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.
3sinx + 4cosx + r is always greater than or equal to 0. What is the smallest value ‘r’ can to take?
A. 5
B. -5
C. 4
D. 3
Choice A
5
Sin2014x + Cos2014x = 1, x in the range of [-5π, 5π], how many values can x take?
A. 0
B. 10
C. 21
D. 11
Choice C
21
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?
A. 1 : √3
B. 1 : 2√3
C. 1 : 2
D. 3 : 4√3
Choice B
1 : 2√3
Find the maximum and minimum value of 8 cos A + 15 sin A + 15
A. 11√2+15 ; 15
B. 30 ; 8
C. 32 ; -2
D. 23 ; 8
Choice C
32 ; -2
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
A. 4
B. 3
C. 6
D. 1
Choice B
3
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 :-
A.
B.
C.
D. Any two of the above
Choice D
Any two of the above
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°)
A.
B. -1
C. 1
D. None of these
Choice D
None of these
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?
A.
B. 5√3
C. Both A and B
D. Cannot be determined
Choice C
Both A and B
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?
A. 20√3 minutes
B. 10 minutes
C. 10√3 minutes
D. 5 minutes
Choice B
10 minutes
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?
A. 74
B. 52
C. 13
D. 23
Choice D
23
If tan? + sin? = m, tan? ? sin? = n, Find the value of m2 - n2
A. 2√mn
B. 4√mn
C. m - n
D. 2mn
Choice B
4√mn
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.
A. 35 m
B. 73.2 m
C. 50 m
D. 75 m
Choice B
73.2 m
If Cos x – Sin x = √2 Sin x, find the value of Cos x + Sin x:
A. √2 Cos x
B. √2 Cosec x
C. √2 Sec x
D. √2 Sin x Cos x
Choice A
√2 Cos x
If
A.
B. t
C. √t Secx
D.
Choice B
t
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.
A. 27√3 + 39
B. 12√3 + 10
C. 15√3 + 21
D. Insufficient Data
Choice C
15√3 + 21
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.
A. 3√3 m
B. 1.5√3 m
C.
D.
Choice B
1.5√3 m
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