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QUESTION: 1

Practice Quiz or MCQ (Multiple Choice Questions) with solutions are available for Practice, which would help you prepare for **"Trigonometry"** under Quantitative Aptitude. You can practice these practice quizzes as per your speed and improvise the topic. The same topic is covered under various competitive examinations like - CAT, GMAT, Bank PO, SSC and other competitive examinations.

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

Solution:

QUESTION: 2

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

Solution:

We know that Sin^{2}x + Cos^{2}x = 1 for all values of x.

If Sin x or Cos x is equal to –1 or 1, then Sin^{2014}x + Cos^{2014}x will be equal to 1.

Sin x is equal to –1 or 1 when x = –4.5π or –3.5π or –2.5π or –1.5π or –0.5π or 0.5π or 1.5π or 2.5π or 3.5π or 4.5π.

Cosx is equal to –1 or 1 when x = –5π or –4π or –3π or –2π or –π or 0 or π or 2π or 3π or 4π or 5π.

For all other values of x, Sin^{2014} x will be strictly lesser than Sin^{2}x.

For all other values of x, Cos^{2014} x will be strictly lesser than Cos^{2}x.

We know that Sin^{2}x + Cos^{2}x is equal to 1. Hence, Sin^{2014}x + Cos^{2014}x will never be equal to 1 for all other values of x. Thus there are 21 values.

Answer choice (C)

QUESTION: 3

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?

Solution:

Let the hexagon ABCDEF be of side ‘a’. Line AD = 2a. Let towers at B and D be B’B and D’D respectively.

From the given data we know that ∠B´AB = 30° and ∠D´AB = 45°. Keep in mind that the Towers B’B and D´D are not in the same plane as the hexagon.

QUESTION: 4

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

Solution:

QUESTION: 5

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

Solution:

Given,

Cos A = 1- Cos^{2}A

=) Cos A = Sin^{2} A

=) Cos^{2}A = Sin^{4}A

=) 1 – Sin^{2} A = Sin^{4} A

=) 1 = Sin^{4} A + Sin^{2} A

=) 1^{3} = (Sin^{4}A + Sin^{2}A)^{3}

=) 1 = Sin^{12} A + Sin^{6}A + 3Sin^{8} A + 3Sin^{10} A

=) Sin^{12} A + Sin^{6}A + 3Sin^{8} A + 3Sin^{10} A – 1 = 0

On comparing,

a = 1, b = 3 , c = 3 , d = 1

QUESTION: 6

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 :-

Solution:

If you are quick at observing , this question can be solved just by looking at the options as ,

We can draw the figure as :-

Answer choice (D)

QUESTION: 7

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°)

Solution:

Writing the equation as :-

(log sin 1° - log cos 89°) + (log sin 2° - log cos 88°) + (log sin 3° - log cos 87°)………… + log tan 1°. log tan 89° + log tan 2°. log tan 88° + …….

=) (log sin 1° - log sin 1°) +(log sin 2° - log sin 2°)+……..+ log tan 1°cot 1° + log tan 2°cot 2°

=) log 1 = 0

QUESTION: 8

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?

Solution:

QUESTION: 9

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?

Solution:

QUESTION: 10

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?

Solution:

We know that,

h^{2} = p^{2} + b^{2} Given, p and b are positive integer, so h2 will be sum of two perfect squares. We see

a) 72 + 52 = 74

b) 62 + 42 = 52

c) 32 + 22 = 13

d) Can’t be expressed as a sum of two perfect squares

The question is "Which of the following value can h2 not take, given that p and b are positive integers? "

Hence, the answer is 23

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