SSC CGL level Question Set 56, Trigonometry 5

56th SSC CGL level Question Set, topic Trigonometry 5

SSC CGL level question set 56 trigonometry 5

This is the 56th question set for the 10 practice problem exercise for SSC CGL exam and 5th on topic Trigonometry.

We repeat the method of taking the test. It is an important Test preparation method to follow even in practice test environment for continuous skill-set improvement, as metrics or performance measurement is built-in.

Method of taking the test for getting the best results from the test:

  1. Before start, go throughTutorial on Basic and rich concepts in Trigonometry and its applications or any short but good material to refresh your concepts if you so require.
  2. Answer the questions in an undisturbed environment with no interruption, full concentration and alarm set at 12 minutes.
  3. When the time limit of 12 minutes is over, mark up to which you have answered, but go on to complete the set.
  4. At the end, refer to the answers from the companion solution set to mark your score at 12 minutes. For every correct answer add 1 and for every incorrect answer deduct 0.25 (or whatever is the scoring pattern in the coming test). Write your score on top of the answer sheet with date and time.
  5. Identify and analyze the problems that you couldn't do to learn how to solve those problems.
  6. Identify and analyze the problems that you solved incorrectly. Identify the reasons behind the errors. If it is because of your shortcoming in topic knowledge improve it by referring to only that part of concept from the best source you can get hold of. You might google it. If it is because of your method of answering, analyze and improve those aspects specifically.
  7. Identify and analyze the problems that posed difficulties for you and delayed you. Analyze and learn how to solve the problems using basic concepts and relevant problem solving strategies and techniques.
  8. Give a gap before you take a 10 problem practice test again.

Important: both practice tests and mock tests must be timed, analyzed, improving actions taken and then repeated. With intelligent method, it is possible to reach highest excellence level in performance.

Resources that should be useful for you

Before taking the test it is recommended that you refer to

Tutorial on Basic and rich concepts in Trigonometry and its applications.

Tutorial on Basic and rich concepts in Trigonometry part 2, proof of compound angle functions

Tutorial on Trigonometry concepts part 3, maxima or minima of Trigonometric expressions

You may also refer to the related resources:

7 steps for sure success in SSC CGL tier 1 and tier 2 competitive tests or section on SSC CGL to access all the valuable student resources that we have created specifically for SSC CGL, but generally for any hard MCQ test.

If you like, you may subscribe to get latest content on competitive exams published in your mail as soon as we publish it.

Now set the stopwatch alarm and start taking this test. It is not difficult.


56th question set- 10 problems for SSC CGL exam: 5th on Trigonometry - 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. $\displaystyle\frac{\sin^2 \theta}{\cot \theta - \sec \theta}$

You will find answers and the detailed conceptual solutions to these questions in SSC CGL level Solution Set 56 on Trigonometry 5.


Resources on Trigonometry and related topics

You may refer to our useful resources on Trigonometry and other related topics especially algebra.

Tutorials on Trigonometry

Basic and rich concepts in Trigonometry and its applications

Basic and Rich Concepts in Trigonometry part 2, proof of compound angle functions

Trigonometry concepts part 3, maxima (or minima) of Trigonometric expressions

General guidelines for success in SSC CGL

7 steps for sure success in SSC CGL tier 1 and tier 2 competitive tests

Efficient problem solving in Trigonometry

How to solve not so difficult SSC CGL level problem in a few light steps, Trigonometry 9

How to solve a difficult SSC CGL level problem in a few concepual steps, Trigonometry 8

How to solve not so difficult SSC CGL level problem in a few light steps, Trigonometry 7

How to solve a difficult SSC CGL level problem in few quick steps, Trigonometry 6

How to solve a School Math problem in a few direct steps, Trigonometry 5

How to solve difficult SSC CGL level School math problems in a few quick steps, Trigonometry 5

How to solve School Math problem in a few steps and in Many Ways, Trigonometry 4

How to solve a School Math problem in a few simple steps, Trigonometry 3

How to solve difficult SSC CGL level School math problems in a few simple steps, Trigonometry 4

How to solve difficult SSC CGL level School math problems in a few simple steps, Trigonometry 3

How to solve School math problems in a few simple steps, Trigonometry 2

How to solve School math problems in a few simple steps, Trigonometry 1

A note on usability: The Efficient math problem solving sessions on School maths are equally usable for SSC CGL aspirants, as firstly, the "Prove the identity" problems can easily be converted to a MCQ type question, and secondly, the same set of problem solving reasoning and techniques have been used for any efficient Trigonometry problem solving.

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SSC CGL level Solution Set 40 on Trigonometry 4

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SSC CGL level Solution Set 19 on Trigonometry

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