SSC CGL Tier II level Question Set 7, Trigonometry 1

Submitted by Atanu Chaudhuri on Tue, 08/11/2016 - 14:54

7th SSC CGL Tier II level Question Set, topic Trigonometry 1

SSC CGL Tier 2 question set 7 trigonometry1

This is the 7th question set of 10 practice problem exercise for SSC CGL Tier II level exam and 1st 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:

Before start, go throughTutorial on Basic and rich concepts in Trigonometry and its applications, Tutorial on Basic and rich concepts in Trigonometry Part 2, Compound angle functions or any short but good material to refresh your concepts if you so require.
Answer the questions in an undisturbed environment with no interruption, full concentration and alarm set at 15 minutes.
When the time limit of 15 minutes is over, mark up to which you have answered, but go on to complete the set.
At the end, refer to the answers given at the end to mark your score at 15 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.
Identify and analyze the problems that you couldn't do to learn how to solve those problems.
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.
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.
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, Compound angle functions.

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.

7th question set- 10 problems for SSC CGL Tier II exam: 1st on Trigonometry - testing time 15 mins

Problem 1.

If $x=rsin\alpha {cos\beta}$, $y=rsin\alpha{sin\beta}$ and $z=rcos\alpha$, then,

$x^2-y^2+z^2=r^2$
$x^2+y^2+z^2=r^2$
$x^2+y^2-z^2=r^2$
$y^2+z^2-x^2=r^2$

Problem 2.

With $\angle \theta$ acute, the value of the expression, $\left(\displaystyle\frac{5\ cos \theta - 4}{3-5\ sin \theta} - \displaystyle\frac{3+5\ sin \theta}{4+5\ cos \theta}\right)$ is,

$1$
$0$
$\displaystyle\frac{1}{2}$
$\displaystyle\frac{1}{4}$

Problem 3.

If $4+ 3\ tan \alpha=0$, where $\displaystyle\frac{\pi}{2} \lt \alpha \lt \pi$, the value of $2\ cot \alpha - 5\ cos \alpha + \sin \alpha$ is,

$\displaystyle\frac{23}{10}$
$-\displaystyle\frac{53}{10}$
$\displaystyle\frac{37}{10}$
$\displaystyle\frac{7}{10}$

Problem 4.

If $\ sin \theta + \ sin^2 \theta=1$, then which of the following is true?

$\ cos \theta +\ cos^2 \theta=1$
$\ cos^2 \theta +\ cos^3 \theta=1$
$\ cos^2 \theta +\ cos^4 \theta=1$
$\ cos \theta -\ cos^2 \theta=1$

Problem 5.

If $a=\sec \theta+\tan \theta$, then $\displaystyle\frac{a^2-1}{a^2+1}$ is,

$\sec \theta$
$\cos \theta$
$\tan \theta$
$\sin \theta$

Problem 6.

The value of $\displaystyle\frac{cot \theta + cosec \theta - 1}{cot \theta -cosec \theta +1}$ is,

$cosec \theta - cot \theta$
$cosec \theta + cot \theta$
$sec \theta + cot \theta$
$cosec \theta + tan \theta$

Problem 7.

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

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

Problem 8.

If $asec \theta+btan \theta +c=0$, and $psec \theta +qtan \theta +r=0$, then the value of $(br-qc)^2-(pc-ar)^2$ is,

$(aq+bp)^3$
$(aq-bp)^3$
$(aq+bp)^2$
$(aq-bp)^2$

Problem 9.

If $\alpha + \beta + \gamma=\pi$, then the value of $(sin^2 \alpha + sin^2 \beta - sin^2 \gamma)$ is,

$2sin \alpha{sin \beta}cos \gamma$
$2sin \alpha$
$2sin \alpha{cos \beta}sin \gamma$
$2sin \alpha{sin \beta}sin \gamma$

Problem 10.

If $sin\alpha sin\beta-cos\alpha cos\beta + 1=0$, then the value of $cot\alpha tan\beta$ is,

$-1$
$1$
$0$
None of these

The answers are given below, but you will find the detailed conceptual solutions to these questions in SSC CGL Tier II level Solution Set 7 on Trigonometry 1.

Answers to the problems

Problem 1. Answer: b: $x^2+y^2+z^2=r^2$.

Problem 2. Answer: b: 0.

Problem 3. Answer: a: $\displaystyle\frac{23}{10}$.

Problem 4. Answer: c: $cos^2\theta + cos^4\theta=1$

Problem 5. Answer: d: $sin \theta$.

Problem 6. Answer: b: $cosec \theta + cot \theta$.

Problem 7. Answer: d: 1.

Problem 8. Answer: d: $(aq-bp)^2$.

Problem 9. Answer: a: $2sin\alpha sin\beta cos \gamma$.

Problem 10. Answer: a: $-1$.

Resources on Trigonometry and related topics

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

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.