Trigonometric Ratios & Identities PYQs Set 18 (PDF)

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Set 18 of 18 · Questions 511-519 of 519

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Mere Teacher · Previous Year Questions JEE Main Mathematics · Trigonometric Ratios & Identities · Set 18 (Q511-519)
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511. $In △ ABC, if the sides a, b, c are in geometric progression and the largest angle exceeds the smallest angle by 60^{\circ}, then cos B is equal to$ (1) $\frac{13 + 1}{4}$ (2) $\frac{1 - 13}{4}$ (3) $1$ (4) $\frac{13 - 1}{4}$ 512. $If f (x) = cos^{2} x + cos^{2} 2 x + cos^{2} 3 x, then the number of values of x \in [0, 2 π] for which f (x) = 1 is$ (1) $4$ (2) $6$ (3) $8$ (4) $10$ 513. $The value of cos (sin^{- 1} \frac{π}{3} + cos^{- 1} \frac{π}{3})$ (1) $1$ (2) $-1$ (3) $Does not exist$ (4) $0$ 514. $In a △ ABC, if a = 3, b = 4 and sin A = \frac{3}{4}, then ∠ CBA is equal to$ (1) $60^{\circ}$ (2) $75^{\circ}$ (3) $90^{\circ}$ (4) $45^{\circ}$ 515. $In a triangle ABC, \frac{a}{b} = 2 + 3 and ∠ C = 60^{\circ} . Then the measure of ∠ A is$ (1) $95^{\circ}$ (2) $65^{\circ}$ (3) $105^{\circ}$ (4) $115^{\circ}$ 516. $In △ ABC, if a : b : c = 4 : 5 : 6, then the ratio of the circumradius to its inradius is$ (1) $16 : 7$ (2) $7 : 16$ (3) $4 : 5$ (4) $5 : 4$ 517. $In △ ABC, ∠ B = \frac{π}{4} and ∠ C = \frac{π}{3} . If the area of the triangle is 54 + 183 sq units, then a is equal to$ (1) $3 + 1$ (2) $2 (3 + 1)$ (3) $4 (3 + 1)$ (4) $6 (3 + 1)$ 518. $In a △ A B C, with usual notation, match the items in List-I with the items in List-II and choose the correct option, List-I (A) r_{1} r_{2} (\frac{4 R - r _{1} - r _{2}}{r _{1} + r _{2}}) (B) \frac{r _{2} ( r _{3} + r _{1} )}{r _{1} r _{2} + r _{2} r _{3} + r _{3} r _{1}} (C) \frac{a}{c} = \frac{s i n ( A - B )}{s i n ( B - C )} (D) b c cos^{2} \frac{A}{2} List-II 1. b 2. a^{2}, b^{2}, c^{2} are in A P 3. Δ 4. R r_{1} r_{2} r_{3} 5. s (s - a) A B C D$ (1) $4 3 1 5$ (2) $5 4 3 2$ (3) $3 1 2 5$ (4) $4 5 2 1$ 519. $In a △ A B C, let a, b, c, s, r, R, I, S, r_{1}, r_{2}, r_{3} stand for their usual meaning. Then Match the items of List-I with those of the items of List-II. List-I A. tan \frac{A}{2} = \frac{r}{s - a} B. r C. (S I)^{2} + 2 R r D. r_{1}^{2} + r_{2}^{2} + r_{3}^{2} List-II I. (A I) (\frac{( s - b ) ( s - c )}{b c}) II. R^{2} III. (4 R + r + 2 s) (4 R + r - 2 s) IV. \frac{R r}{S} V. \frac{( s - b ) ( s - c )}{Δ} The correct match is A B C D$ (1) $I V IV III$ (2) $V I II III$ (3) $V I IV III$ (4) $I IV III II$