# Inverse Trigonometric Functions MCQ Questions Class 12 Mathematics

Please refer to MCQ Questions for Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions with answers below. These multiple-choice questions have been prepared based on the latest NCERT book for Class 12 Mathematics. Students should refer to MCQ Questions for Class 12 Mathematics with Answers to score more marks in Grade 12 Mathematics exams. Students should read the chapter Inverse Trigonometric Functions and then attempt the following objective questions.

**MCQ Questions for Class 12 Mathematics Chapter 2 Inverse Trigonometric Functionswith answers**

**MCQ Questions for Class 12 Mathematics Chapter 2 **provided below covers all important topics given in this chapter. These MCQs will help you to properly prepare for exams.

**Question. The value of cos (2cos ^{−1} x + sin^{−1} x) at x = 1/5 is**

(a) − 2√6/5

(b) − 2√6

(c) −√6/5

(d) None of these

**Answer**

A

**Question. tan ^{–1}x−1/x−2 + tan^{–1}x+1/x+2 = π/4**

(a) 1/√2

(b) −1/√2

(c) ± 1/√2

(d) 0

**Answer**

C

**Question. tan ^{–1}(1/4) + tan^{–1}(2/9) is equal to**

(a) 1/2cos

^{–1}(3/5)

(b) 1/2sin

^{–1}(3/5)

(c) 1/2tan

^{–1}(3/5)

(d) tan

^{–1}(1/2)

**Answer**

D

**Question. Which of the following is the principal value branch of cos ^{–1}x?**

**Answer**

C

**Question. **

(a) α/β

(b) β/α

(c) α + β/1+ αβ

(d) α + β/1− αβ

**Answer**

D

**Question. Principal value of tan ^{–1}1 + cos^{–1}(−1/2) + sin^{–1}(−1/2) is equal to**

(a) 2π/3

(b) 3π/4

(c) π/2

(d) 6π

**Answer**

B

**Question. The value of tan (1/2 cos ^{−1}√5/3) is**

(a) 3+√5/2

(b) 3 −√5/2

(c) √5/6

(d) None of these

**Answer**

B

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

(a) 0

(b) 1

(c) –1

(d) 1/2

**Answer**

B

**Question. If tan ^{–1}x – tan^{–1}y= tan^{–1}A, then A is equal to**

(a) x – y

(b) x + y

(c) x − y/1+ xy

(b) x + y/1− xy

**Answer**

C

**Question. The number of roots of equation tan ^{−1}2x + tan^{−1}3x = π/4 is**

(a) 0

(b) 1

(c) 2

(d) infinite

**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. **

**where a, x ∈ [0,1], then the value of x is**

(a) 0

(b) a/2

(c) a

(d) 2a/1− a^{2}

**Answer**

D

**Question. If 2 tan ^{–1} (cos x) = tan^{–1} (2 cosec x) then value of x is**

(a) 0

(b) π/3

(c) π/4

(d) π/2

**Answer**

C

**Question. If 6 sin ^{–1}(x^{2} – 6x + 8.5) = π, then x is equal to**

(a) 1

(b) 2

(c) 3

(d) 8

**Answer**

B

**Question. If x, a ∈ R, where −a/√3 < x < a/√3 , then tan ^{–1} ( 3a^{2}x – x^{3}/ a^{3} – 3ax^{2}) is equal to**

(a) 3 tan

^{–1}(x/a)

(b) – 3 tan

^{–1}(x/a)

(c) 3 tan

^{–1}(a/x)

(d) None of these

**Answer**

A

**Question. The value of cos ^{–1} (cos(33π/5)) is**

(a) 3π/5

(b) −3π/5

(c) π/10

(d) −π/10

**Answer**

A

**Question. If k ≤sin ^{−1} x + cos^{−1} x + tan^{−1} x ≤ K, then**

(a) k = –π, K = π

(b) k = 0, K = π/2

(c) k = –π/4, K = 3π/4

(d) k = 0, K = π

**Answer**

C

**Question. Principal value of sin ^{−1}(−1/2) is equal to **

(a) π/3

(b) −π/3

(c) π/6

(d) −π/6

**Answer**

D

**Question. If tan ^{–1}(cot θ) = 2θ, then θ is equal to**

(a) π/3

(b) π/4

(c) π/6

(d) None of these

**Answer**

C

**Question. The value of tan [ 2 tan ^{–1}1/5 − π/4] is**

(a) 5/18

(b) −3/2

(c) −7/17

(d) 3/8

**Answer**

C

**Question. The solution of sin ^{–1} x – sin^{ –1}2x = ±π/3 is**

(a) ±1/3

(b) ±1/4

(c) ±√3/2

(d) ±1/2

**Answer**

D

**Question. The value of cos(1/2 cos ^{−1}1/8) is**

(a) 3/4

(b) 2/3

(c) 4/3

(d) −3/4

**Answer**

A

**Question. If sin ^{–1} x = cosec^{–1}(2) has the value k π/12, then value of k is**

(a) 1

(b) 2

(c) 4

(d) 5

**Answer**

D

**Question. The value of sin ^{–1}(1/√5) + cot^{–1} (3) is**

(a) π/6

(b) π/4

(c) π/3

(d) π/2

**Answer**

B

**Question. The value of x satisfying the equation ****3 tan ^{−1}1/2+√3 − tan^{−1}1/x = tan^{−1}1/3 is**

(a) x = 2

(b) x = 1/2

(c) x = 1/2−√3

(d) None of these

**Answer**

A

**Question. Solve for x : {x cos(cot ^{–1}x) + sin(cot^{–1} x)}^{2} = 51/50,**

(a) 1/√2

(b) 1/5√2

(c) 2√2

(d) 5√2

**Answer**

B

**Question. If sin ^{–1} x = tan ^{–1} y, what is the value of 1/x^{2} − 1/y^{2 }?**

(a) 1

(b) –1

(c) 0

(d) 2

**Answer**

A

**Question. The equation sin ^{–1}x – cos^{–1}x = cos^{–1} (√3/2) has**

(a) unique solution

(b) no solution

(c) infinitely many solutions

(d) None of these

**Answer**

A

**Question. The value of cos[tan ^{–1}{tan(15π/4)}] is**

(a) −1/√2

(b) 0

(c) 1/√2

(d) 1/2√2

**Answer**

C

**Case Study **

A group of students of class XII visited India Gate on an education trip. The teacher and students had interest in history as well. The teacher narrated that India Gate, official name Delhi Memorial, originally called All-India War Memorial, monumental sandstone arch in New Delhi, dedicated to the troops of British India who died in wars fought between 1914 and 1919. The teacher also said that India Gate, which is located at the eastern end of the Raj path (formerly called the Kingsway), is about 138 feet (42 metrs) in height.

**Question. What is the angle of elevation if they are standing at a distance of 42m away from the monument?**

(a) tan^{−1} 1

(b) sin^{−1} 1

(c) cos^{−1} 1

(d) sec^{−1} 1

## Answer

A

**Question. They want to see the tower at an angle of sec−1 2. So, they want to know the distance where they should stand and hence find the distance.**

(a) 42 m

(b) 20.12 m

(c) 25.24 m

(d) 24.64 m

## Answer

C

**Question. Domain of sin−1 𝑥 is……..**

(a) (-1, 1)

(b) {-1,1}

(c) [ -1,1]

(d) none of these

## Answer

C