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
    Choice A
    5

  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
    Choice C
    21

  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
    Choice B
    1:2√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
    Choice C
    32; -2

  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
    Choice B
    3

  6. CAT Geometry: Trigonometry - Trigonometric Identities

    CAT Question - Trigonometry - Trigonometric Identities
    There is an equilateral triangle with a square inscribed inside it. One of the sides of the square lies on a side of the equilateral △. What is the ratio of the area of the square to that of the equilateral triangle?

    1. \\frac{w}{sinα(1+cos2α)}\\)
    2. \\frac{w}{sin2αcosα}\\)
    3. \\frac{w}{1+sin2α}\\)
    4. Any two of the above
    Choice D
    Any two of the above

  7. CAT Geometry: Trigonometry - Trigonometry and Logarithm

    Find the value of :- (log sin 1° + log sin 2° ………..+ log sin 89°) + (log tan 1° + log tan 2° + ……… + log tan 89°) - (log cos 1° + log cos 2° + ……… + log cos 89°)

    1. \\frac{log√2}{(1+√2)}\\)
    2. -1
    3. 1
    4. None of these
    Choice D
    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
    Choice C
    Both A and B

  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
    Choice B
    10 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
    Choice D
    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
    Choice B
    4√mn

  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
    Choice B
    73.2 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
    Choice A
    √2 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}\\)
    Choice B
    4√3

  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 tree, 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
    Choice C
    15√3 + 21

  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
    Choice B
    1.5√3 m


CAT Preparation Online | CAT Geometry - Trigonometry Videos On YouTube


Other useful sources for Geometry Questions | Trigonometry Questions


CAT Questions | CAT Quantitative Aptitude

CAT Questions | CAT DILR

CAT Questions | Verbal Ability for CAT


Where is 2IIM located?

2IIM Online CAT Coaching
A Fermat Education Initiative,
10-C, Kalinga Colony, Bobbili Raja Salai
K.K.Nagar, Chennai. India. Pin - 600 078

How to reach 2IIM?

Phone: (91) 44 4505 8484
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now
Email: prep@2iim.com