$\sin \left(120°\right)\cos \left(150°\right) - \cos \left(240°\right)\sin \left(330°\right) \mathrm{is} \mathrm{equal} \mathrm{to} :$

• 1

• - 1

• $\frac{2}{3}$

• $- \left(\frac{\sqrt{3} + 1}{4}\right)$

$\csc \left(15°\right) + \sec \left(15°\right) \mathrm{is} \mathrm{equal} \mathrm{to} :$

• $2\sqrt{2}$

• $\sqrt{6}$

• $2\sqrt{6}$

• $\sqrt{6} + \sqrt{2}$

If 5cos(x) + 12cos(y) = 13, then the maximum value of 5 sin(x) + 12sin(y) is :

• 12

• $\sqrt{120}$

• $\sqrt{20}$

• 13

$$\begin{gathered} \mathrm{The} \mathrm{quadratic} \mathrm{equation} \mathrm{whose} \mathrm{roots} \mathrm{are} \\ {\sin }^2\left(18°\right) \mathrm{and} {\cos }^2\left(36°\right) \mathrm{is} : \end{gathered}$$

• 16x² - 12x + 1 = 0

• 16x² + 12x + 1 = 0

• 16x² - 12x - 1 = 0

• 16x² + 12x + 1 = 0

205.

For allvalues of $\mathrm{\theta }$, the value $3 - \cos \left(\mathrm{\theta }\right) + \cos \left(\mathrm{\theta } + \frac{\mathrm{\pi }}{3}\right)$ lie in the interval :

• [- 2, 3]

• [- 2, 1]

• [2, 4]

• [1, 5]

If x = tan(15°), y = csc(75°) and z = 4sin(18°),then :

• x < y < z

• y < z < x

• z < x < y

• x < z < y

$\mathrm{If}, \mathrm{in} ∆\mathrm{ABC}, \tan \left(\frac{\mathrm{A}}{2}\right) = \frac{5}{6} \mathrm{and} \tan \left(\frac{\mathrm{C}}{2}\right) = \frac{2}{5}, \mathrm{then} \mathrm{a}, \mathrm{b}, \mathrm{c} \mathrm{are} \mathrm{such} \mathrm{that}\hspace{0.17em}:$

• b² = ac

• 2b = a + c

• 2ac = b(a + c)

• a + b = c

The angles of a triangle are in the ratio 3 : 5 : 10. Then the ratio of the smallest side to the greatest side is

• 1 : sin(10°)

• 1 : 2sin(10°)

• 1 : cos(10°)

• 1 : 2cos(10°)

$\mathrm{If} \mathrm{b} + \mathrm{c} = 3\mathrm{a}, \mathrm{then} \cot \left(\frac{\mathrm{B}}{2}\right)\cot \left(\frac{\mathrm{C}}{2}\right)\mathrm{is} \mathrm{equal} \mathrm{to} :$

• 3

• 1

• 4

• 2

The elevation of an object on a hill is observed from a certain point in the horizontal plane through its base, to be 30°. After walking 120metres towards it on level ground the elevation is found to be 60°. Then the height of the object(in metres) is :

• 120

• $60\sqrt{3}$

• $120\sqrt{3}$

• 60