# MCQs for Mathematics Class 12 with Answers Chapter 2 Inverse Trigonometric Functions

Students of class 12 Mathematics should refer to MCQ Questions Class 12 Mathematics Inverse Trigonometric Functions with answers provided here which is an important chapter in Class 12 Mathematics NCERT textbook. These MCQ for Class 12 Mathematics with Answers have been prepared based on the latest CBSE and NCERT syllabus and examination guidelines for Class 12 Mathematics. The following MCQs can help you to practice and get better marks in the upcoming class 12 Mathematics examination

**Chapter 2 Inverse Trigonometric Functions MCQ with Answers Class 12 Mathematics**

MCQ Questions Class 12 Mathematics Inverse Trigonometric Functions provided below have been prepared by expert teachers of grade 12. These objective questions with solutions are expected to come in the upcoming Standard 12 examinations. Learn the below provided MCQ questions to get better marks in examinations.

**Question. tan ^{-1}3 + tan^{-1}λ(3 +λ / 1-3λ) is valid for what values of λ?**

(a) λ∈(-1/3 , 1/3)

(b) λ> 1/3

(c) λ < 1/3

(d) All real values of λ

## Answer

C

**Question. If tan ^{-1}(1/2) tan^{-1}(2/11 =) tan^{-1} a then a is equal to**

(a) 1/4

(b) 1/2

(c) 3/4

(d) 1

## Answer

C

**Question. The value of cot (sin ^{–1} x) is**

(a) √(1+x2) /x

(b) x/√(1+x2)

(c) 1/x

(d) √(1 – x2) /x

## Answer

D

**Question. If cos ^{–1} x cos^{–1} y = π/2 , then the value of sin^{–1}x + sin^{–1}y is**

(a) 0

(b) π/2

(c) p

(d) 2π/3

## Answer

B

**Question. The value of sin ^{–1}(cosπ/9) is**

(a) π/9

(b) 5π/9

(c)-5π/9

(d) 7π/18

## Answer

D

**Question. The principal value of sin ^{–1 }(-√3/2) is**

(a) -2π/3

(b) -π/3

(c) 4π/3

(d) 5π/3

## Answer

B

**Question. Let q = sin ^{–1}(sin (–600°)), then value of q is**

(a) π/3

(b) π/2

(c) 2π/3

(d) -2π/3

## Answer

A

**Question. If 3 tan ^{–1} x + cot^{–1} x = p, then x equals**

(a) 0

(b) 1

(c) –1

(d) 1/2

## Answer

B

**Question. The value of tan (cos ^{-1} 3/5 + tan^{-1} 1/4) is**

(a) 19/8

(b) 8/19

(c) 19/12

(d) 3/4

## Answer

A

**Question. The value of the expression 2 sec ^{-1}2 sin^{-1}(1/2) is**

(a) π/6

(b) 5π/6

(c) 7π/6

(d) 1

## Answer

B

**Question. tan ^{-1}(x/y)-tan^{-1}(x-y /x+y) is equal to**

(a) π/2

(b) π/3

(c) π/4

(d) -3π/4

## Answer

C

**Question. The value of tan ^{2} (sec^{–1} 2) + cot^{2} (cosec^{–1} 3) is**

(a) 5

(b) 11

(c) 13

(d) 15

## Answer

B

**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

## Answer

A

**Question. If α ≤ 2 sin ^{–1}x + cos^{–1}x ≤ β , then**

(a) α= -π/2 , β = π/2

(b) α= 0 , β = π

(c) α= -π/2 , β = 3π/2

(d) a = 0, b = 2π

## Answer

B

**Question. tan(sin ^{-1} 3/5+tan^{-1} 3/4) is equal to**

(a) 7/24

(b) 24/7

(c) 3/2

(d) 3/4

## Answer

B

**Question. sin (tan ^{–1} x), |x|< 1 is equal to**

(a) x/√(1-x

^{2})

(b) 1√(1-x

^{2})

(c) 1√(1+x

^{2})

(d) x/√(1+x

^{2})

## Answer

D

**Question. If cos ^{–1}α + cos^{–1}β + cos^{–1}γ = 3π, then α (β + γ) + β (γ + α) + γ(α + β) equals**

(a) 0

(b) 1

(c) 6

(d) 12

## Answer

C

**Question. The value of cot [cos ^{-1}(7/25)] is**

(a) 25/24

(b) 25/7

(c) 24/25

(d) 7/24

## Answer

D

**Question. Which of the following corresponds to the principal value branch of tan ^{–1} x?**

(a) (-π/2 , π/2)

(b) [-π/2 , π/2]

(c) (-π/2 , π/2) -[0]

(d) (0, π)

## Answer

A

**Question. If sin ^{-1}x + sin^{-1}y = π/2 , then value of cos^{–1} x + cos^{–1} y is**

(a) π/2

(b) π

(c) 0

(d) 2π/3

## Answer

A

**Question. If tan ^{–1} x + 2 cot^{–1} x = π, then x equals**

(a) 0

(b) 1

(c) –1

(d) 1/2

## Answer

A

**Question. The value of tan ^{–1}(√3h+ cos^{–1} (1/2) corresponding to principal branches is**

(a) -π/12

(b) 0

(c) π

(d) π/3

## Answer

C

**Case Study **

A Satellite flying at height h is watching the top of the two tallest mountains in Uttarakhand and Karnataka, them being Nanda Devi (height 7,816m) and Mullayanagiri (height 1,930 m). The angles of depression from the satellite, to the top of Nanda Devi and Mullayanagiri are cot−1 √3 andtan−1 √3 respectively. If the distance between the peaks of the two mountains is 1937 km, and the satellite is vertically above the midpoint of the distance between the two mountains. (Image 17)

**Question. The distance of the satellite from the top of Nanda Devi is**

(a) 1139.4 km

(b) 577.52 km

(c) 1937 km

(d) 1025.36 km

## Answer

A

**Question. The distance of the satellite from the top of Mullayanagiri is**

(a) 1139.4 km

(b) 577.52 km

(c) 1937 km

(d) 1025.36 km

## Answer

C

**Question. The distance of the satellite from the ground is**

(a) 1139.4 km

(b) 577.52 km

(c) 1937 km

(d) 1025.36 km

## Answer

B

**Question. What is the angle of elevation if a man is standing at a distance of 7816m from Nanda Devi?**

(a) sec^{−1} 2

(b) cot−^{1} 1

(c) sin^{−1} √3

(d) cos^{−1} 1

## Answer

B

We hope the above multiple choice questions for Class 12 Mathematics for Chapter 2 Inverse Trigonometric Functions provided above with answers based on the latest syllabus and examination guidelines issued by CBSE, NCERT and KVS are really useful for you. Inverse Trigonometric Functions is an important chapter in Class 12 as it provides very strong understanding about this topic. Students should go through the answers provided for the MCQs after they have themselves solved the questions. All MCQs have been provided with four options for the students to solve. These questions are really useful for benefit of class 12 students. Please go through these and let us know if you have any feedback in the comments section.