Mock Test

Exam: SSC CGL Subject: Quantitative Aptitude Topic: Trigonometry

Total Questions: 20

Q1. What is the value of sin(30°)?

1 1/2 √3/2 0
Q2. The word 'trigonometry' originates from which language?

Latin French Greek German
Q3. What is tan(180°)?

0 1 -1 undefined
Q4. The value of $\sec^2 \theta - 1$ is:

$\sin^2 \theta$ $\cos^2 \theta$ $\tan^2 \theta$ $-\tan^2 \theta$
Q5. In trigonometry, which geometric figure is most commonly studied?

Circle Square Triangle Rectangle
Q6. Which of the following represents the definition of the tangent function in terms of sine and cosine?

tan(θ) = sin(θ) * cos(θ) tan(θ) = sin(θ) + cos(θ) tan(θ) = sin(θ) / cos(θ) tan(θ) = cos(θ) / sin(θ)
Q7. If $\tan^{-1} x = \frac{\pi}{4} - \tan^{-1} y$, then:

$x+y = 1-xy$ $x+y = 1+xy$ $x-y = 1-xy$ $x-y = 1+xy$
Q8. What is the formula for tan(A + B)?

(tan A + tan B) / (1 - tan A tan B) (tan A - tan B) / (1 + tan A tan B) (tan A + tan B) / (1 + tan A tan B) (tan A - tan B) / (1 - tan A tan B)
Q9. Consider the identity $\sin(3x) = 3\sin x - 4\sin^3 x$. What is the value of $\sin(3 \times 20^{\circ})$?

$3 \sin 20^{\circ}$ $\sin 60^{\circ}$ $3 \sin 20^{\circ} - 4 \sin^3 20^{\circ}$ $\cos 30^{\circ}$
Q10. If cos(θ) = x, what is the value of sin(θ) in terms of x, given θ is in the first quadrant?

√(1-x²) √(x²-1) 1/(1-x²) 1/(x²-1)
Q11. The formula for cos(A + B) is:

sin A cos B + cos A sin B cos A cos B - sin A sin B sin A sin B - cos A cos B cos A sin B - sin A cos B
Q12. If $y = \tan^{-1}(\frac{a\sin x + b\cos x}{b\sin x - a\cos x})$, then $\frac{dy}{dx}$ is:

$0$ $1$ $\frac{b^2+a^2}{b^2-a^2}$ $\frac{a^2+b^2}{a^2-b^2}$
Q13. What is the value of cosec(30°)?

1/2 √3/2 2 1
Q14. 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
Q15. For a small angle $\theta$ in radians, what is the best approximation for $\sin(2\theta)$?

$2\theta$ $\theta$ $2\theta - \frac{(2\theta)^3}{6}$ $\theta - \frac{\theta^3}{6}$
Q16. If $\cos x = \frac{1}{2}$, what is the value of $\sin 2x$?

$\frac{\sqrt{3}}{2}$ $-\frac{\sqrt{3}}{2}$ $1$ $0$
Q17. If sin(θ) = 3/5 and cos(θ) = 4/5, what is tan(θ)?

3/4 4/3 5/4 5/3
Q18. Evaluate $\int \tan^2 x \sec^4 x \ dx$

$\frac{1}{3}\tan^3 x + \frac{1}{5}\tan^5 x + C$ $\frac{1}{3}\tan^3 x - \frac{1}{5}\tan^5 x + C$ $\frac{1}{3}\tan^3 x + \tan x + C$ $\tan^3 x + \frac{1}{5}\tan^5 x + C$
Q19. What is the value of sec(0°)?

0 1 Undefined Infinity
Q20. sin(270° - θ) is equal to?

sin(θ) cos(θ) -sin(θ) -cos(θ)

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