# MCQs For NCERT Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions

Please refer to the MCQ Questions for Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions with Answers. The following Inverse Trigonometric Functions Class 12 Mathematics MCQ Questions have been designed based on the latest syllabus and examination pattern for Class 12. Our experts have designed MCQ Questions for Class 12 Mathematics with Answers for all chapters in your NCERT Class 12 Mathematics book.

## Inverse Trigonometric Functions Class 12 MCQ Questions with Answers

See below Inverse Trigonometric Functions Class 12 Mathematics MCQ Questions, solve the questions and compare your answers with the solutions provided below.

Question. If sin–1 (x/5) + cosec–1 (5/4) = π/2 , then the value of x is
(a) 4
(b) 5
(c) 1
(d) 3

D

Question.

(a) -π/2
(b) zero
(c) π/2
(d) π

C

Question. The greatest and the least values of (sin-1 x)3+ (cos-1 x)3  are respectively

C

Question. Sum of infinite terms of the series

(a) π/4
(b) tan -1(2)
(c) tan -1
(d) None of these

B

Question. If f (x)= sin-1(√3/2 X -1/2√1-X2),-1/2≤X≤1, then f(x) is equal to

B

Question. If θ and Φ are the roots of the equation 8x2+ 22x+5=0, then
(a) both sin-1 θ and sin-1Φ are equal
(b) both sec-1 θ and secf-1 Φare real
(c) both tan-1 θ and tan -1Φ are real
(d) None of the above

C

Question.

(a) β
(b) π/2-β
(c) π-β
(d) -β

B

Question. The number of triplets (x,y,z ) satisfying sin-1 x+ cos-1 y + sin-1 z= 2π   is
(a) 0
(b) 2
(c) 1
(d) infinite

C

Question.

where, k is equal to
(a) 1
(b) 2
(c) 4
(d) None of these

B

Question.

(a) -2/π
(b) 2/π
(c) -p/π
(d) p/π

C

Question.

(a) 0
(b) 1
(c) 2
(d) 3

C

Question.

where, k is equal to
(a) 1
(b) 2
(c) 4
(d) None of these

B

Question. The value of tan-1

(a) 2 θ
(b) θ
(c) θ /2
(d) independent of q

B

Question. If [cot-1 x] [cos-1 x] =0, where x is a non-negative real number and [.] denotes the greatest integer function, then complete set of values of x is
(a) (cos1,1 ]
(b) (cot 1,1)
(c) (cos,1,cot 1)
(d) None of these

B

Question. The sum of the infinite series

(a) π/8
(b) π/4
(c) π/2
(d) π

C

Question.

(A,C)

On the basis of above information, answer the following questions.
Question.

(a)π/4
(b) π/2
(c) π
(d) None of these

A

Question.

(a) π/ 2
(b) cot -1 2
(c) tan -1 2
(d) None of these

D

Question. If a ≤ tan-1x+cot-1x+sin-1x≤b,  then
(a) a = 0
(b) b =π/p
(c) a =π/p
(d) b = π

(A,D)

Question.

(a) π
(b) 3π/4
(c) π /2
(d) π/4

D

Question. cot (π/4 − 2cot−13) =
(a) 7
(b) 6
(c) 5
(d) None of these

A

Question. The domain of the function defined by f (x) = sin–1 √x –1 is
(a) [1, 2]
(b) [–1, 1]
(c) [0, 1]
(d) None of these

A

Question. The value of sec2(tan–12) + cosec2(cot–13) is
(a) 12
(b) 5
(c) 15
(d) 9

C

Question. The principal value of sin–1 √3/2 is:
(a) –π/3
(b) π/6
(c)–2π/3
(d) 2π/3

A

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

A

Question. tan–11/3 + tan–11/5 + tan–11/8 =
(a) π
(b) π/2
(b) π/4
(d) 3π/4

B

Question. The value of tan–1(1) + tan–1(0) + tan–1(2) + tan–1(3) is equal to
(a) π
(b) 5π/4
(c) π/2
(d) None of these

A

Question. Given that sin–1(sin 3π/4) = 2π/k , then k =
(a) 3
(b) 8
(c) 6
(d) 9

B

Question. The value of expression tan –1(1/2 cos–12/√5) is
(a) 2 + √5
(b) √5 – 2
(c) √5 + 2/2
(d) 5 + √2

B

Question. If tan–1(x – 1) + tan–1x + tan–1(x + 1) = tan–13x, then the value of x are
(a) ±1/2
(b) 0, 1/2
(c) 0,−1/2
(d) 0,±1/2

D

Question. If cos(sin–1 2/5 + cos–1x) = 0, then x is equal to
(a) 1/5
(b) 2/5
(c) 0
(d) 1

B

Question. If sin–1(x2 – 7x + 12) = nπ, ∀ n ∈ I, then x =
(a) –2
(b) 4
(c) –3
(d) 5

B

Question. Principal value of cosec−1(−2/√3) is equal to
(a) −π//3
(b) π/3
(c) π/2
(d) −π/2

A

Question. The principal value of sin–1 (sin 5π/3) is
(a) −5π/3
(b) 5π/3
(c) −π/3
(d) 4π/3

C

Question. The value of sin (tan –1x + cot –1x)/sin(sin–1 x cos –1x) is
(a) 1
(b) 2
(c) 4
(d) 5

A

Question. tan–1 (x/y)−tan–1 (x − y/x + y) is equal to (Where x > y > 0)
(a) −π/4
(b) π/4
(c) 3π/4
(d) None of these

B

Question. If sin–1x + sin–1y + sin–1z = 3π/2 , then what is the value of x + y + z ?
(a) –3
(b) 3
(c) –1/3
(d) 1/3

B

Question. Prinicpal value of tan–1 (√3) is equal to
(a) π/6
(b) π/3
(c) 2π/3
(d) 5π/3

B

Question. If tan–1k – tan–1 3 = tan–11/13 ,then k =
(a) 1
(b) 2
(c) 4
(d) 5

C

Question. The value of cot(cosec–15/3 + tan–12/3) is
(a) 5/17
(b) 6/17
(c) 3/17
(d) 4/17

B

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

A

Question. If 4 cos–1x + sin–1x = π, then the value of x is
(a) 3/2
(b) 1/√2
(c) √3/2
(d) 2/√3

C

ASSERTION- REASON TYPE QUESTIONS

(a) Assertion is correct, reason is correct; reason is a correctexplanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

Question. Assertion: The value of tan {cos –1 4/5 + tan –1 2/3} is 17/6.
Reason: tan–1 x + tan–1 y = tan–1 (x − y/1 + xy)

C

Question. Assertion: The value of sin [tan–1(−√3) + cos–1(−√3/2)] is 1.
Reason: tan–1(–x) = tan x and cos–1(–x) = cos–1x.

C

Question. Assertion: The domain of the function sec–1 x is the setof all real numbers.
Reason: For the function sec–1x, x can take all real valuesexcept in the interval (–1, 1).

D

Question. Assertion: tan–11/3 + tan–12/9 + tan–1 4/33 + …. ∞ = π/4
Reason : If xy < 1 then tan–1x + tan–1y = tann–1x + y/1−xy

B

Question. Assertion: If 2(sin–1x)2 – 5 (sin–1x) + 2 = 0, then x has 2 solutions.
Reason: sin–1 (sin x) = x if x ∈ R.

D

Question. Assertion: The function f(x) = sin x does not possess inverse if x ∈ R.
Reason: The function f(x) = sin x is not one-one onto if x ∈ R.