Lista de Exercicios Matematica-93

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[7]Quest Tutorials
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Quest
Q.50
sec
sec
8 1
4 1
θ
θ
−
− is equal to
(A) tan 2θ cot 8θ (B) tan 8θ tan 2θ (C) cot 8θ cot 2θ (D) tan 8θ cot 2θ
Q.51 In a ∆ABC if b = a ( )13 − and ∠C = 300 then the measure of the angle A is
(A) 150 (B) 450 (C) 750 (D) 1050
Q.52 Number of values of θ π∈[ , ]0 2 satisfying the equation cotx – cosx = 1 – cotx. cosx
(A) 1 (B) 2 (C) 3 (D) 4
Q.53 The exact value of cos273º + cos247º + (cos73º . cos47º) is
(A) 1/4 (B) 1/2 (C)3/4 (D) 1
Q.54 In a ∆ABC, a = a
1
 = 2 , b = a
2
 , c = a
3
 such that a
p+1
 = 




 −
−−
− pp
p2
pp2
p
a
5
2p4
2a
3
5
where p = 1,2 then
(A) r
1
 = r
2
(B) r
3
 = 2r
1
(C) r
2
 = 2r
1
(D) r
2
 = 3r
1
Q.55 The expression, 
( ) ( )tan cos
cos( )
3
2
3
2
2
π π
α α
π α
− −
−
 + cos α
π
−






2
 sin (π − α) + cos (π + α) sin α
π
−






2
 when
simplified reduces to :
(A) zero (B) 1 (C) − 1 (D) none
Q.56 The expression [1 − sin (3π − α) + cos (3π + α)] 1
3
2
5
2
− −





 + −











sin cos
π
α
π
α when simplified
reduces to :
(A) sin 2α (B) − sin 2α (C) 1 − sin 2α (D) 1 + sin 2α
Q.57 If ‘O’ is the circumcentre of the ∆ ABC and R
1
, R
2
 and R
3
 are the radii of the circumcircles of triangles
OBC, OCA and OAB respectively then 
a
R
b
R
c
R1 2 3
+ + has the value equal to:
(A) 
a b c
R2 3 (B) 
R
a b c
3
(C) 
4
2
∆
R
(D) 2R4
∆
Q.58 The maximum value of ( 7 cosθ + 24 sinθ ) × ( 7 sinθ – 24 cosθ ) for every R∈θ .
(A) 25 (B) 625 (C) 
2
625
(D) 
4
625
Q.59 4 sin50 sin550 sin650 has the values equal to
(A) 
3 1
2 2
+
(B) 
3 1
2 2
−
(C) 
3 1
2
−
(D) 
3 3 1
2 2
−d i