Class 11 Mathematics Trigonometric Functions MCQs Set B

Question: An aeroplane flying horizontally 1 km above the ground is observed at an elevation of 60° and after 10 s the elevation is observed to be 30°. The uniform speed of the aeroplane (in km/h) is
a) 240
b) 240√3
c) 60√3
d) None of the options
Answer: b

Question: cos2θ + 2cos θ is always
a) greater πthan -3/2
b) less than or equal to 3/2
c) greater than or equal to -3/2 and less than or equal to 3
d) None of the options
Answer: c,b

Question: A house of height 100msubtends a right angle at the window of an opposite house. If the height of the window be 64 m, then the distance between the two houses is
a) 48 m
b) 36 m
c) 54 m
d) 72 m
Answer: a

Question: In a ΔABC, cosec A (sin Bcos C + cos Bsin C) is equal to
a) c/a
b) a/c
c) 1
d) c/ab
Answer: c

Question: In an acute angled ΔABC, r + r1 = r1+ r2 + r3 and ∠B >π/3, then
a) b + 2c < 2a < 2b + 2c
b) b + 4c < 4a < 2b + 4c
c) b + 4c < 4a < 4b + 4c
d) b + 3c < 3a < 3b + 3c
Answer: d

Question: ABis a vertical pole with Bat the ground level and A at the top. A man finds that the angle of elevation of the point A from a certain point C on the ground is 60°. He moves away from the pole along the line BC to a point D such that CD = 7m. From D the angle of elevation of the point A is 45°. Then, the height of the pole is
a) 7√3/2(1/√3+1)m
b) 7√3/2(1/√3-1)m
c) 7√3/2(√3+1)m
d) 7√3/2(√3-1)m
Answer: c

Question: Let ABC be an isosceles triangle with base BC. If r is the radius of the circle inscribed in the ΔABC and r₁ be the radius of the circle escribed opposite to the angle A, then the product r₁r can be equal to where R is the radius of the circumcircle of the ΔABC.
a) R₂ sin²A
b) R₂ sin²B
c) 1/2a²
d) a²/4
Answer: c

Question: A ladder rests against a wall making an anglea with the horizontal. The foot of the ladder is pulled away from the wall through a distance x, so that it slides a distance y down the wall making an angle b with the horizontal. The correct relation is
a) x = y tan(α+β/2)
b) y = x tan (α+β/2)
c) x = y tan(α+β)
d) y = x tan (α+β)
Answer: a

Question: Difference between the greatest and the least angle is
a) cos-1 4/5
b) tan-1 3/4
c) cos-1 3/5
d) None of the options
Answer: b

Question: In a triangle (1-r₁/r₂)(1-r₁/r₃)=2 then the triangle is
a) right angled
b) equilateral
c) isosceles
d) None of the options
Answer: a

Question: The maximum value of

a) 4 +√2
b) 3 +√2
c) 9
d) 4
Answer: a

Question: Points D, E are taken on the side BC of a ΔABC such that BD = DE = EC. If ∠BAD =x , ∠DAE =y , ∠EAC = z, then the value of sin(x+y) sin (y+z) /sinx sinz is equal to
a) 1
b) 2
c) 4
d) None of the options
Answer: c

Question: sin A : sin C = sin (A – B) : sin (B – C), then a² , b² , c₂ , and are in
a) AP
b) GP
c) HP
d) None of the options
Answer: d

Question: A flag staff 20 m long standing on a wall 10 m high subtends an angle whose tangent is 0.5 at a point on the ground. If q is the angle subtended by the wall at this point, then
a) tan θ = 1
b) tan θ = 3
c) tan θ = 1/2d)
d) None of the options
Answer: a

Question: The greatest and least value of sinX cos x are respectively
a) 1, 1
b) 1/2,1/2
c) 1/4,-1/4
d) 2, -2
Answer: b

Question: If x, y and z are perpendicular drawn from the vertices of triangle having sides a , b and c, then the value of bx/c +cy/a +az/b will be
a) (a² + b² + c²)/2R
b) (a² + b² + c²)/R
c) (a² + b² + c²)/4R
d) 2(a² + b² + c²)/R
Answer: a

Question: At a distance 2 hm from the foot of a tower of height h m the top of the tower and a pole at the top of the tower subtend equal angles. Height of the pole should be
a) (5h/3)m
b) (4h/3)m
c) (7h/5)m
d) (3h/2)m
Answer: a

Question: The radii r₁ r₂ r₃ , of the described circles of the DABC are in HP. If the area of the triangle is 24 2 cm and its perimeter is 24 cm, then the length of its largest side
is
a) 10
b) 9
c) 8
d) 7
Answer: a

Question: The minimum value of 3 cosX+4 sin x + 8 is
a) 5
b) 9
c) 7
d) 3
Answer: d

Question: A tower stands at the centre of a circular park. A and B are two points on the boundary of the park such that AB(= a) subtends an angle of 60° at the foot of the tower and the angle of elevation of the top of the tower from A or B is 30°. The height of the tower is
a) 2a/√3
b) 2a√3
c) a/√3
d) √3
Answer: c

Question: The horizontal distance between two towers is 60 m and the angle of depression of the top of the first tower as seen from the top of the second is 30°. If the height of the second tower be 150 m, then the height of the first tower is
a) (150 – 60√3) m
b) 90 m
c) (150 – 20√3) m
d) None of the options
Answer: d

Question: From the top of a cliff of height a , the angle of depression of the foot of a certain tower is found to be double the angle of elevation of the top of the tower of height h. If q be the angle of elevation, then its value is (a) rcosec sinβ (b) rcosec α sin
a) cos^-1√(2h/a)
b) sin^-1 √(2h/a)
c) sin^-1 √(a/2-h)
d) tan^-1√(3 -2h/a)
Answer: d

Question: When the elevation of sun changes from 45° to 30°, the shadow of a tower increases by 60 m, then the height of the tower is
a) 30 √3 m
b) 30( √2 + 1) m
c) 30( √3 – 1) m
d) 30( √3 + 1) m
Answer: d

Question: In a ΔABC, if a = 2 x, b = 2y and ÐC = 120°, then the area of the triangle is
a) xy sq unit
b) xy √3 sq unit
c) 3xy sq unit
d) 2 xy sq unit
Answer: b

Question: In a ∠ABC, a : b : c = 4 :5 :6. The ratio of the radius of the circumcircle to that of the incircle is
a) 16/9
b) 16/7
c) 11/7
d) 7/16
Answer: b

Question: ABCD is a square plot. The angle of elevation of the top of a pole standing at Dfrom A orC is 30° and that from B is q, then tan q is equal to
a) 6
b) 1/√6
c) √3/2
d) √(2 /3)
Answer: b

Question: Circumradius R is equal to
a) 2.5
b) 3.5
c) 1.5
d) 4.2
Answer: a

Question: From the bottom of a pole of height h the angle of elevation of the top of a tower is a and the pole subtends an angle b at the top of the tower. The height of the tower is
a) h tan(α-β) /tan(α-β) -tanα
b) h cot(α-β) /cot(α-β) -cotα
c) cot(α-β) / cot(α-β) -cotα
d) None of the options
Answer: b

Question: An observer on the top of tree, finds the angle of depression of a car moving towards the tree to be 30°.After 3 min this angle becomes 60°. After how much more time, the car will reach the tree ?
a) 4 min
b) 4.5 min
c) 1.5 min
d) 2 min
Answer: c

Question: If A and B are two points on one bank of a straight river and C, D are two other points on the other bank of river. If direction from A to B is same as that from C to D and AB = a, ∠CAD = a, ∠DAB = b, ∠CBA = g, then CD is equal to
a) a sinβ sinγ /sinαsin(α + β + γ)
b) a sinα sinγ /sinβsin(α + β + γ)
c) a sinα sinβ /sinβsin(α + β + γ)
d) None of the options
Answer: b

Question: A flag staff is upon the top of a building. If at a distance of 40 m from the base of building the angles of elevation of the topes of the flag staff and building are 60° and 30° respectively, then the height of the flag staff is
a) 46.19 m
b) 50 m
c) 25 m
d) None of the options
Answer: a

Question: The area of the circle and the area of a regular polygon of n sides and of perimeter equal to that of the circle are in the ratio of
a) tan(π/n) : π/n
b) cos (π/n) : π/n
c) sin (π/n) : π/n
d) cot (π/n) : π/n
Answer: a

Question: The top of a hill observed from the top and bottom of a building h is at angles of elevation p and q, respectively. The height of hill is
a) h cot q/ cotq – cotp
b) h cot p/ cotp – cotq
c) h tan p /tanp – tanq
d) None of the options
Answer: b

Question: For a ΔABC, R = 5/2 and r = 1. Let I be the incentre of the triangle and D, E and F be the feet of the perpendiculars from I to BC, CA and AB,respectively. The value of ID X IE X IF/IA X IB X IC is equal to
a) 5/2
b) 5/4
c) 1/10
d) 1/5
Answer: c

Question: In ΔABC, if tan A/2 tan C/2 = 1/2 then a , band c are in
a) AP
b) GP
c) HP
d) None of the options
Answer: d

Question: The angle of elevation of the top of a tower from a point A due South of the tower is a and from a point Bdue East of the tower isb. If AB= d, then the height of the tower is
a) d/√tan²α – tan²β
b) d/√tan²α + tan²β
c) d/√cot²α + cot²β
d) d/√cot²α – cot²β
Answer: c

Question: For a regular polygon, let r and R be the radii of the inscribed and the circumscribed circles. A false statement among the following is
a) there is a regular polygon with r/R = 1/2
b) there is a regular polygon with r/R = 1/√2
c) there is a regular polygon with r/R = 2/3
d) there is a regular polygon with r/R =√3/2
Answer: d

Question: At a point on the ground the angle of elevation of a tower is such that its cotangent is 3/5 . On walking 32 m towards the tower the cotangent of the angle of elevation is 2/5. The height of the tower is
a) 160 m
b) 120 m
c) 64 m
d) None of the options
Answer: a

Question: A vertical tower stands on a declivity which is inclined at 15° to the horizon. From the foot of the tower a man ascends the declivity for 80 ft and then, finds that the tower subtends an angle of 30°. The height of tower is
a) 20(√6 – √2) ft
b) 40(√6 – √2) ft
c) 40(√6 + √2) ft
d) None of the options
Answer: b

Question: If A, B, C, D are the angles of a quadrilateral, then ∑tanA/∑cotA is equal to
a) π tan A
b) π cot A
c) ∑ tan² A
d) ∑ cot² A
Answer: a

Question: The angle of elevation of the top of a hill from a point is a. After walking b m towards the top up a slope inclined at an ∠β to the horizon, the angle of elevation of the top becomes γ. Then, the height of the hill is
a) b sinα sin (γ – β)/sin (γ – α)
b) b sinα sin (γ – α)/sin (γ – β)
c) b sin(γ – β) /sin (γ – α)
d) sin(γ – β)/b sinα sin(γ – α)
Answer: a

Question: Each side of a square subtends an angle of 60° at the top of a towerh metres high standing in the centre of the square. If ais the length of each side of the square, then
a) 2a² = h²
b) 2h² = h²
c) 3a² = 2h²
d) 2h² = 3a²
Answer: b

Question: A flag staff stands in the centre of a rectangular field whose diagonal is 1200 m and subtends angles 15° and 45° at the mid-points of the sides of the field. The height of the flag staff is
a) 200 m
b) 300 √2 + √3 m
c) 300 √2 – √3 m
d) 400 m
Answer: c

Question: In an isosceles D ABC, AB = AC. If vertical ΔA is 20°, then a³ + b³ is equal to
a) 3a²b
b) 3b²c
c) 3c²a
d) abc
Answer: c

Question: Two vertical poles 20 m and 80 m stands apart on a horizontal plane. The height of the point of intersection of the lines joining the top of each pole to the foot of the other is
a) 15 m
b) 16 m
c) 18 m
d) 50 m
Answer: a

Question: In a ΔABC, (a + b + c)(b + c – a) = kbc, if
a) k < 0
b) k > 6
c) 0 < k < 4
d) k > 4
Answer: c

Question: At each end of a horizontal line of length 2a, the angular elevation of the peak of a vertical tower is q and that at its middle point it is f. The height of the peak is
a) a sin θ sin Φ
b) a sin θ sin Φ /√sin(θ+Φ)sin(θ-Φ)
c) a cosθ cosΦ /√cos(θ+Φ)cos(θ-Φ)
d) None of the options
Answer: b

Question: ABC is a triangular park with AB = AC = 100 m. A clock tower is situated at the mid-point of BC. The angles of elevation of the top of the tower at A and B are cot-1 3.2 and cosec-1 2.6, respectively. The height of the tower is
a) 50 m
b) 25 m
c) 40 m
d) None of the options
Answer: b

Question: The angle of elevation of a cloud at a point 2500 m high above a lake is 15° and the angle of depression of its image in the lake is 45°, the height of the cloud above the surface of the lake is
a) 2500√3 m
b) 2500 m
c) 500√3 m
d) 500 m
Answer: b

Question: If PQbe a vertical tower subtending anglesa, b and g at the points A, B and C respectively on the line in the horizontal plane through the foot Dof tower and on the same side of it, then BC cota – CA cotb + ABcot g is equal to
a) 0
b) 1
c) 2
d) None of the options
Answer: a

Question: An observer standing on a 300 m high tower observes two boats in the same direction their angles of depression are 60° and 30°, respectively. The distance between boats is
a) 173.2 m
b) 346.4 m
c) 25 m
d) 72 m
Answer: b

Question: In a cubical hall ABCDPQRS with each side 10 m,G is the centre of the wall BCRQand T is the mid-point of the side AB. The angle of elevation of G at the point T is
a) sin-1 (1/√3)
b) cos-1 (1/√3)
c) cot-1 (1/√3)
d) None of the options
Answer: a

Question: From a point a metres above a lake the angle of elevation of a cloud is α and the angle of depression of its reflection is β. The height of the cloud is
a) asin(α+β) /sin(α-β) m
b) asin(α+β)/sin(β-α) m
c) asin(β-α)/sin(α+β) m
d) None of the options
Answer: b

Question: Consider the following statements
I. If in a ΔABC , sin A/sin C = sin(A-B)sin(B-C) then a²,b² and c² are in AP.
II. If exradius r₁, r₂ and r₃ of a DABC are in HP, then the sides a , b and c are in AP.
Which of these is/are correct ?
a) Only (I)
b) Only (II)
c) Both (I) and (II)
d) None of the options
Answer: c

Question:

Answer: a