Topper’s Package Mathematics - XI Trigonometry Unit ......2020/07/06 · Topper’s Package...

TrigonometryTopper’s Package Mathematics - XI

15

1. TRIGONOMETRICAL RATIO

1. The sum of the series n 1

n!sin720

is :

(a) sin sin sin180 360 540

(b) sin sin sin sin6 30 120 360

(c) sin sin sin sin6 30 120 360

+

sin720

(d) sin sin180 360

2. The value of 2 22cot ( /6) 4tan ( /6)

3cosec /6 is :(a) 2 (b) 4(c) 4/3 (d) 3

3. If sinA 6 cos A 7 cos A then

cos A + 6 sinA is equal to :

(a) 6 sinA (b) 7 sinA

(c) 6 cos A (d) 7 cos A

4. If 3cos2

and 3sin2

, where does

not lie and lies in the third quadrant, then

22tan 3 tan

cot cos

is equal to :

(a)722 (b)

522

(c)922 (d)

225

5. If sec m and tan= n, then

1 1(m n)m (m n)

is equal to :

(a) 2 (b) 2m(c) 2n (d) mn

6. If 2cos x cos x 1 , then the value of12sin x 10 8 63sin x 3sin x sin x 1 is :

(a) 2 (b) 1(c) –1 (d) 0

7. If 0,4

and tan

1 2t (tan ) ,t = cot(tan ) ,

cot3t (cot ) and tan

4t (cot ) , then :

(a) 1 2 3 4t t t t (b) 4 3 1 2t t t t

(c) 3 1 2 4t t t t (d) 2 3 1 4t t t t

8. The expression 10 8cos cos13 13 +

3cos13

+

5cos13

is equal to :(a) –1 (b) 0(c) 1 (d) None of these

9. If sin cosec 2 , then the value of10 10sin cosec is :

(a) 2 (b) 210

(c) 29 (d) 1010. If sin 3sin( 2 ) , then the value of

tan( ) 2tan is :(a) 3 (b) 2(c) –1 (d) 0

11. If tan = k cot ,then cos( )cos( )

is equal to :

(a)1 k1 k

(b)1 k1 k

(c)k 1k 1

(d)k 1k 1

12. The value of 2 4tan 2tan 4cot

5 5 5 is :

(a) cot5

(b)2cot5

(c) 4cot5

(d)3cot5

13. In a right angled triangle, if the hypotenuse is

2 2 times the length of perpendicular drawn

TRIGONOMETRYUnit

2


16

from the opposite vertex on the hypotenuse,then the other two angles are :

(a) ,3 6

(b) ,4 4

(c)3,

8 8

(d)5,

12 8

14. If 3cos2 1cos23 cos2

, then tan is equal to :

(a) 2 tan (b) tan

(c) sin2 (d) 2cot

15. Ifn

3m

m 0sin xsin3x C cos mx

is an identity in

x, where 0, 1 nC C ,...C are constants and nC 0then teh value of n is(a) 2 (b) 4(c) 6 (d) 8

16. If tan1sin sin 2 ,5 tan

A BB A B then

A

(a)53

(b) 23

(c)32

(d) 35

17. The value of0 0 0

10 10 10log tan1 log tan 3 ... log (tan89 ) isgiven by(a) 45 (log10 tan 10) (b) 45 log10 (tan 890)(c) 1 (d) 0

18. The value of the expression

11

11

2

sincos

cossin

sincos

yy

yy

yy

is equal to

(a) 0 (b) 1(c) sin y (d) cos y

19. The expression

cos cos coscos cos cos6 6 4 15 2 10

5 5 3 10x x x

x x x+ + +

+ +is equal to

(a) cos 2x (b) 2cos x(c) cos2 x (d) 1+cos x

20. If Pnn n cos sin . ,then 2 3 16 4p p- + =

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

21. If A-B =4

, then (1+tan A) (1-tan B) is equal to:

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

22. cot = sin2 ( n ,n integer ) if equals(a) 45° and 60° (b) 45° and 90°(c) 45° only (d) 90°only

23. If A lies in the 2nd quadrant and 3 tan A + 4 = 0then the value of 2 cot A-5 cos A + sin A is equal to

(a) 5310 (b)

3710

(c)2310 (d)

710

.

24. If tan 17

110

and sin where

02

2

, , then is equal to

(a)

4 (b)

34

(c)

8 (d)

38 2 .

25. If sin 2 2 12

sin ,

cos cos , cos2 2 32

2 then b g

(a)38 (b)

54

(c)34 (d)

58

26. If sin sin ,x x 2 1 then the value of

cos cos cos cos12 10 8 63 3 1x x x x is equal to(a) 0 (b) 1(c) –1 (d) 2

27. If p is the product of the sine of angle of atriangle and q be the product of their cosine,then tangent of the angle are root of theequation :

(a) 3 2 (1 ) 0qx qx p x q

(b) 3 2 (1 ) 0px qx p x q

(c) 3 2 2(1 ) 0q x px px qx p (d) none of the above

28. If and are +ve acute angles and


17

tan( ) , tan ( ) , 1 13

equals

(a) 7 300 (b) 37 300

(c) 52 300 (d) 60 300 29. If A + B + C =180°, then the value of

cot cot cot cot cot cotB C C A A B b gb gb g will be(a) sec A sec B sec C(b) cosec A cosec B cosec C(c) tanA tan B tan C(d) 1

30. If A + B + C =1800, then the value of

cot cot cotA B C will be2 2 2

(a) cot cot cotA B C2 2 2 (b) 4

2 2 2cot cot cotA B C

(c) 22 2 2

cot cot cotA B C (d) 8

2 2 2cot cot cotA B C

.

31. The value of cos cos cos 7

27

47

is

(a) 18 (b)

14

(c) 1

16 (d) 3

1632. The least value of 3 sin x – 4 cos x + 7 is

(a) 0 (b) 2(c) 3 (d) 6

33. If tan m 1;tan ,thenm 1 2m 1

(a)2 (b)

3

(c)4 (d) none of these

34. Which of the following numbers is / arerational?

(a) sin150 (b) cos150

(c) sin cos15150 0 (d) sin cos15 750 0

35. If cos A B b g 35 and tan A tan B = 2 , then

(a) cos cosA B 15 (b) cos cosA B

15

(c) sin sinA B 25 (d) sin sinA B

15

36. If cos coscos

,

2 12 then the value of tan

2 is

equal to :

(a) 32

tan (b) tan 2

(c)13 2

tan (d) 32

tan

37. a b ccos sin , then a bsin cos b g2 -is

equal to(a) a2 + b2 (b) b2 + c2

(c) c2 + a2 (d) a2 + b2 – c2

38. If tan x x for all xb g b gtan ,1 then value of

must be

(a) 00 (b) 300

(c) 450 (d) 600

39. The value of tan81 tan63 tan27 tan9 is :(a) 1 (b) 2(c) 3 (d) 4

40. If tan x ba

then the value of , a cos 2x + b sin2x

is :(a) a (b) a – b(c) a + b (d) b

41. If sin cos ,30 600 0 d i d i then :

(a) 300 (b) 0

(c) 600 (d) 600

42. If sin cos 2,cos sin

then the value of is

(a) 900 (b) 600

(c) 450 (d) 300

43. If sin + cos =1, then the value of sin cos

is :

(a) 1 (b)12

(c) 0 (d) 244. The expression

3 32

34 4s in s in F

HGIKJ

LNM

OQPb g


18

FHG

IKJ

LNM

OQP2

256 6sin sin

b gis equal to :(a) 0 (b) 1

(c) 3 (d) sin cos4 6

45. If sin sin sin , 1 2 3 3 thencos cos cos 1 2 3 (a) 3 (b) 2(c) 1 (d) 0

46. If for real value of x, cos = x + 1/x ,then

(a) is an acute angle

(b) is a right angle

(c) is an obtuse angle

(d) no value of is possible.

47. The expression 1tan cotA A

simplifies to

(a) sec A cosec A (b) sin A cos A(c) tan 2A (d) sin 2 A

48. The value of 23

cos x FHG

IKJ

is

(a) cos sinx x 3 (b) 3 2cos sinx x

(c) cos sinx x 3 (d) 3 2cos sinx x

49. If A+ B+C= , then cos B + cos C is equal to

(a) 22 2

cos cosA B C(b) 2

2 2sin cosA B C

(c) 22 2

cos cosC A B(d) 2

2 2cos cos .B C

50. In a triangle PQR, R 2

. If tan P2 and tan

Q2

are the roots of the equation

ax bx c a o then2 0 ( ), :

(a) a + b = c (b) b + c = a(c) a + c = b (d) b = c

51. If tan = t, then tan2 + sec2 =

(a)11

tt (b)

11

tt

(c)2

1tt

(d)2

1tt

52. The number of integral values of K for whichthe equation 7cos x + 5 sin x = 2k +1 has asolution is(a) 4 (b) 8(c) 10 (d) 12

53. If sin and cos are the roots of theequation ax bx c2 0 , then a, b, c satisfythe relation

(a) b a ac2 2 2 (b) a b ac2 2 2

(c) a b c2 2 2 (d) b a ac2 2 2

54. If cos cos20 2 10 2 k and x k ,then thepossible values of x between 00 and 3600 are(a) 1400 (b) 400 and 1400

(c) 500 and 1300 (d) 400 and 3200

55. tan tan tan tan20 40 3 20 400 0 0 0 is equal to

(a)3

2(b)

34

(c) 3 (d) 1

56. The value of

sin sin sin sin2 2 2 2

838

58

78

(a) 1 (b) 2

(c) 118 (d) 2 1

8

57. The value of tan tan

434

LNM

OQP L

NMOQP is :

(a) – 2 (b) 2(c) 1 (d) – 1

58. The value of sin sin sin 14

314

514

is :

(a)1

16 (b) 18

(c)12 (d) 1

59. sec22

4

xyx yb g is true if :

(a) x y 0 (b) x y x , 0

(c) x y (d) x y 0 0,


19

60. If sin cosx ec x 2 , then sin cosn nx ec x isequal to

(a) 2 (b) 2n

(c) 2 1n (d) 2 2n

61. sin22

4

x yxy

b g where x R , y R gives real

if and only if(a) x + y = 0 (b) x = y (c) |x | = |y | 0 (d) none of these

62. If 0 1800 0 then

2 2 2 2 1 .... cosb g there being n

number of 2’s, is equal to

(a) 22

cos n (b) 22 1cos

n

(c) 22 1cos

n (d) none of these

63. tan .tan .tan3 3

is equal to

(a) tan2 (b) tan3

(c) tan3 (d) none of these

64. If tan tan tan

FHG

IKJ F

HGIKJ3 3

= ktan 3then k is equal to(a) 1 (b) 3(c) 1/3 (d) none of these

65. The value of tan tan tan20 2 50 700 0 0 is(a) 1 (b) 0

(c) tan500 (d) none of these

66. If 4n then cot . cot 2 . cot 3 ....

cot 2 1n b g is equal to

(a) 1 (b) -1(c) (d) none of these

67.r

n rn

1

12cos

is equal to :

(a)n2 (b)

n 12

(c)n2

1 (d) none of these

68. The value of sin n n n

ton sin sin ...3 5

terms is equal to :(a) 1 (b) 0

(c)n2 (d) none of these

69. The sum to 20 terms of the series

1 1 1sin .sin2 sin2 .sin3 sin3 .sin4

+ .......

(a) 1 tan tan21cos

(b) 1 cot cot21cos

(c) 1 tan tan21sin

(d) 1 cot cos21cos

70. The value of 3 cos 20 sec20ec is(a) 2 (b) –2(c) –4 (d) 4

71. The value of the expressioncos1 .cos2 ...cos179 equals :(a) 0 (b) 1

(c)12 (d) –1

72. If ,2

, then the value of tanequals:

(a) tan tan (b) 2(tan tan )

(c) tan 2tan (d) 2tan tan 73. The value of

2 2 2 2sin 5 sin 10 sin 15 ... sin 90 is :(a) 9.5 (b) 9(c) 10 (d) 8.

74. Angles A, B and Cof a triangle are in AP withcommon difference 15 degree, then angle A isequal to(a) 45° (b) 60°(c) 75° (d) 30°

2. MAXIMUM VALUE, MINIMUM VALUE

75. The maximum value of f(x) sinx(1 cos x) is:


20

(a)3 3

4(b)

3 32

(c) 3 3 (d) 3

76. The maximum value of 2cos x3

–

2cos x3

is :

(a) 32

(b)12

(c)32

(d)32

77. The maximum value of 5cos 3cos3

+3 is :(a) 5 (b) 11(c) 10 (d) –1

78. The maximum value of 24sin x 12sinx 7 is

(a) 25 (b) 4(c) does not exit (d) none of these

79. The maximum value of sin cosx xFHG

IKJ F

HGIKJ

6 6

in

the interval 02

, FHG

IKJ is attained at

(a)

12 (b)6

(c)3 (d)

2

80. Maximum value of 5 33

1cos cos

FHG

IKJ is

(a) 5 (b) 6(c) 7 (d) 8

81. Maximum value of f x x x isb g sin cos

(a) 1 (b) 2

(c)12 (d) 2

82. The smallest value of satisfing

3 4cot tan b g is :

(a)23

(b)3

(c)6 (d)

12

83. sin cos is maximum when is equal to

(a) 300 (b) 450

(c) 600 (d) 900

84. The maximum value ofcos . cos .... cos , 1 2b g b g b gn under the restrictions

021 2 , ,..... n and

(a)1

2 2n/ (b)1

2n

(c)12 (d) 1

85. If A sin cos20 48 , then for all valuesof :(a) A 1 (b) 0 1 A(c) 1 3 A (d) none of these

86. If e ex xsin sin 4 0 then the number f realvalues of x is :(a) 0 (b) 2(c) 1 (d) Infinite

87. If A B A B 0 03

, , and y = tan A. tan B

then(a) the maximum value of y is 3

(b) the minimum value of y is 13

(c) the maximum value of y is 13

(d) the minimum value of y is 0

3. TRIGONOMETRICAL EQUATION

88. The sum of the solutions in (0,2 ) of the

equation cos xcos x3

cos x

3

=

14 is :

(a) 4 (b)

(c) 2 (d) 3

89. Let f(x)= xsin x,x 0 . Then, for all natural

numbers n, f (x) vanishes at :

(a) a unique point in the interval 1n,n2

(b) a unique point in the interval 1n ,n 12

(c) a unique point in the interval (n +1, n + 2)(d) two points in the interval (n, n + 1)

90. If cos x sin xlog tanx log cot x 0 , then the mostgeneral solution of x is :


21

(a) 32n4

, n Z (b) 2n4

, n Z

(c) n4

, n Z (d) None of these

91. The number of real solutions of the equations3 2x x 4x 2sinx 0 in 0 x 2 is :

(a) four (b) two(c) one (d) 0

92. The positive values of n>3 satisfying the

equation 1 1 1

2 3sin sin sinn n n

is :

(a) 8 (b) 6(c) 5 (d) 7

93. The solution of trigonometric equation4 4cos x sin x = 2cos(2x )cos(2x ) is

(a)1n 1x sin

2 5

(b) n

1n ( 1) 2 2x sin4 4 3

(c) 1n 1x cos

2 5

(d)n

1n ( 1) 1x cos4 4 5

94. If

sinx cos x cos xcos x sinx cos xcos x cos x sinx

= 0, then the number of

distinct real roots of this equation in the

interval

,

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

95. Solution of the equation 3tan( 15 ) =tan( 15 ) is :

(a) = n 3

(b) n3

(c) n4

(d) n4

96. The solution of the equation1 sin2x[sinx cos x] =2, x is :

(a) 2

(b)

(c) 4

(d)34

97. General solution of sin x cos x =a Rmin

2{1,a 4a 6} is :

(a) nn ( 1)2 4 (b) n2n ( 1)

4

(c) n 1n ( 1)4

(d) nn ( 1)

4 4

98. The number of solutions of the equation

sinxcos3x = sin3x cos5x in 0,2

is :

(a) 3 (b) 4(c) 5 (d) 6

99. If 21 sin sin .... 4 2 3 ;0 2

then :

(a) 3

(b) 6

(c) or3 6

(d)2or

3 3

100. If tan cot4 4

then :

(a) 0 (b) 2n

(c) 2n 1

(d) 2(2n 1) for all n is an integer101. The number of solutions of the pair of equation

22sin cos2 0 and 22cos 3sin 0 in

the interval [0,2 ] is :(a) 0 (b) 1(c) 2 (d) 4

102. The set of values of satisfying the inequation22sin 5sin 2 0 wheren 0 2 is :

(a)50, ,2

6 6

(b)

50, ,26 6

(c)20, ,2

3 3

(d) None of these

103. The set of values of x for which

tan3 tan 2 11 tan3 tan 2

x x

x x is :

(a) (b) 4


22

(c) , 1,2,3,...4

n n

(d) 2 , 1,2,3,...4

n n

104. The equationa x b x csin cos where c a b 2 2 has :(a) a unique solution(b) infinite no. of solution(c) no solution(d) none of these

105. The solution of tan2 tan 1 is :

(a)3 (b) 6 1

6n b g

(c) 4 16

n b g (d) 2 16

n b g

106. The number of solutions of sin cos2 3 3

in , is

(a) 4 (b) 2(c) 0 (d) none of these

107. The number of all possible triplets

a a a1 2 3, ,b g such that a a x a x1 2 322 0 cos sin

for all x is :(a) 0 (b) 1

(c) 2 (d) infinite108. For n general solution of the equation

3 1 3 1 2 e j e jsin cos is :

(a)

24 12

n

(b)

n n14 12

b g

(c)

24 12

n

(d)

n n14 12

b g109. The smallest positive angle satisfying the

equation sin cos2 2 14

0 is :

(a)2 (b)

3

(c)4 (d)

6

110. If sin 6 + sin 4 + sin 2 = 0 ,then =

(a)n or n

4 3 (b)

n or n

4 6

(c)n or n

42

6 (d) none of these

111. If sin cos ,

0 02

and then is equal

to :

(a)2 (b)

4

(c)6 (d) 0

112. If 3 2cos sin , then the value of willbe :

(a) 26

n (b) 2

3n

(c) 212

n (d) 2

12n

113. If sin cos cos sin ,b g b g then which of thefollowing is correct ?

(a) cos 3

2 2 (b) cos

FHG

IKJ 2

12 2

(c) cos

FHG

IKJ 4

12 2 (d) cos .

F

HGIKJ 4

12 2

114. The number of solutions of sin cos2 3 3

in , is

(a) 4 (b) 2(c) 0 (d) none of these

115. The most general solutions of2 31 |cos x| cos x |cos x| ....to2 = 4 are given by

(a) n n Z

3

, (b) 23

n n Z

,

(c) 2 23

n n Z

, (d) none of these

116. The set of values of satifying the inequation22sin 5sin 2 0, where 0 2 , is:

(a) 50, ,26 6

(b)

50, ,26 6


23

(c) 20, ,23 3

(d) none of these

117. If exp 2 4 6(sin sin sin .... )log 2ex x x

satisfies the equation 2 9 8 0x x . Then

the value of cos ,0

cos sin 2x x

x x

.

(a) 3 1 (b) 3 1

(c)1

3 1 (d)1

3 1

118. The value of (s) of in the interval ,2 2

of the equation

22 tan(1 tan )(1 tan )sec 2 0 is

(a)3

(b)3

(c)4

(d)3

4. INVERSE TRIGONOMETRIC FUNCTION

119. 1 1cos [cos{2cot ( 2 1)} is equal to :

(a) 2 1 (b) 4

(c)34

(d) 0

120. Given, 10 x2

, then the value of :2

1 1x 1 xtan sin sin x2 2

is :

(a) 1 (b) 3

(c) –1 (d)13

121. The value of 23 n

1

n 1 k 1cot cos 1 2k

:

(a)2325 (b)

2523

(c)2324 (d)

2423

122. If 1 1asin x bcos x c , then 1asin x +1bcos x is equal to :

(a)ab c(a b)

a b

(b) 0

(c)ab c(a b)

a b

(d) 2

123. 1 2 1 2 1 2cot (2.1 ) cot (2.2 ) cot (2.3 ) ... upto

(a) 4

(b) 3

(c) 2

(d) 5

124. If 1 12 2

acot(cos x) sec tanb a

then x is

equal to :

(a) 2 2

b

2b a(b) 2 2

a

2b a

(c)2 22b aa (d)

2 22b ab

125. If 9 x 1 , then 21 x 1[{x cos(cot x) +

sin 1 2 1/2(cot x)} 1] is equal to :

(a) 2

x

1 x(b) x

(c) 2x 1 x (d) 21 x

126. If 2

1 12 2

1 x 2x5cos 7sin1 x 1 x

– 14tan

22x

1 x

1tan x 5 then x is equal to :

(a) 3 (b) 3

(c) 2 (d) 3

127. If 1 2 1sec 1 x cosec 2

11 y 1coty z

= then x + y + z is equal to :(a) xyz (b) 2xyz(c) xyz2 (d) x2yz

128. The value of 1 11sin sin sec (3)

3

+ cos

1 11tan tan (2)2

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

129. If 1 1 1 1tan a tan b sin 1 tan c, then :

(a) a b c abc


24

(b) ab bc ca abc

(c)1 1 1 1a b c abc =0

(d) ab + bc + ca = a + b + c

130. If sin sin tan

LNM

OQP

LNM

OQP

12

12

121

21

2aa

bb

x , then

x is equal to

(a)a b

ab1 (b)

bab1

(c)bab1 (d)

a bab1

5. PROERTIES OF TRIANGLE131. In a triangle, the lengths of two larger sides

are 10 cm and 9 cm. If the angles of the triangleare in AP, then the length of the third side is :

(a) 5 6 (b) 5 6

(c) 5 6 (d) 5 6

132. In any ABC ,

2 2(a b c)(b c a)(c a b)(a b c)

4b c

equals

(a) 2sin B (b) 2cos A(c) 2cos B (d) 2sin A

133. In a ABC , a = 8 cm, b = 10 cm, c = 12 cm. Thenrelation between angles of the tirangle is :(a) C = A+B (b) C = 2B(c) C = 2A (d) C = 3A

134. If the angles A, B and C of a triangle are in anarithmetic progression and if a, b and c denotethe lengths of the sides opposite to A, B and Crespectively, then the value of the expressiona csin2c sin2Ac a

is :

(a)12 (b)

32

(c) 1 (d) 3

135. In ABC , If 2 2A Bsin ,sin2 2 and 2 Csin

2 are in

H.P.Then a,b, and c will be in :(a) AP (b) GP(c) HP (d) None of these

136. In a ABC , if a = 3, b = 4, c = 5 then the

distance between its incentre andcircumcentre is :

(a)12 (b)

32

(c)32 (d)

52

137. In an equilateral triangle of side 2 3 cm, thecircumradius is :

(a) 1 cm (b) 3cm(c) 2 cm (d) 2 3 cm

138. In ABC , A2

b= 4, c =3 then the value ofRr is :

(a)52 (b)

72

(c)92 (d)

3524

139. The circumradius of the triangle whose sidesare 13, 12 and 5 is :

(a) 15 (b)132

(c)152 (d) 6

140. In any ABC if 2 cos B ac

, then the triangle

is :(a) right angled (b) equilateral(c) isosceles (d) none of these

141. In a triangle ABC, sin sin sinA B C 1 2 andcos cos cosA B C 2 , then the triangle is(a) equilateral(b) isosceles(c) right angled(d) right angled isosceles

142. In a triangle ABC cos cos cosA B C 32

,

then the triangle is(a) isosceles (b) right angled(c) equilateral (d) none of these

143. In a triangle ABC, if 1 1 3

a c b c a b c

,

then C is equal to(a) 300 (b) 600

(c) 450 (d) 900


25

144. If in a , r r r r1 2 3 , then the is

(a) obtuse angled(b) right angled(c) isosceles right angled(d) none of these

145.1 2 3

1 1 1r r r

(a)1r (b) r

(c)2r (d) none of these

146. In a C , r r r r r r1 2 2 3 3 1 (a) s (b) (c) s2 (d) 2

147. In a C , 1 2 3r.r .r .r is equal to

(a) 2 (b) 2

(c)abc

R4 (d) none of these

148. If in a triangle R and r are the circumradiusand in-radius respectively, then the H.M. of theex-radii of the triangle is(a) 3r (b) 2R(c) R r (d) none of these

149. In a C , 2ac sin A B C LNM

OQP 2

(a) a b c2 2 2 (b) c a b2 2 2 (c) b c a2 2 2 (d) c a b2 2 2

150. 4R sin A sin B sin C is equal to :

(a) a + b + c (b) a b c r b g(b) a b c R b g (d) a b c r

R b g

151. If in a triangle ABC2 2cos cos cos ,A

aB

bC

cabc

bca

then the

value of the angle A is

(a)3 (b)

4

(c)2 (d)

6

152. If in a C AC

A BB C

, sinsin

sinsin

,

b gb g then

(a) a, b, c are in A.P.

(b) a b c are in A P2 2 2, , . .(c) a,b,c are in H.P.

(d) a b c arein H P2 2 2, , . .153. In an equilateral triangle circumradius :

in-radius : ex-radius r1b g (a) 1 : 1 : 1 (b) 1 : 2 : 3(c) 2 : 1 : 3 (d) 3 : 2 : 4

154. In a triangle ABC, a b c b c a bc if b gb g

(a) 0 (b) 0

(c) 0 4 (d) 4

155. In a ABC c bc b

A, tan 2 is equal to

(a) tan A B2F

HGIKJ (b) cot A B

2F

HGIKJ

(c) tan A BF

HGIKJ2 (d) none of these

156. In a ABC c a b a b c ab, . b gb g The

measure of C is

(a)3 (b)

6

(c)23

(d) none of these

157. If in a triangle ABC,b c c a a b

11 12 13, then

cos A is equal to :

(a)15 (b)

57

(c)1935 (d) none of these

158. If a cos A=b cos B, then ABC is(a) isosceles only(b) right angled only(c) equilateral(d) right angled or isosceles.

159. If the angled of a triangle are in the ratio1 : 2 : 3, the corresponding sides are in theratio :(a) 2 : 3 : 1 (b) 3 2 1: :


26

(c) 2 3 1: : (d) 1 3 2: :

160. In a ABC, if Aa

Bb

Cc

cos cos cos and side a

= 2, then area of the triangle is(a) 1 (b) 2

(c)3

2(d) 3

161. 3 cos( ) a B C

(a) 3 abc (b) 3 (a + b + c)(c) abc (a + b + c) (d) 0.

162. In a ABC, 2ac sin A B C FHG

IKJ 2

(a) a b c2 2 2 (b) c a b2 2 2

(c) b c a2 2 2 (d) c a b2 2 2

163. The ex-radii of a triangle r r r1 2 3, , , are in H.P.Then the three sides of the triangle a,b and care in(a) A.P. (b) H.P.(c) G.P. (d) none of these

164. The area of the circle and the area of a regularpolygon of n sides and of perimeter equal tothat of the circle are in the ratio :

(a) tan : n n

FHG

IKJ (b) cos :

n nFHG

IKJ

(c) sin : n n

FHG

IKJ (d) cot : .

n nFHG

IKJ

165. In a ABC,8 2 2 2 2R a b c , then the triangle is(a) equilateral (b) isoscles(c) right angled (d) obtuse angled.

166. The value of 1 1 1 12

12

22

32r r r r

is equal to :

(a)a b c2 2 2

(b)

a b c2 2 2

2

(c)2 2 2

22a b c

(d) none of these

167. If R is the radius of the circumcircle of ABCand is its area , then :

(a) R abc

4 (b) R abc

(c) R a b c

(d) R a b c

4

168. In a ABC A B A B,cot tan 2 2

is equal to :

(a)a ba b

(b)a ba b

(c)a a bb a b

b gb g (d) none of these

169. In a ABC, if tan A2

56

and tan B2

2037

then

(a) 2a = b + c (b) a > b > c(c) 2c = a + b (d) none of these

170. If in a ABC aA

bB

then,cos cos

,

(a) 2 sin A sin B sin C = 1

(b) sin sin sin2 2 2A B C (c) 2 sin cos sinA B C(d) none of these

171. If in a ABC , 2 cos A sin C = sin B then thetriangle is :(a) equilatereal (b) isosceles(c) right angled (d) none of these

172. If the sides of a triangle are proportional tothe cosines of the opposite angles then thetriangle is :(a) right angled (b) equilateral(c) obtuse angled (d) none of these

173. The sides of a triangle are in AP and its area

is 35 (area of an equilateral triangle of the

same perimeter). Then the ratio of the sidesis(a) 1 : 2 : 3 (b) 3 : 5 : 7(c) 1 : 3 : 5 (d) none of these

174. In a ABC R circumradius and r = inradius.

The value of a A b B C

a b ccos cos cos

is equal to:

(a)Rr (b)

Rr2

(c)rR (d)

2rR

175. In an equilateral triangle, (circumradius):(inradius): (exradius) is equal to


27

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

176. Inradius of a circle which is inscribed in aisosceles triangle one of whose angle is 2 /3,is 3 , then area of triangle is :

(a) 4 3 (b) 12 7 3

(c) 12 7 3 (d) none of these

177. If the radius of the circumcircle of an isoscelestriangle PQR is equal to PQ = PR, then the angleP is:

(a)6

(b)3

(c)2

(d)23

178. If sides a, b, c are in the ratio 19 : 16 : 5, then

cot : cot : cot2 2 2A B C

equals :

(a) 1:15 : 4 (b) 15 :1: 4(c) 4 :1:15 (d) 1: 4 :15

6. HEIGHT AND DISTANCE179. ABCD is a square plot. The angle of elevation

of the top of a pole standing at D from A or Cis 30° and that from B is , then tan isequal to:

(a) 6 (b) 1/ 6

(c) 3 /2 (d) 2 /3

180. A vertical pole PO is standing at the centre Oof a square ABCD. If AC subtends an 90 atthe top P of the pole then the angle subtendedby a side of the square at P is :(a) 30° (b) 45°(c) 60° (d) None of these

181. A ladder rests against a wall so that its toptouches the roof of the hourse. If the laddermakes an angle of 60° with the horizontal andheight of the house is 6 3 m, then the lengthof the ladder is :

(a) 12 3 m (b) 12 m

(c)12 m

3 (d) None of these

182. The angles of elevation of the top of a tower attwo points, which are at distance a and b fromthe foot in the same horizontal line and on thesame side of the tower, are complementary.The height of the tower is :

(a) ab (b) ab

(c) a /b (d) b/a

183. ABC is a triangular park with AB = AC = 100m. A clock tower is situated at the mid point ofBC. The angle of elevation, if the top of thetower at A and B are cot–13.2 and 1cosec 2.6

respectively. The height of the tower is :(a) 16 m (b) 25 m(c) 50 m (d) None of these

184. From the top of a hill h meteres high, theangles of depressions of the top and the bottomof a pillar are and , respectively. The height(in metres) of the pillar is :

(a)h(tan tan )

tan

(b)h(tan tan )

tan

(c)h(tan tan )

tan

(d)h(tan tan )

tan

185. A round balloon of radius r substends an angle

at the eye of the observer, while the angleof elevation of its centre is . The height ofthe centre of balloon is :

(a) rcosec sin2

(b) rsin cosec2

(c) rsin cosec2

(d) rcosec sin2

186. The angle of elevation of the top of a TV towerfrom three points A, B and C in a straight linethrough the foot of the tower are , 2 and3 respectively. If AB = a, then height of thetower is :

(a) a tan (b) a sin(c) a sin2 (d) a sin3

187. A flagpole stands on a building of height 450 ftand an observer on a level ground is 300 ft fromthe base of the building. The angle of elevationof the bottom of the flagpole is 30° and theheight of the flagpole is 50 ft. If is the angle ofelevation of the top of the flagpole, then tan is

(a) 4

3 3 (b)32


28

(c)92 (d)

35

188. From an aeroplane flying vertically above ahorizontal road, the angles of depression of twoconsecutive stones on the same side of theaeroplane are observed to be 30° and 60°,respectively. The height (in km) at which theaeroplane is flying, is :

(a)43 (b)

32

(c)23 (d) 2

189. The elevation of an object on a hill is observedfrom a certain point in the horizontal plane

through its base, to be 30°. After walking 120m towards it on level ground, the elevation iffound to be 60°. Then, the height (in metres)of the object is :

(a) 120 (b) 60 3(c) 120 3 (d) 60

190. A house subtends a right angle at the windowof an opposite house and the angle of elevationof the window from the bottom of the first houseis 60°. If the distance between the two housesis 6 m, then the height of the first house is :

(a) 8 3 m (b) 6 3m

(c) 4 3 m (d) None of these

INTEGER TYPE QUESTIONS

1. tan20°tan40°tan60°tan80° =

2. If tan – cot = a and sin + cos = b, then(b2 – 1)2 (a2 + 4) is equal to ________

3. In a ABC, if b2 + c2 = 3a2, then cotB + cot C –cotA = ____________

4. The number of points of intersection of 2y = 1and y = sinx, in –2 x 2 is _______

5. The number of pairs (x, y) satisyfing theequations sinx + siny = sin(x + y) and |x| +|y| = 1 is __________

6. If 0 x 2, then the number of solutions ofthe equation sin8x + cos6x = 1 ________

7. The number of values of x in the interval[0, 3] satisfying the equation 2sin2x + 5sinx– 3 = 0 ____________

8. The number of values of x in the interval[0, 5] satisfying the equation 3sin2x – 7sinx +2 = 0 _______

9. The maximum value of the expression

2 21

sin 3sin cos 5cos is

10. The 3sinA + 5cosA = 5, then the value of(3cosA – 5sinA)2 is _________


29

1. (C), 2. (C), 3. (B), 4. (B), 5. (A), 6. (D), 7. (B),8. (B), 9. (A), 10. (D), 11. (A), 12. (A), 13. (C), 14. (A),

15. (C), 16. (C), 17. (D), 18. (D), 19. (B), 20. (C), 21. (A),22. (B), 23. (C), 24. (A), 25. (D), 26. (A), 27. (A), 28. (A),29. (B), 30. (A), 31. (A), 32. (B), 33. (C), 34. (C), 35. (A),36. (A), 37. (D), 38. (C), 39. (D), 40. (A), 41. (B), 42. (C),43. (C), 44. (B), 45. (D), 46. (D), 47. (B), 48. (A), 49. (B),50. (A), 51. (A), 52. (A), 53. (A), 54. (D), 55. (C), 56. (B),57. (D), 58. (D), 59. (C), 60. (A), 61. (C), 62. (A), 63. (B),64. (B), 65. (B), 66. (A), 67. (C), 68. (B), 69. (B), 70. (C),71. (A), 72. (C), 73. (A), 74. (A), 75. (A), 76. (C), 77. (A),78. (D), 79. (A), 80. (B), 81. (D), 82. (C), 83. (B), 84. (A),85. (B), 86. (A), 87. (D), 88. (C), 89. (B), 90. (B), 91. (C),92. (D), 93. (B), 94. (C), 95. (D), 96. (C), 97. (D), 98. (C),99. (D), 100. (D), 101. (C), 102. (A), 103. (A) 104. (C), 105. (B),

106. (D), 107. (D), 108. (A), 109. (B), 110. (A), 111. (B), 112. (C),113. (C), 114. (D), 115. (B), 116. (A), 117. (C), 118. (D), 119. (C),120. (A), 121. (B), 122. (A), 123. (A), 124. (A), 125. (C), 126. (D),127. (A), 128. (A), 129. (C), 130. (D), 131. (D), 132. (D), 133. (C),134. (D), 135. (C), 136. (D), 137. (C), 138. (A), 139. (B), 140. (C),141. (D), 142. (C), 143. (B), 144. (B), 145. (A), 146. (A), 147. (B),148. (A), 149. (B), 150. (D), 151. (C), 152. (B), 153. (C), 154. (C),155. (A), 156. (C), 157. (A), 158. (D), 159. (D), 160. (D), 161. (A),162. (B), 163. (B), 164. (A), 165. (A), 166. (B), 167. (A), 168. (A),169. (B), 170. (A), 171. (B), 172. (B), 173. (B), 174. (C), 175. (C),176. (C), 177. (B), 178. (D), 179. (B), 180. (C), 181. (B), 182. (B),183. (B), 184. (A), 185. (D), 186. (C), 187. (A), 188. (B), 189. (B),190. (A),

1. (3) 2. (4) 3. (0) 4. (4) 5. (6) 6. (5) 7. (4)8. (6) 9. (2) 10. (9)

INTEGER TYPE QUESTIONS

Topper’s Package Mathematics - XI Trigonometry Unit ......2020/07/06 · Topper’s Package...

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