinA \space -\space cosA}{1 \space + \space sinA \space + \space cosA} \) is equal to:

SSC CHSL 2021

A)

 \(-\frac{2}{5}\)

B)

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

C)

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

D)

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

8)

If  \(\rm secθ = \frac{65}{63}\)  and θ is an acute angle, then the value of 8(cosecθ - cotθ) is: 

SSC CHSL 2021

A)

4

B)

1

C)

8

D)

2

9)

If cotθ = √2 + 1, then cosecθsecθ = ?

SSC CHSL 2021

A)

\(\frac{\sqrt2}{2}\)

B)

\(\frac{\sqrt2}{4}\)

C)

2√2

D)

4√2

10)

If 5sin²θ = 3(1 + cosθ), 0° < θ < 90°, then the value of cosecθ + cotθ is:

SSC CHSL 2021

A)

\(\sqrt{\frac{7}{3}}\)

B)

\(\frac{4}{\sqrt{21}}\)

C)

\(\frac{5}{\sqrt{21}}\)

D)

\(\sqrt{\frac{3}{7}}\)