AND ANDHERI HERI / BOR BORIVAL IVALII / DADA DADAR R / THANE HANE / POWA POWAII / CHEM CHEMBU BUR R / NER NERUL / KHARG HARGHA HAR R
IIT – JEE: 2017
TW TEST
TIME: 1H 1 HR
MARKS: 60
TOPIC: TRIGONOMEYTRY
DATE: 31 31/05/15
SECTION-I This section contains 20 contains 20 multiple multiple choice choice questions. questions. Each Each question has 4 choices (A), (B), (C) and (D) for its answer, out which ONLY which ONLY ONE is ONE is correct. (+3, (+3, - 1) 1) 1.
If cos x + cos 2x = 1, then the value of sin 12x + 3 sin10x + 3 sin8x + sin6x – 1 is equal to (a ) 2 (b) 1 (c) –1 (d) 0
2.
If tan θ – cot θ = a and sin θ – cos θ = b , then (b2 – 1) 2 (a2 + 4) is equal to: (a ) 2 (b) 3 (c) 6 (d) 4
3.
The sum of the the ser series: cos
21 (b) 1/2
(a ) 1
4.
If S = cos 2
π 24
+ cos2
(a ) 1
5.
3π
24
(b)
3π 21
+ cos
θ 2
+ ... upto 10 terms is:
21 (c ) 0
(d) −1 2
11π
, then the value of S is 24 (c ) 5 (d) None of these
b − 2c θ is + b tan + c = 0 than the value of 2
1
a
(c) 1
2
(b) 61
30
5π
+ .... + cos2
cos ec ecθ + cot θ = 5 6 then the value of cot 30
θ 2
+ tan
(d) 3
θ
is 2 (c) 61 15
π , then α is equal to 16 π
(d) 61
60
If (1 + tan α ) (1 + tan 4 α ) = 2, α ∈ 0, (a)
8.
5π
If 2 sin θ + 5 cos θ = 3 and a tan 2
1 1 (a) 11
7.
+ cos
+ cos2
24 (b) 3
(a ) 0 6.
π
π
(b)
20
If f ( θ ) = (a ) 0
sin θ sin θ + cos θ
π 30
(c)
40
(d)
π 60
π − θ is 2
then the value of f ( θ ) + f (b) 1
(c ) 2
(d) depends on θ
CENT CENTER ERS: S: MU MUMB MBAI AI / DELH DELHII / AKOL AKOLA A / KOLK KOLKAT ATA A / LUCK LUCKNO NOW W / NASH NASHIK IK / GOA GOA / PUNE PUNE #
1
9.
The expression
2 sin 7 θ cos 5θ − sin 4 θ − sin 2 θ cos10 θ + cos 6 θ
(a) 2sin2θ 10.
(c)
12.
13.
If
p 2
(b)
p 2 + (1 − q )2 1
(d)
p2 − (1 − q )2 3π
< α < π , then
4 (a) 1 + cot α
If A, B, C are the angles of a triangle, then (b) –1
sin 6 x + cos 6 x = 1
( p + q )
2
(c) −1 − cot α
(d) −1 + cot α
3
(d) 1/2
cot A + cot B tan A + tan B (c) 0
+
cot B + cot C
+
cot C + cot A
tan B + tan C tan C + tan A (d) 2
is:
(c) 8
9
9
(d) None of these
5 −1 64
(b)
5 −1
(c)
16
5 +1 64
(d)
5 +1 16
−5π 5π , is 6 6
The range of sin x; ∀x ∈
If tan θ = (a) 1
18.
p 2
then the value sin 2 2x is (b) 4
9
1 1 (b) − , 2 2
(a) [–1, 1]
17.
p 2 + q 2
0 The value of sin14 sin18 0 sin 460 sin 740 sin 780 is
(a)
16.
p 2
The value of tan10 tan20 tan30 …. tan890 is: (a) 1 (b) 0 (c) 2
(a) 1
15.
(d) cos4θ
cos ec2α + 2 cot α is: (b) 1 − cot α
(a) 1 14.
(c) sin4θ
Given that tan A and tan B are the roots of x 2 – px + q = 0, then the value of sin 2 (A + B) is: (a)
11.
(b) 2cos2θ
simplifies to
4 3
, then the value of (b) 2
1 2
1 (c) − ,1 2
1 (d) −1, 2
( 24 cos ec2θ − 7 sec 2 θ ) is: (c) 5
(d) 4
If A, B, C are the angles of a triangle, then cos 2A + cos 2B + cos 2C + 4 cos A cos B cos C equals: (a) 1 (b) 2 (c) 3 (d) None of these
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2
19.
In a right angled triangle, the hypotenuse is
4 3
times the length of perpendicular drawn from the
opposite vertex on the hypotenuse, then the other two angles are π π π π π 3π (a) , (b) , (c) , 3 6 4 4 8 8 20.
(d)
π 5π
, 12 12
If x = h + a sec θ, and y = k + b cosec θ, then: (a)
(c)
a2
(x + h)
2
(x − h)
2
a
2
−
b2 2
(y + k)
a2
=1
(b)
=1
(d) x2 + y 2 = a2 + b2
(x − h)
2
+
b2 2
(y − k)
=1
2
−
(y − k) b
2
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ANDHERI / BORIVALI / DADAR / THANE / POWAI / CHEMBUR / NERUL / KHARGHAR
TOPIC: TRIGONOMEYTRY (ANSWER KEY)
1.
(D)
2.
(D)
3.
(B)
4.
(B)
5.
(A)
6.
(B)
7.
(A)
8.
(B)
9.
(A)
10.
(A)
11.
(C)
12.
(A)
13.
(A)
14.
(C)
15.
(C)
16.
(A)
17.
(C)
18.
(D)
19.
(A)
20.
(B)
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