Mock Test

Exam: SSC CGL Subject: Quantitative Aptitude Topic: Trigonometry

Total Questions: 20

Q1. From the top of a hill 100 meters high, the angle of depression of a car is 30 degrees. After traveling for some time, the angle of depression becomes 60 degrees. How far has the car traveled?

50√3 meters 100/√3 meters 200/√3 meters 100√3 meters
Q2. The derivative of $\sin(3x)$ is:

$3\cos(3x)$ $-3\cos(3x)$ $\cos(3x)$ $-3\sin(3x)$
Q3. If $\sin \theta = -5/13$ and $\theta$ is in the third quadrant, what is the value of $\cos \theta$?

$\frac{12}{13}$ $-\frac{12}{13}$ $0$ $1$
Q4. What is the value of cos(90°)?

0 1 1/2 √3/2
Q5. The value of $\sin(15^{\circ})$ is:

$\frac{\sqrt{3}+1}{2\sqrt{2}}$ $\frac{\sqrt{3}-1}{2\sqrt{2}}$ $\frac{\sqrt{2}-1}{2\sqrt{2}}$ $\frac{\sqrt{2}+1}{2\sqrt{2}}$
Q6. Evaluate the limit: $\lim_{x \to 0} \frac{\tan(x)}{x - \sin(x)}$

2 -2 0 Undefined
Q7. If $\sin(\theta) = \frac{\sqrt{3}}{2}$, find the value of $2\cos^2(\theta) - 1$.

$\frac{1}{2}$ $-\frac{1}{2}$ 0 1
Q8. What is the value of tan(60°) * cot(30°)?

1 √3 3 1/√3
Q9. If tan(θ) = 1/√3, what is sin(θ)? (Assume θ is in the first quadrant)

1/2 √3/2 1/√3 1
Q10. A flag pole is divided into two parts by a point which is 10m from the top. If the angle of elevation of this point from a point on the ground 20m from the base of the pole is 45 degrees, the total height of the pole is:

30 m 40 m 20 m 50 m
Q11. What is the value of tan(45°)?

1/√3 √3 1 Undefined
Q12. The derivative of $\sin(kx)$ with respect to $x$ is:

$k\cos(kx)$ $-k\cos(kx)$ $k\sin(kx)$ $-k\sin(kx)$
Q13. What is the value of tan(0°)?

0 1/√3 1 undefined
Q14. What is the approximate value of tan(0.02) in radians?

0.02 0.0004 0.04 1
Q15. What is the value of sin(0°)?

0 1/2 1 √3/2
Q16. What is the value of cos(60°)?

1/2 √3/2 1/√2 0
Q17. If $\cos \theta = \frac{\sqrt{3}}{2}$, find the value of $\sin \theta$ where $\theta$ is acute.

$\frac{1}{2}$ $1$ $0$ $-\frac{1}{2}$
Q18. What is the amplitude of the function y = 3sin(x)?

1 2 3 1/3
Q19. If $\sin^{-1} x = 2\cos^{-1} x$, then $x$ is equal to:

$\frac{1}{\sqrt{2}}$ $\frac{\sqrt{3}}{2}$ $\frac{1}{2}$ $1$
Q20. Which of the following is equivalent to $\frac{\sin \theta}{\cos \theta}$?

$\cot \theta$ $\tan \theta$ $1$ $\sec \theta$

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