CBSE Class 12 Mathematics Inverse Trigonometric Functions MCQs Set 03

Question: if 3 sin^-1 2x/1+x² -4cos^-1 1-x²/1+x² +2 tan^-1 2x/1-x²=π/3, then value of x is
(a) √3
(b) 1/√3
(c) 1
(d) None of the options 
Answer: b

Question: The sum of the infinite series cot ^-1 2+cot^-1 8+cot^-1 18+ cot^-1 32+…is 
(a) π
(b) π/2
(c) π/4
(d) None of the options 
Answer: c

Question: The value of cos ( 2cos^-1 x+ sin^-1x) at x =1/5 is
(a) 1
(b) 3
(c) 0
(d) -2√6/5
Answer: d

Question: If co^-1 x+cos^-1 y + cos^-1 z= π, then
(a) x² + y² = z² 
(b) x² + y² + z² = 0 
(c) x² + y² + z² = 1-2xyz
(d) None of the options 
Answer: c

Question: 4 tan ^-1 1/5- tan ^-1 1/239 is equal to
(a) π
(b) π/2
(c) π/3
(d) π/4 
Answer: d

Question: If tan-1(a/x)+ tan-1(b/x)=π/2,then x is equal to
(a) √ab
(b) √2ab
(c) 2ab
(d) ab 
Answer: a

Question: The value of the expression tan(1/2 cos ^-1 2/√5) is
(a) 2 √5 
(b) √5-2 
(c) √5+2
(d) 5+√2
Answer: b

Question: If tan^-1(x-1/x+2)+ tan^-1 (x+1/x+2)=π/4, then x is equal to
(a) 1/√2
(b) -1/√2
(c) ±√5/2
(d) ±1/2 
Answer: c

Question: If tan θ +tan (π/3+θ) +tan (-π/3+θ )=a tan 3θ,then a is equal to
(a) 1/3
(b) 1
(c) 3
(d) None of the options 
Answer: c

Question: The value of cot^-1(xy+1/x-y) +cot^-1(yz+1/y-z)+cot^-1(zx+1/z-x) is
(a) 0
(b) 1
(c) cot^-1 x+cot^-1y +cot^-1 z 
(d) None of the options 
Answer: a

Question: The value of the expression sin(2 tan^-1 1/3) + cos (tan-1 2√2) 
a) 13/15
(b) 14/15
(c) 11/15
(d) None of the options 
Answer: b

Question: If in a Δ ABC, ∠A =tan ^-12 and ∠B= tan -13, then ∠C is equal to
(a) π/2
(b) π/3
(c) π/4
(d) None of the options 
Answer: c

Question: If 2 tan^-1 (cos x) = tan^-1 (2cosec x), then the value of x is
(a) 3π/4
(b) π/4
(c) π/3
(d) None of the options
Answer: b

Question: If tan^–1 x + tan^–1 y = 4π/5, then cot^–1x + cot^–1 y equals
(a) π/5
(b) 2π/5
(c) 3π/5
(d) p
Answer: a

Question: The principle value of the expression cos^–1[cos(–680°)] is
(a) 2π/9
(b) − 2π/9
(c) 34π/9
(d) π/9
Answer: a

Case Based Questions

The Government of India is planning to fix a hoarding board at the face of a building on the road of a busy market for awareness on COVID-19 protocol. Ram, Robert and Rahim are the three engineers who are working on this project. ‘A’ is considered to be a person viewing the hoarding board 20 metres away from the building, standing at the edge of a pathway nearby, Ram Robert and Rahim suggested to the film to place the hoarding board at three different locations namely C, D and E. ‘C’ is at the height of 10 metres from the ground level. For the viewer ‘A’, the angle of elevation of ‘D’ is double the angle of elevation of ‘C’. The angle of elevation of ‘E’ is triple the angle of elevation of ‘C’ for the same viewer.
Look at the figure given and based on the above information answer the following:

Question: Measure of ∠EAB
(a) tan^–1 (11)
(b) tan^–1 (3)
(c) tan^–1 (2/11)
(d) tan^–1 (11/2)
Answer: d

Question: Measure of ∠CAB =
(a) tan^–1 (2)
(b) tan^–1 (1/2)
(c) tan^–1 (1)
(d) tan^–1 (3)
Answer: b

Question: Measure of ∠DAB =
(a) tan^–1 3/4
(b) tan^–1(3)
(c) tan–1 (4/3)
(d) tan^–1(4)
Answer: c

Question: A’ is another viewer standing on the same line of observation across the road. If the width of the road is 5 meters, then the difference between ∠CAB and ∠CA’B is
(a) tan^–1 (1/12)
(b) tan^–1 (2/8
(c) tan^–1 (2/5)
(d) tan^–1 (11/25)
Answer: a

Two men on either side of a temple of 30 meters high observe its top at the angles of elevation a and β respectively (as shown in the given figure). The distance between the two men is 40√3 meters and the distance between the first person A and the temple is 30√3 meters.
Based on the above information answer the following:

Question: ∠BCA = β =
(a) tan^–1 (1/2)
(b) tan^–1 (2)
(c) tan^–1(1/√3)
(d) tan^–1 (√3)
Answer: d

Question: ∠ABC =
(a) π/4
(b) π/6
(c) π/2
(d) π/3
Answer: c

Question: Domain and Range of cos–1 x =
(a) (1, 1), (0, p)
(b) [–1, –1], [0, p]
(c) [–1, 1], [0, p]
(d) (-1, 1), (-π/2,π/2)
Answer: c

If f (x) = sin–1 x
Based on the above function answer the following question:

Question: If function is f(–x) then equal to
(a) –f(x)
(b) f(x)
(c) cos f(–x)
(d) None of the options
Answer: a

Question: f(x) is
(a) Odd
(b) Even
(c) Neither odd nor even
(d) not defined
Answer: a

IF f(X) = tan^-1[2x/1-x²]

Based on the above function answer the following question:

Question: Maximum value of f(x)
(a) [–1, 1]
(b) [0, ∞)
(c) (–∞, 0]
(d) not maxima Sol.
(d) not maxima
Answer: d

Question: Which of the following is the principal value branch of cosec^-1 x?
(a) (−π/2, π/2)
(b) (0, π) – {π/2}
(c) [−π/2, π/2]
(d) [−π/2, π/2] – [0]
Answer: d

Question: If 3 tan^-1 x + cot^-1 x = π, then x equals
(a) 0
(b) 1
(c) -1
(d) 12
Answer: b

Question: The domain of the function cos^-1 (2x – 1) is
(a) [0, 1]
(b) [-1, 1]
(c) [-1, -1]
(d) [0, π]
Answer: a

Question: If cos(sin^-12/5 + cos^-1 x) = 0 then x is equal to
(a) 1/5
(b) 2/5
(c) 0
(d) 1
Answer: b

Question: The value of sin (2 tan^-1 (0.75)) is equal to
(a) 0.75
(b) 1.5
(c) 0.96
(d) sin (1.5)
Answer: c

Question: The value of cos^-1 (cos3π/2) is equal to
(a) π/2
(b) 3π/2
(c) 5π/2
(d) –7π/2
Answer: a

Question: The value of expression 2 sec^-1 (2) + sin^-1 (1/2) is
(a) π/6
(b) 5π/6
(c) 7π/6
(d) 1
Answer: b

Question: If sin-1(2a/1+a²) + cos^-1(1−a²/1+a²) = tan-1(2x/1−x²) where a, x ∈ |0, 1| then the value of x is
(a) 0
(b) a2
(c) a
(d) 2a/1−a²
Answer: d

Question: The value of sin [cos^-1(7/25)] is
(a) 25/24
(b) 25/7
(c) 24/25
(d) 7/24
Answer: c

Question: sin^-1(−1/2)
(a) π/3
(b) –π/3
(c) π/6
(d) –π/6
Answer: d

Question: sec^-1(−2/√3)
(a) π/6
(b) π/3
(c) 5π/6
(d) –2π/3
Answer: c

Question: cos^-1(1/2)
(a) –π/3
(b) π/3
(c) π/2
(d) 2π/3
Answer: b

Question: cosec^-1(−2/√3)
(a) –π/3
(b) π/3
(c) π/2
(d) –π/2
Answer: a

Question: cot^-1(1)
(a) π/3
(b) π/4
(c) π/2
(d) 0
Answer: b

Question: cos^-1(√3/2)
(a) 5π/6
(b) π/6
(c) 4π/9
(d) 2π/3
Answer: a

Question: cosec^-1(2)
(a) π/6
(b) 2π/3
(c) 5π/6
(d) 0
Answer: a

Question: sec^-1(2)
(a) π/6
(b) π/3
(c) 2π/3
(d) 5π/6
Answer: b

Question: tan^-1(√3)
(a) π/6
(b) π/3
(c) 2π/3
(d) 5π/6
Answer: b

Question: cot^-1(-√3)
(a) 5π/6
(b) π/3
(c) π/2
(d) π/4
Answer: a

Question: tan-1 (√3) + sec^-1 (-2) – cosec^-1(2/√3)
(a) 5π/6
(b) 2π/3
(c) π/3
(d) 0
Answer: d

Question: cos^-1 (−1/2) + 2sin^-1 (−1/2)
(a) π/3
(b) 2π/3
(c) 3π/4
(d) 5π/8
Answer: a