AP EAMCET (EAPCET) Mathematic Multiple Choice Questions (MCQs)

121. Which of the following is the correct range of the inverse sine function, \( \sin^{-1}(x) \)?

• a) \( -\pi/2 \leq x \leq \pi/2 \)
• b) \( 0 \leq x \leq \pi \)
• c) \( -\pi/2 \leq x \leq \pi/2 \)
• d) \( 0 \leq x \leq \pi/2 \)

Answer: c) \( -\pi/2 \leq x \leq \pi/2 \)

122. Which of the following is the domain of the inverse cosine function, \( \cos^{-1}(x) \)?

• a) \( -1 \leq x \leq 1 \)
• b) \( 0 \leq x \leq 1 \)
• c) \( -1 \leq x \leq 0 \)
• d) \( -\infty \leq x \leq \infty \)

Answer: a) \( -1 \leq x \leq 1 \)

123. The range of the inverse tangent function, \( \tan^{-1}(x) \), is:

• a) \( -\pi/2 \leq x \leq \pi/2 \)
• b) \( 0 \leq x \leq \pi \)
• c) \( -\pi/4 \leq x \leq \pi/4 \)
• d) \( -\pi/2 \leq x \leq \pi/2 \)

Answer: d) \( -\pi/2 \leq x \leq \pi/2 \)

124. Which of the following inverse trigonometric functions has a range of \( [0, \pi] \)?

• a) \( \sin^{-1}(x) \)
• b) \( \cos^{-1}(x) \)
• c) \( \tan^{-1}(x) \)
• d) \( \cot^{-1}(x) \)

Answer: b) \( \cos^{-1}(x) \)

125. What is the correct graph of the function \( y = \sin^{-1}(x) \)?

• a) A decreasing curve starting at \( (-1, -\pi/2) \) and ending at \( (1, \pi/2) \)
• b) An increasing curve starting at \( (0, -\pi/2) \) and ending at \( (1, \pi/2) \)
• c) A curve starting at \( (-1, 0) \) and ending at \( (1, 0) \)
• d) A curve starting at \( (-1, -1) \) and ending at \( (1, 1) \)

Answer: a) A decreasing curve starting at \( (-1, -\pi/2) \) and ending at \( (1, \pi/2) \)

126. The inverse trigonometric function \( \tan^{-1}(x) \) is used to find:

• a) The angle whose sine is \( x \)
• b) The angle whose cosine is \( x \)
• c) The angle whose tangent is \( x \)
• d) The angle whose cotangent is \( x \)

Answer: c) The angle whose tangent is \( x \)

127. Which of the following identities is true for inverse trigonometric functions?

• a) \( \sin^{-1}(\sin x) = x \)
• b) \( \cos^{-1}(\cos x) = x \)
• c) \( \tan^{-1}(\tan x) = x \)
• d) All of the above

Answer: d) All of the above

128. The derivative of \( y = \sin^{-1}(x) \) with respect to \( x \) is:

• a) \( \frac{1}{\sqrt{1 - x^2}} \)
• b) \( \frac{1}{\sqrt{x^2 + 1}} \)
• c) \( \frac{1}{x\sqrt{1 - x^2}} \)
• d) \( \frac{1}{\sqrt{x^2 + 1}} \)

Answer: a) \( \frac{1}{\sqrt{1 - x^2}} \)

129. Which of the following properties is true for the inverse tangent function \( \tan^{-1}(x) \)?

• a) \( \tan^{-1}(-x) = -\tan^{-1}(x) \)
• b) \( \tan^{-1}(-x) = \tan^{-1}(x) \)
• c) \( \tan^{-1}(-x) = \tan^{-1}(-x) \)
• d) \( \tan^{-1}(-x) = x \)

Answer: a) \( \tan^{-1}(-x) = -\tan^{-1}(x) \)

130. Which of the following is the correct range for the inverse cotangent function, \( \cot^{-1}(x) \)?

• a) \( (0, \pi) \)
• b) \( (0, 2\pi) \)
• c) \( (-\pi, \pi) \)
• d) \( (-\pi/2, \pi/2) \)

Answer: a) \( (0, \pi) \)