Competitive Exams : Quantitative Aptitude - Trig (Set 7) | Concept of Maths

Question 1

Find the maximum value of the expression $f(x) = 5\cos x + 3\cos(x + \frac{\pi}{3}) + 8$.

Accepted Answer

B) 15

Answer

A) 13

Answer

C) 11

Answer

D) 18

Question 2

If $ an \alpha = \frac{1}{7}$ and $ an \beta = \frac{1}{3}$, where $\alpha, \beta$ are acute angles, then what is the value of $\cos 2\alpha - \sin 4\beta$?

Accepted Answer

C) 0

Answer

A) $\frac{1}{2}$

Answer

B) $\frac{24}{25}$

Answer

D) 1

Question 3

In a $ riangle ABC$, if $\cos A + 2\cos B + \cos C = 2$, then the sides a, b, c are in:

Accepted Answer

A) Arithmetic Progression

Answer

B) Geometric Progression

Answer

C) Harmonic Progression

Answer

D) None of these

Question 4

Find the minimum value of $4\sec^2 heta + 9\csc^2 heta$ for $0 < heta < \frac{\pi}{2}$.

Accepted Answer

D) 25

Answer

A) 13

Answer

B) 20

Answer

C) 15

Question 5

If $3\sin heta + 5\cos heta = 5$, then what is the value of $(3\cos heta - 5\sin heta)^2$?

Accepted Answer

C) 9

Answer

A) 0

Answer

B) 25

Answer

D) 16

Question 6

Find the value of $\cos 20^\circ \cos 40^\circ \cos 60^\circ \cos 80^\circ$.

Accepted Answer

A) $\frac{1}{16}$

Answer

B) $\frac{1}{8}$

Answer

C) $\frac{3}{16}$

Answer

D) $\frac{1}{32}$

Question 7

A ladder 20 m long reaches a window which is 10 m above the ground on one side of a street. Keeping its foot at the same point, the ladder is turned to the other side of the street to reach a window $10\sqrt{3}m$ high. The width of the street is:

Accepted Answer

B) $10(1 + \sqrt{3})m$

Answer

A) 20 m

Answer

C) 30 m

Answer

D) $10\sqrt{3}m$

Question 8

If $ an x + an y + an z = an x an y an z$, then what is the value of $\sum \frac{2 an x}{1 - an^2 x}$ in terms of the product?

Accepted Answer

D) $\prod 	an 2x$

Answer

A) 0

Answer

B) 1

Answer

C) $\sum 	an 2x$

Question 9

If $\cos x + \cos^2 x = 1$, find the value of $\sin^{12} x + 3\sin^{10} x + 3\sin^8 x + \sin^6 x - 1$.

Accepted Answer

C) 0

Answer

A) 1

Answer

B) 2

Answer

D) -1

Question 10

The value of $\cot 7.5^\circ$ is:

Accepted Answer

B) $\sqrt{6} + \sqrt{3} + \sqrt{2} + 2$

Answer

A) $\sqrt{6} - \sqrt{3} + \sqrt{2} - 2$

Answer

C) $\sqrt{6} + \sqrt{4} + \sqrt{3} - \sqrt{2}$

Answer

D) $\sqrt{3} + \sqrt{2} + 1$