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## Thursday 28 January 2021

### CBSE Class 12 Maths - MCQ and Online Tests - Unit 2 - Inverse Trigonometric Functions

#### CBSE Class 12 Maths – MCQ and Online Tests – Unit 2 – Inverse Trigonometric Functions

Every year CBSE conducts board exams for 12th standard. These exams are very competitive to all the students. So our website provides online tests for all the 12th subjects. These tests are also very effective and useful for those who preparing for competitive exams like NEET, JEE, CA etc. It can boost their preparation level and confidence level by attempting these chapter wise online tests.

These online tests are based on latest CBSE Class 12 syllabus. While attempting these our students can identify the weak lessons and continuously practice those lessons for attaining high marks. It also helps to revise the NCERT textbooks thoroughly.

#### CBSE Class 12 Maths – MCQ and Online Tests – Unit 2 – Inverse Trigonometric Functions

Question 1.
The value of cos-1 (cos$$\frac{3π}{2}$$) is equal to
(a) $$\frac{π}{2}$$
(b) $$\frac{3π}{2}$$
(c) $$\frac{5π}{2}$$
(d) –$$\frac{7π}{2}$$

Answer: (a) $$\frac{π}{2}$$

Question 2.
The value of expression 2 sec-1 2 + sin-1 ($$\frac{1}{2}$$) is
(a) $$\frac{π}{6}$$
(b) $$\frac{5π}{6}$$
(c) $$\frac{7π}{6}$$
(d) 1

Answer: (b) $$\frac{5π}{6}$$

Question 3.
The value of sin [cos-1($$\frac{7}{25}$$)] is
(a) $$\frac{25}{24}$$
(b) $$\frac{25}{7}$$
(c) $$\frac{24}{25}$$
(d) $$\frac{7}{24}$$

Answer: (c) $$\frac{24}{25}$$

Question 4.
If cos-1 x > sin-1 x, then
(a) $$\frac{1}{√2}$$ < x ≤ 1
(b) 0 ≤ x < $$\frac{1}{√2}$$
(c) -1 ≤ x < $$\frac{1}{√2}$$ (d) x > 0

Answer: (b) 0 ≤ x < $$\frac{1}{√2}$$

Question 5.
sin-1($$\frac{-1}{2}$$)
(a) $$\frac{π}{3}$$
(b) –$$\frac{π}{3}$$
(c) $$\frac{π}{6}$$
(d) –$$\frac{π}{6}$$

Answer: (d) –$$\frac{π}{6}$$

Question 6.
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

Question 7.
If sin-1 x + sin-1 y = $$\frac{2π}{3}$$ then cos-1 x + cos-1 y =
(a) $$\frac{2π}{3}$$
(b) $$\frac{π}{4}$$
(c) $$\frac{π}{3}$$
(d) $$\frac{π}{2}$$

Answer: (c) $$\frac{π}{3}$$

Question 8.
tan-1$$\frac{1}{2}$$ + tan-1$$\frac{1}{3}$$ =
(a) $$\frac{π}{4}$$
(b) $$\frac{π}{2}$$
(c) $$\frac{π}{3}$$
(d) π

Answer: (a) $$\frac{π}{4}$$

Question 9.
cos-1(cos$$\frac{7π}{6}$$) is equal to
(a) $$\frac{7π}{6}$$
(b) $$\frac{5π}{6}$$
(c) $$\frac{π}{3}$$
(d) $$\frac{π}{6}$$

Answer: (b) $$\frac{5π}{6}$$

Question 10.
Principal value of sin-1($$\frac{1}{√2}$$)
(a) $$\frac{π}{4}$$
(b) $$\frac{3π}{4}$$
(c) $$\frac{5π}{4}$$
(d) None of these

Answer: (a) $$\frac{π}{4}$$

Question 11.
If sin-1($$\frac{2x}{1+x^2}$$) + sin-1$$\frac{2y}{1+y^2}$$ = 2 tan-1 a then a is equal to
(a) $$\frac{x-y}{1+xy}$$
(b) $$\frac{y}{1+xy}$$
(c) $$\frac{y}{1-xy}$$
(d) $$\frac{x+y}{1-xy}$$

Answer: (d) $$\frac{x+y}{1-xy}$$

Question 12.
Princal value of tan-1 (-1) is
(a) $$\frac{π}{4}$$
(b) $$\frac{-π}{2}$$
(c) $$\frac{5π}{4}$$
(d) $$\frac{-π}{4}$$

Answer: (d) $$\frac{-π}{4}$$

Question 13.
If x + $$\frac{1}{x}$$ = 2 then the principal value of sin-1 x is x
(a) $$\frac{π}{4}$$
(b) $$\frac{π}{2}$$
(c) π
(d) $$\frac{3π}{2}$$

Answer: (d) $$\frac{3π}{2}$$

Question 14.
The principle value of sin-1(sin$$\frac{2π}{3}$$) is
(a) $$\frac{2π}{3}$$
(b) $$\frac{π}{3}$$
(c) $$\frac{-π}{6}$$
(d) $$\frac{π}{6}$$

Answer: (b) $$\frac{π}{3}$$

Question 15.
Algebraic expression for sin (cot-1 x) is
(a) $$\frac{1}{1+x^2}$$
(b) $$\frac{1}{\sqrt{1+x^2}}$$
(c) $$\frac{x}{\sqrt{1+x^2}}$$
(d) None of these

Answer: (b) $$\frac{1}{\sqrt{1+x^2}}$$

Question 16.
If y = sec-1 x then
(a) 0 ≤ y ≤ π
(b) 0 ≤ y ≤ $$\frac{π}{2}$$
(c) –$$\frac{π}{2}$$ < y < $$\frac{π}{2}$$
(d) None of these

Answer: (d) None of these

Question 17.
Princal value of cos-1($$\frac{-1}{√2}$$)
(a) $$\frac{3π}{4}$$
(b) $$\frac{5π}{4}$$
(c) –$$\frac{π}{4}$$
(d) None of these

Answer: (a) $$\frac{3π}{4}$$

Question 18.
tan-1($$\frac{x}{y}$$) – tan-1($$\frac{x-y}{x+y}$$) is equal to
(a) $$\frac{π}{3}$$
(b) $$\frac{π}{4}$$
(c) $$\frac{π}{2}$$
(d) $$\frac{-3π}{4}$$

Answer: (b) $$\frac{π}{4}$$

Question 19.
The value of x for which sin |cot-1(1 – x)| = cos (tan-1 x) is
(a) $$\frac{2}{1}$$
(b) 1
(c) 0
(d) $$\frac{1}{2}$$

Answer: (d) $$\frac{1}{2}$$

Question 20.
tan-1 √3 – sec-1(-2)
(a) π
(b) –$$\frac{π}{3}$$, 0
(c) $$\frac{π}{3}$$
(d) $$\frac{2π}{3}$$

Answer: (b) –$$\frac{π}{3}$$, 0

Question 21.
2 tan-1 $$\frac{1}{3}$$ + tan-1 $$\frac{1}{7}$$ =
(a) tan-1 $$\frac{44}{29}$$
(b) $$\frac{π}{2}$$
(c) 0
(d) $$\frac{π}{4}$$

Answer: (d) $$\frac{π}{4}$$

Question 22.
The principle value of sin-1 $$\frac{√3}{2}$$ is
(a) $$\frac{2π}{3}$$
(b) $$\frac{π}{6}$$
(c) $$\frac{π}{4}$$
(d) $$\frac{π}{3}$$

Answer: (d) $$\frac{π}{3}$$

Question 23.
Simplified form of cos-1 (4x3 – 3x)
(a) 3 sin-1x
(b) 3 cos-1x
(c) π – 3 sin-1x
(d) None of these

Answer: (b) 3 cos-1x

Question 24.
The value of tan(tan-1 $$\frac{4}{5}$$ + tan-1 $$\frac{2}{3}$$) is
(a) $$\frac{6}{17}$$
(b) $$\frac{7}{16}$$
(c) $$\frac{17}{6}$$
(d) None of these

Answer: (d) None of these

Question 25.
Which of the following is the principal value branch of cos-1 x?
(a) [$$\frac{-π}{2}$$, $$\frac{π}{2}$$]
(b) (0, π)
(c) (0, π)
(d) (0, π) – {$$\frac{π}{2}$$}

Answer: (c) (0, π)

Question 26.
If 3 tan-1 x + cot-1 x = π, then x equals
(a) 0
(b) 1
(c) -1
(d) $$\frac{1}{2}$$

Question 27.
The value of cos-1[cos($$\frac{33π}{5}$$)] is
(a) $$\frac{3π}{5}$$
(b) $$\frac{-3π}{5}$$
(c) $$\frac{π}{10}$$
(d) –$$\frac{-π}{10}$$

Answer: (a) $$\frac{3π}{5}$$

Question 28.
If cos(sin-1$$\frac{2}{5}$$ + cos-1 x) = 0 then x is equal to
(a) $$\frac{1}{5}$$
(b) $$\frac{2}{5}$$
(c) 0
(d) 1

Answer: (b) $$\frac{2}{5}$$

Question 29.
The value of sin (2 tan-1 (.75)) is equal to
(a) .75
(b) 1.5
(c) .96
(d) sin 1.5

Question 30.
4 tan-1 $$\frac{1}{5}$$ – tan-1 $$\frac{1}{70}$$ + tan-1 $$\frac{1}{99}$$ is equal to
(a) $$\frac{π}{6}$$
(b) $$\frac{π}{4}$$
(c) $$\frac{π}{3}$$
(d) $$\frac{π}{2}$$

Answer: (b) $$\frac{π}{4}$$

Question 31.
cos-1 ($$\frac{-1}{2}$$) + 2sin-1 ($$\frac{-1}{2}$$)
(a) $$\frac{π}{3}$$
(b) $$\frac{2π}{3}$$
(c) $$\frac{3π}{4}$$
(d) $$\frac{5π}{8}$$

Answer: (a) $$\frac{π}{3}$$

Question 32.
tan-1 (√3) + sec-1 (-2) – cosec-1 ($$\frac{2}{√3}$$)
(a) $$\frac{5π}{6}$$
(b) $$\frac{2π}{3}$$
(c) $$\frac{π}{3}$$
(d) 0

Question 33.
Number of solutions of the equation
tan-1 ($$\frac{1}{2x+1}$$) + tan-1 ($$\frac{1}{4x+1}$$) = tan-1 ($$\frac{2}{x^2}$$)
(a) 1
(b) 2
(c) 3
(d) 4

Question .34
sec-1(2)
(a) $$\frac{π}{6}$$
(b) $$\frac{π}{3}$$
(c) $$\frac{2π}{3}$$
(d) $$\frac{5π}{6}$$

Answer: (b) $$\frac{π}{3}$$

Question 35.
cot-1(-√3)
(a) $$\frac{5π}{6}$$
(b) $$\frac{π}{3}$$
(c) $$\frac{π}{2}$$
(d) $$\frac{π}{4}$$

Answer: (a) $$\frac{5π}{6}$$

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