Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Trigonometric Functions

Multiple Choice Questions

171.

$\tan (θ) + \cot (θ) = 2$ = 2, then $\sin (θ)$ is equal to

$\frac{1}{\sqrt{2}}$
$\frac{1}{\sqrt{3}}$
$\frac{1}{2}$
1

172.

$If θ = \frac{π}{6}, then the 10 th term of 1 + (\cos (θ) + isin (θ)) + {(\cos (θ) + isin (θ))}^{2} + {(\cos (θ) + isin (θ))}^{3} + . . . is equal to$

$i$
- 1
1
$- i$

173.

$\frac{\sin (5 θ)}{\sin (θ)} is equal to$

$16 c o s^{4} (θ) - 12 c o s^{2} (θ) + 1$
$16 \cos^{4} (θ) + 12 \cos^{2} (θ) + 1$
$16 \cos^{4} (θ) - 12 \cos^{2} (θ) - 1$
$16 \cos^{4} (θ) + 12 \cos^{2} (θ) - 1$

174.

$\cos^{2} (\frac{π}{6} + θ) - \sin^{2} (\frac{π}{6} + θ) is equal to$

$\frac{1}{2} \cos (2 θ)$
0
$- \frac{1}{2} \cos (2 θ)$
$\frac{1}{2}$

175.

$In ∆ ABC, \frac{\cos (C) + \cos (A)}{c + a} + \frac{\cos (B)}{b} is equal to$

$\frac{1}{a}$
$\frac{1}{b}$
$\frac{c + a}{b}$
1

176.
$In ∆ ABC, \frac{a}{b^{2} - c^{2}} + \frac{c}{b^{2} - a^{2}} = 0, then B is equal to$

$\frac{π}{2}$

$\frac{π}{4}$

$\frac{2 π}{3}$

$\frac{π}{3}$

$\frac{π}{3}$

$We have, \frac{a}{b^{2} - c^{2}} + \frac{c}{b^{2} - a^{2}} = 0 \Rightarrow \frac{2 Rsin (A)}{4 R^{2} (\sin^{2} (B) - \sin^{2} (C))} + \frac{2 Rsin (C)}{4 R^{2} (\sin^{2} (B) - \sin^{2} (A))} = 0 \Rightarrow \frac{1}{2 R} \frac{\sin (A)}{\sin (B + C) \sin (B - C)} + \frac{1}{2 R} \frac{\sin (C)}{\sin (B + C) \sin (B - A)} = 0 \Rightarrow \frac{1}{2 R} \frac{sinA}{\sin (A) \sin (B - C)} + \frac{1}{2 R} \frac{\sin (C)}{\sin (C) \sin (B - A)} = 0 \Rightarrow \frac{1}{2 R} \frac{1}{\sin (B - C)} + \frac{1}{2 R} \frac{1}{\sin (B - A)} = 0 \Rightarrow \sin (B - C) + \sin (B - A) = 0 \Rightarrow 2 \sin (\frac{2 B - A - C}{2}) \cos (\frac{- C + A}{2}) = 0 \Rightarrow \sin (\frac{2 B - A - C}{2}) = 0 \Rightarrow 2 B = A + C \Rightarrow 2 B = 180 ° - B \Rightarrow 3 B = 180 ° \Rightarrow B = \frac{π}{3}$

177.

$In ∆ ABC, a^{2} \sin (2 C) + c^{2} \sin (2 A) is equal to$

$∆$
$2 ∆$
$3 ∆$
$4 ∆$

178.

$The shadow of a tower standing on a level ground is found to be 60 m longer when the sun' s altitude is 30 ° than when it is 45 ° . The height of the tower is$

$30 m$
$90 m$
$60 \sqrt{3} m$
$30 (\sqrt{3} + 1) m$

179.

$If cosecθ = \frac{p + q}{p - q}, then \cot (\frac{π}{4} + \frac{θ}{4}) is equal to$

$\frac{\sqrt{p}}{q}$
$\sqrt{\frac{q}{p}}$
$\sqrt{pq}$
$pq$

180.

From a point on the level ground, the angle of elevation of top of a pole is $30 °$ on moving 20metres nearer,the angle of elevation is $45 °$ . Then,the height of the pole $(in metres)$ , is

$10 (\sqrt{3} - 1)$
$10 (\sqrt{3} - 1)$
15
20

Previous Year Papers

Test Series

Test Yourself

Multiple Choice Questions

176. In ∆ABC, ab2 - c2 + cb2 - a2 = 0, then B is equal to π2 π4 2π3 π3

176.
$In ∆ ABC, \frac{a}{b^{2} - c^{2}} + \frac{c}{b^{2} - a^{2}} = 0, then B is equal to$

$\frac{π}{2}$

$\frac{π}{4}$

$\frac{2 π}{3}$

$\frac{π}{3}$