AP EAMCET (EAPCET) Mathematic Multiple Choice Questions (MCQs)
AP EAMCET Trigonometry MCQs with Answers
AP EAMCET Mathematics - Trigonometry MCQs with Answers
131. The hyperbolic sine function is defined as:
a) \( \sinh x = \frac{e^x + e^{-x}}{2} \)
b) \( \sinh x = \frac{e^x - e^{-x}}{2} (Answer)
c) \( \sinh x = e^x + e^{-x} \)
d) \( \sinh x = e^x - e^{-x} \)
132. Which of the following is the correct graph of the hyperbolic sine function, \( \sinh x \)?
a) A symmetric curve with respect to the y-axis
b) An increasing curve with respect to x
c) A curve passing through the origin and becoming steeper as \( |x| \) increases (Answer)
d) A curve with asymptotes at \( y = \pm 1 \)
133. The inverse hyperbolic sine function, \( \sinh^{-1}(x) \), is defined as:
a) \( \sinh^{-1}(x) = \ln(x + \sqrt{x^2 + 1}) (Answer)
b) \( \sinh^{-1}(x) = \ln(x + \sqrt{1 - x^2}) \)
c) \( \sinh^{-1}(x) = \sqrt{x^2 + 1} \)
d) \( \sinh^{-1}(x) = \sqrt{1 - x^2} \)
134. Which of the following is the correct graph of the inverse hyperbolic sine function, \( \sinh^{-1}(x) \)?
a) A horizontal line
b) A curve passing through the origin, increasing without bound (Answer)
c) A curve with vertical asymptotes
d) A straight line passing through the origin
135. The hyperbolic cosine function is defined as:
a) \( \cosh x = \frac{e^x + e^{-x}}{2} (Answer)
b) \( \cosh x = \frac{e^x - e^{-x}}{2} \)
c) \( \cosh x = e^x + e^{-x} \)
d) \( \cosh x = e^x - e^{-x} \)
136. Which of the following properties is true for the hyperbolic cosine function, \( \cosh x \)?
a) It is an odd function
b) It is an even function (Answer)
c) It is a periodic function
d) It is always negative
137. The inverse hyperbolic cosine function, \( \cosh^{-1}(x) \), is defined as:
a) \( \cosh^{-1}(x) = \ln(x + \sqrt{x^2 - 1}) (Answer)
b) \( \cosh^{-1}(x) = \ln(x + \sqrt{1 - x^2}) \)
c) \( \cosh^{-1}(x) = \sqrt{x^2 + 1} \)
d) \( \cosh^{-1}(x) = \sqrt{1 - x^2} \)
138. The addition formula for the hyperbolic sine function is:
a) \( \sinh(A + B) = \sinh A + \sinh B \)
b) \( \sinh(A + B) = \sinh A \cdot \sinh B \)
c) \( \sinh(A + B) = \sinh A \cdot \cosh B + \cosh A \cdot \sinh B (Answer)
d) \( \sinh(A + B) = \cosh A + \cosh B \)
139. The inverse hyperbolic cosine function, \( \cosh^{-1}(x) \), has a range of:
a) \( [0, \infty) \)
b) \( [1, \infty) (Answer)
c) \( (-\infty, \infty) \)
d) \( (-1, 1) \)
140. Which of the following is the correct addition formula for the hyperbolic cosine function?
a) \( \cosh(A + B) = \cosh A \cdot \cosh B + \sinh A \cdot \sinh B (Answer)
b) \( \cosh(A + B) = \cosh A + \cosh B \)
c) \( \cosh(A + B) = \cosh A \cdot \cosh B - \sinh A \cdot \sinh B \)
d) \( \cosh(A + B) = \cosh A + \sinh B \)
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