Untitled Document

Question Bank No: 3

1. The sides of a triangle are in the ratio 1: $\sqrt{3}$ :2, then the angles are in the ratio.

a)		1: 3 : 5
b)		2 : 3 : 4
c)		3 :2 : 1
d)		1 :2 : 3

2. In $Δ ABC$ , the correct relation is

a)		(b - c) sin $(\frac{B - C}{2})$ = a cos $\frac{A}{2}$
b)		b -c) cos $\frac{A}{2}$ = a sin $(\frac{B - C}{2})$
c)		(b + c ) sin $(\frac{B + C}{2})$ = a cos $\frac{A}{2}$
d)		(b - c) cos $\frac{A}{2}$ = 2a sin $(\frac{B + C}{2})$

3. The number of values of $x$ in $[0, 5 π]$ satisfying the equation $3 \sin^{2} x - 7 \sin x + 2$ = 0 is

a)		0
b)		5
c)		6
d)		10

4. The solution of sin x+ cos x = 1 is

a)		x =2n $π$
b)		x = 2n $π$ + $\frac{π}{2}$
c)		x = n $π$ + ${(- 1)}^{2} (\frac{π}{4}) - \frac{π}{4}$
d)		none

5. The smallest positive root of the equation tan x- x = 0 is in

a)		$(0, \frac{π}{2})$
b)		$(π, \frac{3 π}{2})$
c)		$(\frac{π}{2}, π)$
d)		$(\frac{3 π}{2}, 2 π)$

6. The values of $θ$ in $[0, \frac{π}{2}]$ satisfying $| \begin{matrix} 1 + \sin^{2} θ & \cos^{2} θ & 4 \sin 4 θ \\ \sin^{2} θ & 1 + \cos^{2} θ & 4 \sin 4 θ \\ \sin^{2} θ & \cos^{2} θ & 1 + 4 \sin 4 θ \end{matrix} |$ = 0 are

a)		$\frac{7 π}{24}$
b)		$\frac{5 π}{24}$
c)		$\frac{14 π}{24}$
d)		$\frac{π}{24}$

7. The number of solution ofthe equation $\tan x + \sec x = 2 \cos x$ in $[0, 2 π]$ is

a)		0
b)		1
c)		2
d)		3

8. The number of integral values of $k$ for which the equation $7 \cos x + 5 \sin x = 2 k + 1$ has a solution is

a)		4
b)		8
c)		10
d)		12

9. The number of distinct roots of $| \begin{matrix} sinx & cosx & cosx \\ cosx & sinx & cosx \\ cosx & cosx & sinx \end{matrix} |$ = 0 in $[- \frac{π}{4}, \frac{π}{4}]$ is

a)		0
b)		1
c)		2
d)		3

10. If cos ( x + iy ) = A+iB, then A equals

a)		cos x cosh y
b)		sin x sinh y
c)		– sin x sinh y
d)		cos x sinh y

11. A cow is tied to a post by a rope. If the cow moves along the circular path always keeping the rope tight, and describes 44 metres, when it has traced out $72^{o}$ at the centre, the length of the rope is

a)		35 metres
b)		22 metres
c)		56 metres
d)		45 metres

12. If sin $θ$ = - $\frac{1}{2}$ and cos $θ$ $\sqrt{3}$ /2, then $θ$ lies in

a)		$1^{st}$ quadrant
b)		${II}^{nd}$ quadrant
c)		${III}^{rd}$ quadrant
d)		${IV}^{th}$ quadrant

13. If tan $θ$ =+ $\frac{1}{\sqrt{5}}$ and $θ$ lies in the $1^{st}$ quadrant, then cos $θ$ is

a)		$\frac{1}{\sqrt{6}}$
b)		- $\frac{1}{\sqrt{6}}$
c)		$\frac{\sqrt{5}}{\sqrt{6}}$
d)		- $\frac{\sqrt{5}}{\sqrt{6}}$

14. The value of $\cos^{2}$ $θ$ + ${Sec}^{2}$ $θ$ is always

a)		less than 1
b)		equal to 1
c)		greater than 1, but less than 2
d)		greater than or equal to 2

15. If cos $20^{o}$ = k and cos x = ${2 k}^{2}$ - 1, then the possible values of x between $0^{o}$ and $360^{o}$ are

a)		$140^{o}$
b)		$40^{o}$ and $140^{o}$
c)		$50^{o}$ and $130^{o}$
d)		$40^{o}$ and $320^{o}$

16. The minimum value of sin $θ$ cos $θ$ is

a)		1
b)		0
c)		- $\frac{1}{2}$
d)		$\frac{1}{2}$

17. If 0 < θ < $90^{o}$ , then sec $θ$ is

a)		greater than 1
b)		less than1
c)		equal to 1
d)		none of these

18. sin $50^{o}$ - sin $70^{o}$ + sin $10^{o}$ is equal to

a)		1
b)		0
c)		$\frac{1}{2}$
d)		2

19. The value of sin $28^{o}$ cos $17^{o}$ + cos $28^{o}$ sin $17^{o}$ is

a)		1/ $\sqrt{2}$
b)		1
c)		- 1/ $\sqrt{2}$
d)		0

20. When x = $\frac{π}{2}$ , then tan x is

a)		+ $\infty$
b)		- $\frac{π}{2}$
c)		$\infty$ or - $\infty$
d)		not defined

21. The value of the expression sin $θ$ + cos $θ$ lies between

a)		-2 and 2 both inclusive
b)		0 and $\sqrt{2}$ both inclusive
c)		- $\sqrt{2}$ and $\sqrt{2}$ both inclusive
d)		0 and 2 both inclusive

22. For m $\neq$ n, if tan m $θ$ = tan n $θ$ , then the different values of $θ$ are in

a)		no particular sequence
b)		G.P.
c)		H.P.
d)		A.P.

23. tan $75^{o}$ - cot $75^{o}$ is equal to

a)		4
b)		2 + $\sqrt{3}$
c)		2 - $\sqrt{3}$
d)		2 $\sqrt{3}$

24. The value of the expression tan $1^{o}$ tan $2^{o}$ tan $3^{o}$ tan $4^{o}$ ….tan $87^{o}$ tan $88^{o}$ tan $89^{o}$ is equal to

a)		0
b)		1
c)		2
d)		$\infty$

25. sin $200^{o}$ + cos $200^{o}$ is

a)		negative
b)		positive
c)		zero
d)		zero or positive

26. If ABCD is a cyclic quadrilateral, then

a)		sin (A + C) = 1
b)		sin (B + C) = 1
c)		cos (A + C) = 1
d)		cos (A + C) = -1

27. The value of cos $20^{o}$ cos $40^{o}$ cos $60^{o}$ cos $80^{o}$ is equal to

a)		3/8
b)		1/8
c)		1/16
d)		3/16

28. The value of sin $\frac{2 π}{8}$ + $\sin^{2} \frac{3 π}{8}$ + $\sin^{2} \frac{5 π}{8}$ + $\sin^{2} \frac{7 π}{8}$ is

a)		1
b)		2
c)		1 $\frac{1}{8}$
d)		2 $\frac{1}{8}$

29. If A = $130^{o}$ and x = sin A + cos A, then

a)		x > 0
b)		x < 0
c)		x = 0
d)		x $\leq$ 0

30. If A = $\sin^{20}$ $θ$ + $\cos^{48}$ $θ$ , then for all values of $θ$ :

a)		A $\geq$ 1
b)		0 < A $<$ 1
c)		1 < A < 3
d)		none of these

31. If in a triangle ABC, tan A + tan B + tan C = 6 and tan A + tan B = 2, then the triangle is

a)		right angled isosceles
b)		acute angled isosceles
c)		obtuse angled
d)		equilateral

32. If sin x + $\sin^{2}$ x = 1, then $\cos^{2}$ x + $\cos^{4}$ x is equal to

a)		1
b)		-1
c)		0
d)		2

33. $\frac{Cos 21^{o} - Sin 21^{o}}{\cos 21^{o} + \sin 21^{o}}$ is equal to

a)		tan $21^{o}$
b)		tan $66^{o}$
c)		tan $24^{o}$
d)		tan $69^{o}$

34. Which of the following is correct

a)		tan 1 > tan 2
b)		tan 1 < tan 2
c)		tan 1 = tan 2
d)		tan 1 = 2/3 tan 2

35. if tan a = $\frac{m}{m + 1}$ , tan b = $\frac{1}{2 m + 1},$ then a + b is equal to

a)		$\frac{π}{2}$
b)		$\frac{π}{4}$
c)		$\frac{π}{6}$
d)		none of these

36. If angle B of the triangle ABC is $45^{o}$ , then (1 + cot A) (1 + cot C) is equal

a)		-1
b)		0
c)		1
d)		2

37. In a triangle ABC, cosec A (sin B cos C + cos B sin C) is equal to

a)		c/a
b)		a/c
c)		1
d)		none of these

38. If e $\frac{- π}{2}$ < $θ$ < $\frac{π}{2}$ , then

a)		cos log $θ$ > log cos $θ$
b)		cos log $θ$ < log cos $θ$
c)		cos log $θ$ = log cos $θ$
d)		cos log $θ$ = 2/3 log cos $θ$

39. If a and b be between 0 and $\frac{π}{2}$ and if cos (a +b) = 12/13 and sin (a – b) = 3/5, then sin2a is equal to

a)		16/15
b)		0
c)		56/65
d)		64/65

40. The value of cos $\frac{π}{7}$ cos $\frac{2 π}{7}$ cos $\frac{4 π}{7}$ is

a)		- $\frac{1}{4}$
b)		- $\frac{1}{16}$
c)		- $\frac{3}{16}$
d)		- $\frac{1}{8}$

41. If cos (a + b) = 0, then sin (a + 2b) is equal to

a)		- sin a
b)		cos a
c)		sin b
d)		cos b

42. If tan $θ$ = 1/7 and tan $φ$ = 1/3, then cos 2 $θ$ equals

a)		4 sin $φ$
b)		2 sin $φ$
c)		sin 3 $φ$
d)		sin 4 $φ$

43. cos $52^{o}$ + cos $68^{o}$ + cos $172^{o}$ =

a)		0
b)		1
c)		2
d)		none of these

44. sin $\frac{π}{10}$ sin $\frac{13 π}{10}$ is equal to

a)		$\frac{1}{2}$
b)		- $\frac{1}{2}$
c)		- $\frac{1}{4}$
d)		1

45. If sin (A + B + C) = 1, tan (A – B) = 1/ $\sqrt{3}$ and sec (A + C) = 2 then,

a)		A = $120^{o}$ , B = $60^{o}$ , C = $0^{o}$
b)		A = $60^{o}$ , B = $30^{o}$ , C = $0^{o}$
c)		A = $90^{o}$ , B = $60^{o}$ , C = $30^{o}$
d)		none of these

46. If tan A = $\frac{1}{2}$ , tan B = $\frac{1}{3}$ , then tan ( 2A + B) is equal to

a)		1
b)		2
c)		3
d)		4

47. tan x is periodic with period

a)		$\frac{π}{2}$
b)		$π$
c)		2 $π$
d)		$\frac{3 π}{2}$

48. The roots of the equation ${4 x}^{2}$ - 2 $\sqrt{5 x}$ + 1 = 0 are

a)		sin $36^{o}$ ,sin $18^{o}$
b)		sin $18^{o}$ ,cos $36^{o}$
c)		sin $36^{o}$ ,cos $18^{o}$
d)		cos $18^{o}$ ,cos $36^{o}$

49. In a right angled triangle, the hypotenuse is four times as long as the perpendicular drawn to it from the opposite vertex. One of the acute angle is

a)		$15^{o}$
b)		$30^{o}$
c)		$45^{o}$
d)		none of these

50. The number of distinct solutions of sin 5 $θ$ cos 3 $θ$ = sin 9 $θ$ cos 7 $θ$ in [0, $\frac{π}{2}$ ] is

a)		4
b)		5
c)		8
d)		9