BITSAT SERIES Mathematics
Trigonometry
71 previous year questions.
Volume: 71 Ques
Yield: High
High-Yield Trend
1
2026 4
2025 10
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2020 5
2019 5
2018 4
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2015 3
2014 4
2013 4
2012 5
2011 4
2010 Chapter Questions 71 MCQs
01
PYQ 2009
medium
mathematics ID: bitsat-2
The period of θ+\sin2θθ+\cos2θ is:
1
2π
2
π
3
2π3
4
π3
02
PYQ 2009
medium
mathematics ID: bitsat-2
If in the expansion of (2x+14x)ⁿ, T₃ = 7T₂ and the sum of the binomial coefficients of second and third terms is 36, then the value of x is:
1
-(1)/(3)
2
-(1)/(2)
3
(1)/(3)
4
(1)/(2)
03
PYQ 2009
medium
mathematics ID: bitsat-2
The line 3x-4y+7=0 is rotated through an angle (π)/(4) in the clockwise direction about the point (-1,1). The equation of the line in its new position is:
1
7y+x-6=0
2
7y-x-6=0
3
7y+x+6=0
4
7y-x+6=0
04
PYQ 2010
medium
mathematics ID: bitsat-2
A flagstaff of 6 metres high placed on the top of a tower throws a shadow of 2\sqrt3 metres along the ground, when the angle (in degrees) which the sun makes with the ground is
1
60^
2
80^
3
75^
4
None of these
05
PYQ 2010
medium
mathematics ID: bitsat-2
The value of ⁻¹x+⁻¹((x)/(2)+(1)/(2)√(3-3x²));
\frac12 x\le1 is
1
-(π)/(3)
2
(π)/(3)
3
(3)/(π)
4
-(3)/(π)
06
PYQ 2010
medium
mathematics ID: bitsat-2
If 12²θ-31θ+32=0, then the value of θ is
1
(3)/(5) or 1
2
(2)/(3) or -(2)/(3)
3
(4)/(5) or (3)/(4)
4
±(1)/(2)
07
PYQ 2010
medium
mathematics ID: bitsat-2
\tan20^+\tan40^+√(3)\tan20^\tan40^ is equal to
1
√(3)/2
2
√(3)/4
3
√(3)
4
1
08
PYQ 2011
medium
mathematics ID: bitsat-2
If sin θ = -(1)/(2) and tan θ = 1√(3), then θ is equal to:
1
2π + (π)/(6)
2
2π + (11π)/(6)
3
2π + (7π)/(6)
4
2π + (π)/(4)
09
PYQ 2011
medium
mathematics ID: bitsat-2
cosθ1-tanθ + sinθ1-cotθ is equal to:
1
sinθ - cosθ
2
sinθ + cosθ
3
tanθ + cotθ
4
tanθ - cotθ
10
PYQ 2011
medium
mathematics ID: bitsat-2
If tan A = (1)/(2) and tan B = (1)/(3), then find the value of A + B.
1
π
2
(π)/(2)
3
(π)/(4)
4
-(π)/(4)
11
PYQ 2011
medium
mathematics ID: bitsat-2
A ladder rests against a wall so that its top touches the roof of the house. If the ladder makes an angle of 60^ with the horizontal and height of the house is 6\sqrt3 meters, then the length of the ladder is:
1
12\sqrt3
2
12
3
12/\sqrt3
4
None of these
12
PYQ 2011
medium
mathematics ID: bitsat-2
The value of sin(4tan⁻¹(1)/(3))-cos(2tan⁻¹(1)/(3)) is:
1
3/7
2
7/8
3
8/21
4
None of these
13
PYQ 2012
medium
mathematics ID: bitsat-2
In a triangle ABC, if , , and , then equals:
1
2
3
4
14
PYQ 2012
medium
mathematics ID: bitsat-2
If , then:
1
2
3
4
None of these
15
PYQ 2012
medium
mathematics ID: bitsat-2
equals to:
1
2
3
4
16
PYQ 2012
medium
mathematics ID: bitsat-2
In , cos cos , then cos is equal to:
1
3/8
2
3/4
3
5/8
4
5/4
17
PYQ 2013
medium
mathematics ID: bitsat-2
If , then the general value of is
1
2
3
and
4
18
PYQ 2013
medium
mathematics ID: bitsat-2
An object is observed from the points A, B and C lying in a horizontal straight line which passes directly underneath the object. The angular elevation at A is , at B is , and at C is . If AB = a, BC = b, and the height of the object is h, then the height of the object is
1
2
3
4
19
PYQ 2013
medium
mathematics ID: bitsat-2
The value of is
1
2
3
3/4
4
20
PYQ 2013
medium
mathematics ID: bitsat-2
The greatest and least values of are respectively
1
and 0
2
and
3
and
4
and
21
PYQ 2014
medium
mathematics ID: bitsat-2
Find the value of .
1
2
3
4
22
PYQ 2014
medium
mathematics ID: bitsat-2
1
2
3
4
23
PYQ 2014
medium
mathematics ID: bitsat-2
The solution of in the interval is:
1
2
3
4
None of these
24
PYQ 2015
medium
mathematics ID: bitsat-2
The period of is
1
2
3
4
None of these
25
PYQ 2015
medium
mathematics ID: bitsat-2
If , then the value of is
1
2
3
4
26
PYQ 2015
medium
mathematics ID: bitsat-2
In a , the lengths of the two larger sides are 10 and 9 units respectively. If the angles are in A.P., then the length of the third side can be
1
2
3
4
None of these
27
PYQ 2015
medium
mathematics ID: bitsat-2
If , then
is equal to
1
2
3
4
28
PYQ 2016
medium
mathematics ID: bitsat-2
If tan(cot x)=cot(tan x), then sin 2x is equal to:
1
2
3
4
(4)/(n(n+1)π)
29
PYQ 2016
medium
mathematics ID: bitsat-2
If and are positive acute angles satisfying
and ,
then the value of is equal to:
and ,
then the value of is equal to:
1
2
3
4
(π)/(6)
30
PYQ 2016
medium
mathematics ID: bitsat-2
If , then
1
0
2
1
3
2
4
3
31
PYQ 2016
medium
mathematics ID: bitsat-2
The general solution of the equation
is:
is:
1
2
3
4
nπ-(π)/(4)
32
PYQ 2016
medium
mathematics ID: bitsat-2
In a , if
,
and the side , then area of triangle is:
,
and the side , then area of triangle is:
1
1
2
2
3
4
\sqrt3
33
PYQ 2016
medium
mathematics ID: bitsat-2
If
,
then the value of is:
,
then the value of is:
1
2
3
4
(a-b)/(1+ab)
34
PYQ 2017
medium
mathematics ID: bitsat-2
The number of roots of the equation in is
1
4
2
5
3
6
4
8
35
PYQ 2017
medium
mathematics ID: bitsat-2
The value of cot⁻17+cot⁻18+cot⁻118 is
1
2
3
4
cot⁻13
36
PYQ 2017
medium
mathematics ID: bitsat-2
If are the angles of a triangle and
are in A.P., then the triangle must be
are in A.P., then the triangle must be
1
right angled
2
isosceles
3
equilateral
4
none of these
37
PYQ 2017
medium
mathematics ID: bitsat-2
An observer on the top of a tree finds the angle of depression of a car moving towards the tree to be 30°. After 3 minutes this angle becomes 60°. After how much more time will the car reach the tree?
1
4 min
2
4.5 min
3
1.5 min
4
2 min
38
PYQ 2018
medium
mathematics ID: bitsat-2
Number of solutions of the equation
are:
are:
1
3
2
2
3
1
4
0
39
PYQ 2018
medium
mathematics ID: bitsat-2
Let be the angles of a plane triangle. If
then is equal to:
then is equal to:
1
2
3
4
(2)/(3)
40
PYQ 2018
medium
mathematics ID: bitsat-2
A pole stands vertically inside a triangular park ABC. If the angle of elevation of the top of the pole from each corner of the park is the same, then the foot of the pole is at the:
1
centroid
2
circumcentre
3
incentre
4
orthocentre
41
PYQ 2018
easy
mathematics ID: bitsat-2
If msinθ=nsin(θ+2α), then tan(θ+α) is equal to:
42
PYQ 2018
medium
mathematics ID: bitsat-2
Number of solutions of the equation sin 9θ=sinθ in the interval [0,2π] is:
1
16
2
17
3
18
4
15
43
PYQ 2019
medium
mathematics ID: bitsat-2
If (cos A)/(cos B)=n, (sin A)/(sin B)=m, then the value of (m²-n²)sin² B is
1
2
3
4
-n²
44
PYQ 2019
medium
mathematics ID: bitsat-2
If , then
1
2
3
4
None of these
45
PYQ 2019
medium
mathematics ID: bitsat-2
In a △ ABC, the lengths of the two larger sides are 10 and 9 units, respectively. If the angles are in A.P., then the length of the third side can be
1
2
3
4
None of these
46
PYQ 2019
medium
mathematics ID: bitsat-2
The period of tan 3θ is
1
2
3
4
None of these
47
PYQ 2019
medium
mathematics ID: bitsat-2
If then is equal to:
1
2
3
4
4-4sin²α
48
PYQ 2020
medium
mathematics ID: bitsat-2
The general solution of the equation
sin 2x + 2sin x + 2cos x +1 =0
is:
1
2
3
4
nπ-(π)/(4)
49
PYQ 2020
medium
mathematics ID: bitsat-2
If
sin⁻1((2a)/(1+a²))
-cos⁻1((1-b²)/(1+b²))
=tan⁻1((2x)/(1-x²)),
then what is the value of x?
1
2
3
4
(a-b)/(1+ab)
50
PYQ 2020
medium
mathematics ID: bitsat-2
In a △ ABC, if
(cos A)/(a)=(cos B)/(b)=(cos C)/(c),
and the side a=2, then area of the triangle is:
1
2
3
4
√(3)
51
PYQ 2020
medium
mathematics ID: bitsat-2
If A and B are positive acute angles satisfying
3cos²A+2cos²B=4 and (3sin A)/(sin B)=(2cos B)/(cos A),
then the value of A+2B is equal to:
1
2
3
4
(π)/(4)
52
PYQ 2020
medium
mathematics ID: bitsat-2
If sintheta₁+sintheta₂+sintheta₃=3, then costheta₁+costheta₂+costheta₃=
1
2
3
4
3
53
PYQ 2021
medium
mathematics ID: bitsat-2
The number of roots of the equation cos 3θ=0 for 0≤θ\le2π is
1
4
2
5
3
6
4
8
54
PYQ 2021
medium
mathematics ID: bitsat-2
The value of cot⁻17+cot⁻18+cot⁻118 is
1
π
2
(π)/(2)
3
cot⁻15
4
cot⁻13
55
PYQ 2021
medium
mathematics ID: bitsat-2
An observer on the top of a tree finds the angle of depression of a car moving towards the tree to be 30^∘. After 3 minutes this angle becomes 60^∘. After how much more time will the car reach the tree?
1
4 min.
2
4.5 min.
3
1.5 min.
4
2 min.
56
PYQ 2021
medium
mathematics ID: bitsat-2
If A, B, C are the angles of a triangle and eⁱA, eⁱB, eⁱC are in A.P., then the triangle must be
1
right angled
2
isosceles
3
equilateral
4
None of these
57
PYQ 2024
medium
mathematics ID: bitsat-2
Number of solutions of equations in the interval is:
1
16
2
17
3
18
4
15
58
PYQ 2024
medium
mathematics ID: bitsat-2
The sum of all values of in , for which is equal to:
1
2
3
4
59
PYQ 2024
medium
mathematics ID: bitsat-2
Let , and are the angles of a triangle and , . Then, is equal to:
1
2
3
4
60
PYQ 2024
medium
mathematics ID: bitsat-2
If , then is:
1
2
3
4
None of these
61
PYQ 2024
medium
mathematics ID: bitsat-2
If , then is equal to:
1
2
3
4
62
PYQ 2024
medium
mathematics ID: bitsat-2
From the top of a cliff 50 m high, the angles of depression of the top and bottom of a tower are observed to be and . The height of the tower is:
1
m
2
m
3
m
4
50(1 - √3/3) m
63
PYQ 2024
medium
mathematics ID: bitsat-2
Given that and , find the conditions under which is invertible.
1
2
3
4
64
PYQ 2024
medium
mathematics ID: bitsat-2
If , then the value of is:
1
2
3
4
65
PYQ 2024
medium
mathematics ID: bitsat-2
If , then:
1
2
3
4
66
PYQ 2024
medium
mathematics ID: bitsat-2
ABC is a triangular park with m. A TV tower stands at the midpoint of . The angles of elevation of the top of the tower at are respectively. The height of the tower is:
1
m
2
m
3
m
4
50(3 −√3) m
67
PYQ 2025
medium
mathematics ID: bitsat-2
If , where , then what is the value of ?
1
1
2
0
3
2
4
Cannot be determined
68
PYQ 2025
medium
mathematics ID: bitsat-2
What is the value of ?
1
2
3
4
69
PYQ 2025
medium
mathematics ID: bitsat-2
If , what is the value of ?
1
2
3
4
70
PYQ 2025
easy
mathematics ID: bitsat-2
If , what is the value of ?
1
0
2
1
3
2
4
-1
71
PYQ 2026
hard
mathematics ID: bitsat-2
Number of solutions of equations in the interval is
1
16
2
17
3
18
4
15