Trigonometry Questions and Answers for Competitive exams SSC CGL 56 | Suresolv

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SSC CGL level Question Set 56, Trigonometry 5

Trigonometry questions and answers for competitive exams SSC CGL 56

Trigonometry questions and answers for competitive exams SSC CGL 56

Trigonometry questions and answers for competitive exams SSC CGL Set 56. The 10 selected questions to be answered in 12 minutes. Verify from answers at the end.

Go through the related solutions to know how to answer the questions comfortably within 12  minutes time. Link is given at the end.

Now set the timer on and take the test like an actual test.


Trigonometry questions and answers for competitive exams SSC CGL Set 56 - testing time 12 mins

Problem 1.

The maximum value of $(2\sin \theta + 3\cos\theta)$ is,

  1. $1$
  2. $2$
  3. $\sqrt{13}$
  4. $\sqrt{15}$

Problem 2.

Find the minimum value of $9\tan^2 \theta + 4\cot^2 \theta$,

  1. $15$
  2. $6$
  3. $9$
  4. $12$

Problem 3.

If $\text{cosec} \theta -\cot \theta= \displaystyle\frac{7}{2}$, the value of $\text{cosec} \theta$ is,

  1. $\displaystyle\frac{49}{28}$
  2. $\displaystyle\frac{53}{28}$
  3. $\displaystyle\frac{47}{28}$
  4. $\displaystyle\frac{51}{28}$

Problem 4.

If $\tan^2 \alpha=1 +2\tan^2 \beta$, where $\alpha$ and $\beta$ both are positive acute angles, find the value of $\sqrt{2}\cos \alpha - \cos \beta$.

  1. $0$
  2. $\sqrt{2}$
  3. $-1$
  4. $1$

Problem 5.

The value of $152(\sin 30^0 + 2\cos^2 45^0 + 3\sin 30^0 +$

$\hspace{30mm}4\cos^2 45^0 + ....+17\sin 30^0+18\cos^2 45^0)$ is,

  1. an irrational number
  2. a rational number but not an integer
  3. an integer but not a perfect square
  4. the perfect square of an integer

Problem 6.

If $\tan \theta + \cot \theta=2$, then the value of $\tan^n \theta + \cot^n \theta$ ($0^0 \lt \theta \lt 90^0$, and $n$ an integer) is,

  1. $2$
  2. $2^{n+1}$
  3. $2^n$
  4. $2n$

Problem 7.

If $\displaystyle\frac{\sin \theta}{1+\cos \theta} + \displaystyle\frac{\sin \theta}{1-\cos \theta} = 4$, the value of $\cot \theta + \sec \theta$ is,

  1. $\sqrt{3}$
  2. $\displaystyle\frac{\sqrt{3}}{7}$
  3. $\displaystyle\frac{\sqrt{3}}{5}$
  4. $\displaystyle\frac{5}{\sqrt{3}}$

Problem 8.

If $\sin \theta + \cos \theta =\sqrt{2}$ with $\angle \theta$ a positive acute angle, then the value of $\tan \theta + \sec \theta$ is,

  1. $\sqrt{3}-1$
  2. $\displaystyle\frac{1}{\sqrt{2}-1}$
  3. $\sqrt{2}-1$
  4. $\sqrt{3}+1$

Problem 9.

If $p=a\sec {\theta}\cos \alpha$, $q =b\sec {\theta}\sin \alpha$, and $r =c\tan \theta$, then the value of $\displaystyle\frac{p^2}{a^2} +\displaystyle\frac{q^2}{b^2}-\displaystyle\frac{r^2}{c^2}$ is,

  1. 0
  2. 1
  3. 4
  4. 5

Problem 10.

$\displaystyle\frac{\sin^2 \theta}{\cos^2 \theta}+\displaystyle\frac{\cos^2 \theta}{\sin^2 \theta}$ is equal to,

  1. $\displaystyle\frac{1}{\sin^2 {\theta}\cos^2 \theta}$
  2. $\displaystyle\frac{1}{\sin^2 {\theta}\cos^2 \theta} -2$
  3. $\displaystyle\frac{1}{\tan^2 \theta - \cot^2 \theta}$
  4. $\displaystyle\frac{\sin^2 \theta}{\cot \theta - \sec \theta}$

Conceptual and quick solution of the questions is at,

SSC CGL Solution set 56 on Trigonometry.

For trigonometry concepts read,

Basic and rich trigonometry concepts and application.


Answers to the questions

Problem 1. Answer: c: $\sqrt{13}$.

Problem 2. Answer: d: $12$.

Problem 3. Answer: b: $\displaystyle\frac{53}{28}$.

Problem 4. Answer: a: $0$.

Problem 5. Answer: d: the perfect square of an integer.

Problem 6. Answer: a: $2$.

Problem 7. Answer: d: $\displaystyle\frac{5}{\sqrt{3}}$.

Problem 8. Answer: b: $\displaystyle\frac{1}{\sqrt{2}-1}$.

Problem 9. Answer: b: 1.

Problem 10. Answer: b: $\displaystyle\frac{1}{\sin^2 {\theta}\cos^2 \theta}-2$.


Guided help on Suresolv Trigonometry

To get the best results out of the extensive range of articles on Quantitative Aptitude Trigonometry problem solving, follow the guide,

Trigonometry Reading and Practice Guide for SSC CGL, SSC CGL Tier II and Other Competitive exams.

The guide contains the full list of concept articles, question and solution sets for SSC CGL Tier I and II, SSC CHSL, SSC CPO. It is a comprehensive resource of Quantitative aptitude Trigonometry.


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