# CAT Questions | CAT Trigonometry Questions

###### CAT Quantitative Aptitude | CAT Trigonometry

A CAT Geometry question from the topic - CAT Trigoneometry that appears in the Quantitative Aptitude section of the CAT Exam broadly tests an aspirant on the concepts - Basic Trigonometric Functions, Heights and Distances, Sine rule, Cosine rule etc . In CAT Exam, one can generally expect to get approx. 1 question from CAT Trigonmetry. Make use of 2IIMs Free CAT Questions, provided with detailed solutions and Video explanations to obtain a wonderful CAT score. If you would like to take these questions as a Quiz, head on here to take these questions in a test format, absolutely free.

1. #### CAT Geometry: Trigonometric Functions

3sinx + 4cosx + r is always greater than or equal to 0. What is the smallest value ‘r’ can to take?

1. 5
2. -5
3. 4
4. 3

2. #### CAT Geometry: Trigonometry - Range of Functions

Sin2014x + Cos2014x = 1, x in the range of [-5π, 5π], how many values can x take?

1. 0
2. 10
3. 21
4. 11

3. #### CAT Geometry: Trigonometry - Maximum and Minimum Value

Consider a regular hexagon ABCDEF. There are towers placed at B and D. The angle of elevation from A to the tower at B is 30 degrees, and to the top of the tower at D is 45 degrees. What is the ratio of the heights of towers at B and D?

1. 1:√3
2. 1:2√3
3. 1:2
4. 3:4√3

4. #### CAT Geometry: Trigonometry - Maximum and Minimum Value

Find the maximum and minimum value of 8 cos A + 15 sin A + 15

1. 11√2+15; 15
2. 30; 8
3. 32; -2
4. 23; 8

5. #### CAT Geometry: Trigonometry - Trigonometric Identities

If cos A + cos2 A = 1 and a sin12 A + b sin10 A + c sin10 A + d sin6 A - 1 = 0. Find the value of a+b/c+d

1. 4
2. 3
3. 6
4. 1

6. #### CAT Geometry: Trigonometry - Trigonometric Identities

In the below figure, the sheet of width W is folded along PQ such that R overlaps S Length of PQ can be written as :-

1. $$frac{log√2}{$1+√2$}$ 2. -1 3. 1 4. None of these 8. #### CAT Geometry: Trigonometry - Height and Distances Ram and Shyam are 10 km apart. They both see a hot air balloon passing in the sky making an angle of 60° and 30° respectively. What is the height at which the balloon could be flying? 1. $\frac{5√3}{2}\\$ 2. 5√3 3. Both A and B 4. Cannot be determined 9. #### CAT Geometry: Trigonometry - Height and Distances A man standing on top of a tower sees a car coming towards the tower. If it takes 20 minutes for the angle of depression to change from 30° to 60°, what is the time remaining for the car to reach the tower? 1. 20√3 minutes 2. 10 minutes 3. 10√3 minutes 4. 5 minutes 10. #### CAT Geometry: Trigonometry - Right Triangle A right angled triangle has a height ‘p’, base ‘b’ and hypotenuse ‘h’. Which of the following value can h2 not take, given that p and b are positive integers? 1. 74 2. 52 3. 13 4. 23 11. #### CAT Geometry: Trigonometry - Trigonometric Identities If tanϕ + sinϕ = m, tanϕ − sinϕ = n, Find the value of m2 - n2 1. 2√mn 2. 4√mn 3. m-n 4. 2mn 12. #### CAT Geometry: Trigonometry - Heights and Distances A student is standing with a banner at the top of a 100 m high college building. From a point on the ground, the angle of elevation of the top of the student is 60° and from the same point, the angle of elevation of the top of the tower is 45°. Find the height of the student. 1. 35 m 2. 73.2 m 3. 50 m 4. 75 m 13. #### CAT Geometry: Trigonometry - Trigonometric Identities If Cos x – Sin x = √2 Sin x, find the value of Cos x + Sin x: 1. √2 Cos x 2. √2 Cosec x 3. √2 Sec x 4. √2 Sin x Cos x 14. #### CAT Geometry: Circles If $\frac {2Sinx}{1+cosx+Sinx}\\$=t, $\frac{1–Cosx+Sinx}{1+Sinx}\\$ can be written as: 1. $\frac{1}{t}\\$ 2. t 3. √t Sec x 4. $\frac{t}{Sinx}\\$ 15. #### CAT Geometry: Trigonometry -Height of a tree A tall tree AB and a building CD are standing opposite to each other. A portion of the tree breaks off and falls on top of the building making an angle of 30°. After a while it falls again to the ground in front of the building, 4 m away from foot of the building, making an angle of 45°. The height of the building is 6 m. Find the total height of the tree in meters before it broke. 1. 27√3 + 39 2. 12√3 + 10 3. 15√3 + 21 4. Insufficient Data 16. #### CAT Geometry: Trigonometry - Height of a flag pole A flag is hoisted on top of a building of height 7√3 m. A man of height √3 m, standing on the ground, sees the top and bottom of the flag pole at 2 different angles of elevation that are found to be complementary. If the man is standing √135 m away from the building, find the height of the flag pole. 1. 3√3 m 2. 1.5√3 m 3. $\frac{2}{√3}\\$ m 4. $\frac{6}{√3}\\$ m The Questions that follow, are from actual CAT papers. If you wish to take them separately or plan to solve actual CAT papers at a later point in time, It would be a good idea to stop here. 1. #### CAT 2019 Question Paper Slot 1 - Trigonometry The number of the real roots of the equation 2cos$x(x + 1)) = 2x + 2-x is

1. 0
2. Infinite
3. 1
4. 2

The Questions that follow, are from actual XAT papers. If you wish to take them separately or plan to solve actual XAT papers at a later point in time, It would be a good idea to stop here.

4. #### IPMAT 2019 Question Paper - IPM Indore Quants

Given that cos x + cos y = 1, the range of sin x - sin y is

1. [-1, 1]
2. [-2, 2]
3. [0, √3]
4. [-√3, √3]

5. #### IPMAT 2019 Question Paper - IPM Indore Quants

If $$sin \theta + \cos \theta = m,\\$ then $\sin ^{6} \theta + \cos ^{6} \theta\\$ equals 1. $\frac{3$m^{2}+1$}{4}$ 2. $\frac{3$m^{2}-1$}{4}$ 3. $1-\frac{3$m^{2}-1$}{4}$ 4. $1-\frac{3$m^{2}-1$^{2}}{4}$ ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2021Enroll at 49,000/- 44,000/- Online Classroom Batches Starting Now! ###### Best CAT Coaching in Chennai Introductory offer of 5000/- Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ## CAT Preparation Online | CAT Geometry - Trigonometry Videos On YouTube #### Other useful sources for Geometry Questions | Trigonometry Questions ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now
Email: prep@2iim.com