Inverse Trigonometric Functions PYQs Set 6 (PDF)

Set 6 of 6 · Questions 151-152 of 152

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Mere Teacher · Previous Year Questions JEE Main Mathematics · Inverse Trigonometric Functions · Set 6 (Q151-152)
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151. $Let Z denote the set of integers. Then match the items in list-I, with those of the items in list-II. List-I (A) sin^{- 1} (\frac{2 2}{3}) + sin^{- 1} \frac{1}{3} (B) sin^{- 1} (\frac{( - 1 ) ^{n}}{2}) = x, n \in Z (C) tan^{- 1} (sec \frac{π}{4} + tan \frac{π}{4}) (D) sin^{- 1} ∣ sin x ∣ = sin^{- 1} ∣ sin x ∣, x \in List-II (I) nπ \pm (- 1)^{n} \frac{π}{6} (II) nπ \pm 1, n \in Z (III) \frac{3}{2} (IV) \frac{3 π}{8} (V) \frac{π}{2} The correct match is A B C D$ (1) $V I III II$ (2) $IV II V I$ (3) $V I IV II$ (4) $IV II V III$ 152. $The number of real solutions of the equation sin^{- 1} (\sum_{i = 1}^{\infty} x^{i + 1} - x \sum_{i = 1}^{\infty} (\frac{x}{2})^{i}) = \frac{π}{2} - cos^{- 1} (\sum_{i = 1}^{\infty} (- \frac{x}{2})^{i} - \sum_{i = 1}^{\infty} (- x)^{i}) lying in the interval (- \frac{1}{2}, \frac{1}{2}) is ____. (Here, the inverse trigonometric functions sin^{- 1} x and cos^{- 1} x assume values in [- \frac{π}{2}, \frac{π}{2}] and [0, π], respectively). (JEE Advanced 2018)$