## Second SSC CGL level Question Set, topic Trigonometry

This is the second Question set of 10 practice problem exercise for SSC CGL exam on topic Trigonometry. Students must complete the this set in prescribed time first and then only refer to the corresponding solution set.

It is emphasized here that answering in MCQ test is not at all the same as answering in a school test where you need to derive the solution in perfectly elaborated steps.

In MCQ test instead, you need basically to deduce the answer in shortest possible time and select the right choice. None will ask you about what steps you followed.

Based on our analysis and experience we have seen that, for accurate and quick answering, the student

- must have complete understanding of the basic concepts of the topics
- is adequately fast in mental math calculation
- should try to solve each problem using the most basic concepts in the specific topic area and
- does most of the deductive reasoning and calculation in his head rather than on paper.

Actual problem solving happens in items 3 and 4 above. But how to do that?

You need to use your **your problem solving abilities** only. There is no other recourse.

**Recommendation:** Before taking the test you should refer to the tutorial on,

* Basic and rich concepts in Trigonometry and its applications,* and,

**Basic and rich algebraic concepts for elegant solutions of SSC CGL problems.**

### Second Question set- 10 problems for SSC CGL exam: topic Trigonometry - time 20 mins

**Q1.** If $0^0 < \theta < 90^0$ and $2sin^2\theta + 3cos\theta = 3$ then the value of $\theta$ is,

- $30^0$
- $60^0$
- $45^0$
- $75^0$

**Q2.** If $sin\theta=\displaystyle\frac{a}{\sqrt{a^2 + b^2}}$, then the value of $cot\theta$ will be,

- $\displaystyle\frac{b}{a}$
- $\displaystyle\frac{a}{b}$
- $\displaystyle\frac{a}{b} + 1$
- $\displaystyle\frac{b}{a} + 1$

**Q3.** If $tan\theta=\frac{3}{4}$ and $0<\theta<\frac{\pi}{2}$ and $25xsin^2\theta{cos\theta}=tan^2\theta$, then the value of $x$ is,

- $\frac{7}{64}$
- $\frac{9}{64}$
- $\frac{3}{64}$
- $\frac{5}{64}$

**Q4.** If $xsin\theta - ycos\theta = \displaystyle\sqrt{x^2 + y^2}$ and $\displaystyle\frac{cos^2\theta}{a^2} + \frac{sin^2\theta}{b^2} = \frac{1}{x^2 + y^2}$ then,

- $\displaystyle\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$
- $\displaystyle\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1$
- $\displaystyle\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$
- $\displaystyle\frac{x^2}{b^2} - \frac{y^2}{a^2} = 1$

**Q5.** The value of $sin^21^0+sin^23^0+sin^25^0+...$

$...+sin^287^0+sin^289^0$ is,

- $22$
- $22\frac{1}{2}$
- $23$
- $22\frac{1}{4}$

**Q6.** The minimum value of $cos^2\theta + sec^2\theta$ is,

- 0
- 1
- 2
- 3

**Q7.** If $cos\theta + sec\theta = 2$ $(0^0\leq{\theta}\leq{90^0})$ then the value of $cos{10}\theta + sec{11}\theta$ is,

- 0
- 1
- 2
- -1

**Q8.** If $tan\theta=\frac{3}{4}$ and $\theta$ is acute then, $cosec\theta$ is equal to,

- $\frac{5}{3}$
- $\frac{5}{4}$
- $\frac{4}{3}$
- $\frac{4}{5}$

**Q9.** If $\displaystyle\frac{sin\theta + cos\theta}{sin\theta - cos\theta} = 3$ then the numerical value of $sin^4\theta - cos^4\theta$ is,

- $\frac{1}{2}$
- $\frac{2}{5}$
- $\frac{3}{5}$
- $\frac{4}{5}$

**Q10.** The minimum value of $2sin^2\theta + 3cos^2\theta$ is,

- 0
- 3
- 2
- 1

You will find the detailed conceptual solutions to these questions in **SSC CGL level Solution Set 2 on Trigonometry.**

And **video solutions** below.

**Note:** You will observe that in many of the Trigonometric problems rich algebraic concepts and techniques are to be used. In fact that is the norm. Algebraic concepts are frequently used for elegant solutions of Trigonometric problems.

### Answers to the questions

**Problem 1. Answer:** Option b: $60^0$.

**Problem 2. Answer:** Option a : $\frac{b}{a}$.

**Problem 3. Answer:** Option d: $\frac{5}{64}$.

**Problem 4. Answer:** Option b: $\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1$.

**Problem 5. Answer:** Option b: $22\frac{1}{2}$.

**Problem 6. Answer:** Option c : 2.

**Problem 7. Answer:** Option c: 2.

**Problem 8. Answer:** Option a: $\frac{5}{3}$.

**Problem 9. Answer:** Option c: $\frac{3}{5}$.

**Problem 10. Answer:** Option c: 2.

### Guided help on Trigonometry in Suresolv

To get the best results out of the extensive range of articles of **tutorials**, **questions** and **solutions** on **Trigonometry **in Suresolv, *follow the guide,*

**The guide list of articles is up-to-date.**