SSC CGL level Question Set 40, Trigonometry 4

40th SSC CGL level Question Set, topic Trigonometry 4

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This is the 40th question set for the 10 practice problem exercise for SSC CGL exam and 4th on topic Trigonometry.

We repeat the method of taking the test. It is important to follow result bearing methods even in practice test environment.

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 given at the end 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.

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.


40th question set- 10 problems for SSC CGL exam: 4th on Trigonometry - test time 12 mins

Problem 1.

The $cosec 39^0=p$, the value of, $\displaystyle\frac{1}{cosec^2 51^0} + sin^2 39^0 + tan^2 51^0 - \displaystyle\frac{1}{sin^2 51^0 sec^2 39^0}$ is,

  1. $p^2 - 1$
  2. $\sqrt{p^2 - 1}$
  3. $1-p^2$
  4. $\sqrt{1-p^2}$

Problem 2.

If $sec \theta=x + \displaystyle\frac{1}{4x}$, where $(0^0 \lt \theta \lt 90^0)$, then $sec \theta + tan \theta$ is,

  1. $\displaystyle\frac{x}{2}$
  2. $2x$
  3. $\displaystyle\frac{2}{x}$
  4. $x$

Problem 3.

If $tan \theta=1$, then the value of $\displaystyle\frac{8sin \theta + 5cos \theta}{sin^3 \theta -2cos^3 \theta + 7cos \theta}$ is,

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

Problem 4.

If $7sin \theta = 24cos \theta$, where $0 \lt \theta \lt \displaystyle\frac{\pi}{2}$, then the value of $14tan \theta - 75cos \theta - 7sec \theta$ is,

  1. 1
  2. 3
  3. 2
  4. 4

Problem 5.

The minimum value of $sin^2 \theta + cos^2 \theta + sec^2 \theta + cosec^2 \theta + tan^2 \theta + cot^2 \theta$ is equal to,

  1. 1
  2. 7
  3. 3
  4. 5

Problem 6.

In a right $\triangle ABC$ with right angle at $\angle ABC$, if $AB=2\sqrt{6}$ and $AC - BC = 2$ then, $sec A + tan A$ is,

  1. $\displaystyle\frac{\sqrt{6}}{2}$
  2. $2\sqrt{6}$
  3. $\sqrt{6}$
  4. $\displaystyle\frac{1}{\sqrt{6}}$

Problem 7.

If $tan 2\theta . tan 4\theta = 1$, then the value of $tan 3\theta$ is,

  1. $\sqrt {3}$
  2. $0$
  3. $\displaystyle\frac{1}{\sqrt{3}}$
  4. $1$

Problem 8.

If $sin \displaystyle\frac{\pi x}{2}=x^2 -2x +2$, then the value of $x$ is,

  1. $0$
  2. $-1$
  3. $1$
  4. none of these

Problem 9.

If $2sin \theta + cos \theta = \displaystyle\frac{7}{3}$, then the value of $(tan^2 \theta - sec^2 \theta)$ is,

  1. $0$
  2. $\displaystyle\frac{7}{3}$
  3. $\displaystyle\frac{3}{7}$
  4. $-1$

Problem 10.

If $(rcos \theta - \sqrt{3})^2 + (rsin \theta - 1)^2 = 0$, then the value of $\displaystyle\frac{rtan \theta + sec \theta}{rsec \theta + tan \theta}$ is,

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

Answers to the questions

Problem 1. Ans: Option a: $p^2 - 1$.

Problem 2. Ans: Option b: $2x$.

Problem 3. Ans: Option b: 2.

Problem 4. Ans: Option c: 2.

Problem 5. Ans: Option b: 7.

Problem 6. Ans: Option c: $\sqrt{6}$.

Problem 7. Ans: Option d: 1.

Problem 8. Ans: Option c: 1.

Problem 9. Ans: Option d: $-1$.

Problem 10. Ans: Option a: $\displaystyle\frac{4}{5}$.

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