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

• 16x² - 12x + 1 = 0

• 16x² + 12x + 1 = 0

• 16x² - 12x - 1 = 0

• 16x² + 12x + 1 = 0

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

The transformed equation of x² + 6xy + 8y² = 10 when the axes are rotated through an angle $\frac{\mathrm{\pi }}{4}$is :

• 15x² - 14xy + 3y² = 20

• 15x² + 14xy - 3y² = 20

• 15x² + 14xy + 3y² = 20

• 15x² - 14xy - 3y² = 20

$$\begin{gathered} \mathrm{If} \mathrm{\theta } \mathrm{Lies} \mathrm{in} \mathrm{the} \mathrm{first} \mathrm{quadrant} \mathrm{and} 5\mathrm{tan\theta } = 4, \\ \mathrm{then} \frac{5\sin \left(\mathrm{\theta }\right) - 3\cos \left(\mathrm{\theta }\right)}{5\sin \left(\mathrm{\theta }\right)- 3\cos \left(\mathrm{\theta }\right)} = ? \end{gathered}$$

• $\frac{5}{14}$

• $\frac{3}{14}$

• $\frac{1}{14}$

• 0

$\frac{\tan \left(80°\right) - \tan \left(10°\right)}{\tan \left(70°\right)} = ?$

• 0

• 1

• 2

• 3