### Trigonometry - Sine and Cosine

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

- 5
- -5
- 4
- 3

**Correct Answer**Choice (A).

5 Correct answer- Explanatory Answer
- Trigonometric Functions
- Medium

### Range of function

Sin

^{2014}x + Cos^{2014}x = 1, x in the range of [-5π, 5π], how many values can x take?- 0
- 10
- 21
- 11

**Correct Answer**Choice (C).

21 Correct answer- Explanatory Answer
- Sine and Cosine
- Medium

### Height and Distances

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 : 2
- 1 : 2
- 3 : 4

**Correct Answer**Choice (B) Correct answer- Explanatory Answer
- Maximum and Minimum Value
- Medium

### Maximum and Minimum Value

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

- 11√2+15; 15
- 30; 8
- 32; -2
- 23; 8

**Correct Answer**Choice (C) Correct answer- Explanatory Answer
- Maximum and Minimum Value
- Hard

### Trigonometric Identities

If cos A + cos

^{2}A = 1 and a sin^{12}A + b sin^{10}A + c sin^{8}A + d sin^{6}A - 1 = 0. Find the value of- 4
- 3
- 6
- 1

**Correct Answer**Choice (B) Correct answer- Explanatory Answer
- Trigonometric Identities
- Medium

### Trigonometric Identities

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

**Correct Answer**Choice (D) Correct answer- Explanatory Answer
- Trigonometric Identities
- Hard

### 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°)

- log √2/(1+√2)
- -1
- 1
- none of these

**Correct Answer**Choice (D) Correct answer- Explanatory Answer
- Trigonometry and Logarithm
- Hard

### 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?

- 5√3
- Both A and B
- Can’t be determined

**Correct Answer**Choice (C) Correct answer- Explanatory Answer
- Height and Distances
- Hard

### 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?

- 20√3 minutes
- 10 minutes
- 10√3 minutes
- 5 minutes

**Correct Answer**Choice (B) Correct answer- Explanatory Answer
- Height and Distances
- Medium

### Right Triangle

A right angled triangle has a height ‘p’, base ‘b’ and hypotenuse ‘h’. Which of the following value can h

^{2}not take, given that p and b are positive integers?- 74
- 52
- 13
- 23

**Correct Answer**Choice (D) Correct answer- Explanatory Answer
- Right Triangle
- Medium

### Trigonometric Identities

If Find the value of m

^{2}= n^{2}- 2√mn
- 4√mn
- m – n
- 2mn

**Correct Answer**Choice (B) Correct answer- Explanatory Answer
- Trigonometric Identities
- Hard

### 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.

- 35 m
- 73.2 m
- 50 m
- 75 m

**Correct Answer**Choice (B) Correct answer- Explanatory Answer
- Heights and Distances
- Medium

### Trigonometric Identities

If Cos x – Sin x = √2 Sin x, find the value of Cos x + Sin x:

- √2 Cos x
- √2 Cosec x
- √2 Sec x
- √2 Sin x Cos x

**Correct Answer**Choice (A) Correct answer- Explanatory Answer
- Trigonometric Identities
- Medium

### Trigonometric Identities

If can be written as:

- t
- √t

**Correct Answer**Choice (B) Correct answer- Explanatory Answer
- Trigonometric Identities
- Medium

### 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.

- 27√3 + 39
- 12√3 + 10
- 15√3 + 21
- Insufficient Data

**Correct Answer**Choice (C) Correct answer- Explanatory Answer
- Height of a tree
- Hard

### 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.

- 3√3 m
- 1.5√3 m
- 2 / √3 m
- 6 / √3 m

**Correct Answer**Choice (B) Correct answer- Explanatory Answer
- Height of a flag pole
- Hard

- Percents Profits & Interests
- DI - Bar Graphs
- Geometry
- VA - Sentence Rearrangement
- Speed Time Races
- DI - Pie Charts
- Coordinate Geometry
- VA - Sentence Elimination
- Ratio Mixtures, Averages
- DI - Multiple Graphs
- Trigonometry
- VA - Sentence Correction
- Logarithms and Exponents
- DI - Word Problems
- Mensuration
- VA - Para Completion
- Pipes Cisterns
- DI - Line Graphs
- Permutation; Probability
- VA - Text Completion