SSC CGL level Question Set 77, Trigonometry 7 | SureSolv

SSC CGL level Question Set 77, Trigonometry 7

77th SSC CGL level Question Set, topic Trigonometry 7

ssc cgl level question set 77 trigonometry 7

This is the 77th question set for the 10 practice problem exercise for SSC CGL exam and 7th on topic Trigonometry. Answers and links to the corresponding solution set are given at the end.

Before taking the test, you may refer to the tutorial,

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


77th question set - 10 problems for SSC CGL exam: 7th on Trigonometry - testing time 12 mins

Problem 1.

If $7\sin^2 \theta+3\cos^2 \theta=4$, then the value of $\tan \theta$, where $\theta$ is acute, is,

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

Problem 2.

If $\alpha + \beta=90^0$, then the expression $\displaystyle\frac{\tan \alpha}{\tan \beta}+ \sin^2 \alpha + \sin^2 \beta$ is equal to,

  1. $\sec^2 \beta$
  2. $\sec^2 \alpha$
  3. $\tan^2 \beta$
  4. $\tan^2 \alpha$

Problem 3.

If $0^0 \lt \theta \lt 90^0$ then the value of $\displaystyle\frac{\tan \theta-\sec \theta-1}{\tan \theta + \sec \theta +1}$ is,

  1. $\displaystyle\frac{1-\cos \theta}{\sin \theta}$
  2. $\displaystyle\frac{\sin \theta +1}{\cos \theta}$
  3. $\displaystyle\frac{1-\sin \theta}{\cos \theta}$
  4. $\displaystyle\frac{\sin \theta-1}{\cos \theta}$

Problem 4.

If $5\sin \theta=3$, then the numerical value of $\displaystyle\frac{\sec \theta - \tan \theta}{\sec \theta + \tan \theta}$ is,

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

Problem 5.

If $\displaystyle\frac{\sec \theta + \tan \theta}{\sec \theta - \tan \theta}=2\displaystyle\frac{51}{79}$, the value of $\sin \theta$ is,

  1. $\displaystyle\frac{39}{72}$
  2. $\displaystyle\frac{91}{144}$
  3. $\displaystyle\frac{65}{144}$
  4. $\displaystyle\frac{35}{72}$

Problem 6.

The value of $\theta$ ($0 \leq \theta \leq 90^0$) satisfying $2\sin^2 \theta=3\cos \theta$ is,

  1. $60^0$
  2. $45^0$
  3. $90^0$
  4. $30^0$

Problem 7.

If $a$, $b$, $c$ are the lengths of three sides of a $\triangle ABC$. If $a$, $b$ and $c$ are related by the relation, $a^2+b^2+c^2=ab+bc+ca$, then the value of $\sin^2 \text{A}+\sin^2 \text{B}+\sin^2 \text{C}$ is,

  1. $\displaystyle\frac{3}{4}$
  2. $\displaystyle\frac{9}{4}$
  3. $\displaystyle\frac{3}{2}$
  4. $\displaystyle\frac{3\sqrt{3}}{2}$

Problem 8.

If $x\cos^2 30^0.\sin 60^0=\displaystyle\frac{\tan^2 45^0.\sec 60^0}{\text{cosec } 60^0}$, then the value of $x$ is,

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

Problem 9.

If $\sec \theta-\cos \theta = \displaystyle\frac{3}{2}$, where $\theta$ is a positive acute angle, the value of $\sec \theta$ is,

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

Problem 10.

If $1+\cos^2 \theta=3\sin \theta.\cos \theta$, then the integral value of $\text{cot } \theta$ $\left(0 \lt \theta \lt \displaystyle\frac{\pi}{2}\right)$ is equal to,

  1. $0$
  2. $3$
  3. $1$
  4. $2$

The answers to the questions are given below, but you will find the detailed conceptual solutions to these questions in SSC CGL level Solution Set 77 on Trigonometry 7.


Answers to the questions

Problem 1. Answer: Option b: $\displaystyle\frac{1}{\sqrt{3}}$.

Problem 2. Answer: Option b: $\sec^2 \alpha$.

Problem 3. Answer: Option d: $\displaystyle\frac{\sin \theta-1}{\cos \theta}$.

Problem 4. Answer: Option b: $\displaystyle\frac{1}{4}$.

Problem 5. Answer: Option c: $\displaystyle\frac{65}{144}$.

Problem 6. Answer: Option a: $60^0$.

Problem 7. Answer: Option b: $\displaystyle\frac{9}{4}$.

Problem 8. Answer: Option c: $2\displaystyle\frac{2}{3}$.

Problem 9. Answer: Option a: $2$.

Problem 10. Answer: Option c: $1$.


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

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