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

301.

$If (1 + \tan (α)) (1 + \tan (4 α)) = 2, α \in (0, \frac{π}{16}), then α = ?$

$\frac{π}{20}$
$\frac{π}{30}$
$\frac{π}{40}$
$\frac{π}{50}$

302.

$If \cos (θ) = \frac{\cos (α) - \cos (β)}{1 - \cos (α) \cos (β)}, then one of the values of \tan (\frac{θ}{2}) is$

$\cot (\frac{β}{2}) \tan (\frac{α}{2})$
$\tan (\frac{α}{2}) \tan (\frac{β}{2})$
$\tan (\frac{β}{2}) \cot (\frac{α}{2})$
$\tan^{2} (\frac{α}{2}) \tan^{2} (\frac{β}{2})$

303.

The value of the expression $\frac{1 + \sin (2 α)}{\cos (2 α - 2 π) \tan (α - \frac{3 π}{4})} - \frac{1}{4} \sin (2 α) [\cot (\frac{α}{2}) + \cot (\frac{3 π}{2} + \frac{α}{2})] is$

0
1
$\sin^{2} (\frac{α}{2})$
$\sin^{2} (α)$

304.

$If \frac{1}{6} \sin (θ), \cos (θ) and \tan (θ) are in geometric progression, then the solution set of θ is$

$2 nπ \pm (\frac{π}{6})$
$2 nπ \pm (\frac{π}{3})$
$nπ + {(- 1)}^{n} (\frac{π}{3})$
$nπ + (\frac{π}{3})$

305.

$In ∆ ABC if x = \tan (\frac{B - C}{2}) \tan (\frac{A}{2}), y = \tan (\frac{C - A}{2}) \tan (\frac{B}{2}) and z = \tan (\frac{A - B}{2}) \tan (\frac{C}{2}), then (x + y + z) = ?$

xyz
- xyz
2xyz
$\frac{1}{2} xyz$

306.

$If A > 0, B > 0 and A + B = \frac{π}{3}, then the maximum value of Atan (B) is$

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

307.

$In ∆ ABC, if bcos (θ) = c - a, (where θ is an acute angle), then (c - a) \tan (θ) = ?$

$2 \sqrt{ca} \cos (\frac{B}{2})$
$2 \sqrt{ac} \sin (\frac{B}{2})$
$2 cacos (\frac{B}{2})$
$2casin (\frac{B}{2})$

308.

$If \tan (α) and \tan (β) are the roots of the equation x^{2} + px + q = 0, then the value of \sin^{2} (α + β) + pcos (α + β) \sin (α + β) + {qcos}^{2} (α + β)$

p + q
p
q
$\frac{p}{p + q}$

309.

$1 + \cos (10 °) + \cos (20 °) + \cos (30 °) = ?$

$4 \sin (10 °) \sin (20 °) \sin (30 °)$
$4 \cos (5 °) \cos (10 °) \cos (15 °)$
$4 \cos (10 °) \cos (20 °) \cos (30 °)$
$4 \sin (5 °) \sin (10 °) \sin (15 °)$

310.
$The value of {(\frac{1 + \sin (\frac{2 π}{9}) + icos (\frac{2 π}{9})}{1 + \sin (\frac{2 π}{9}) - icos (\frac{2 π}{9})})}^{3} is :$

$- \frac{1}{2} (\sqrt{3} - i)$

$\frac{1}{2} (\sqrt{3} - i)$

$\frac{1}{2} (1 - i \sqrt{3})$

$- \frac{1}{2} (1 - i \sqrt{3})$

$- \frac{1}{2} (\sqrt{3} - i)$

${(\frac{1 + \cos (\frac{5 π}{18}) + isin (\frac{5 π}{18})}{1 + \cos (\frac{5 π}{18}) - isin (\frac{5 π}{18})})}^{3} = {(\frac{2 \cos^{2} (\frac{5 π}{36}) + 2 isin (\frac{5 π}{36}) \cos (\frac{5 π}{36})}{2 \cos^{2} (\frac{5 π}{36}) - 2 isin (\frac{5 π}{36}) \cos (\frac{5 π}{36})})}^{3} = {(\frac{\cos (\frac{5 π}{36}) + isin (\frac{5 π}{36})}{\cos (\frac{5 π}{36}) - isin (\frac{5 π}{36})})}^{3} = {(\cos (\frac{5 π}{36}) + isin (\frac{5 π}{36}))}^{6} = \cos (6 \times \frac{5 π}{36}) + i \sin (6 \times \frac{5 π}{36}) = \cos (\frac{5 π}{6}) + isin (\frac{5 π}{6}) \Rightarrow - \frac{\sqrt{3}}{2} + i \frac{1}{2}$

Previous Year Papers

Test Series

Test Yourself

Multiple Choice Questions

310. The value of 1 + sin2π9 + icos2π91 + sin2π9 - icos2π93 is : - 123 - i 123 - i 121 - i3 - 121 - i3

310.
$The value of {(\frac{1 + \sin (\frac{2 π}{9}) + icos (\frac{2 π}{9})}{1 + \sin (\frac{2 π}{9}) - icos (\frac{2 π}{9})})}^{3} is :$

$- \frac{1}{2} (\sqrt{3} - i)$

$\frac{1}{2} (\sqrt{3} - i)$

$\frac{1}{2} (1 - i \sqrt{3})$

$- \frac{1}{2} (1 - i \sqrt{3})$