Trigonometric Ratios & Identities PYQs Set 7 (PDF)

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Set 7 of 18 · Questions 181-210 of 519

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Mere Teacher · Previous Year Questions JEE Main Mathematics · Trigonometric Ratios & Identities · Set 7 (Q181-210)
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181. $\frac{cos 13 ^{\circ} - sin 13 ^{\circ}}{cos 13 ^{\circ} + sin 13 ^{\circ}} + \frac{1}{cot 148 ^{\circ}} is equal to$ (1) $1$ (2) $-1$ (3) $0$ (4) $\frac{1}{2}$ 182. $In a triangle ABC, if b = 7, c = 43 and A = \frac{π}{6} then a sin Bsin C =$ (1) $\frac{13}{12}$ (2) $\frac{13}{7 3}$ (3) $\frac{12}{13}$ (4) $\frac{7 3}{13}$ 183. $If sec θ = m and tan θ = n, then \frac{1}{m} ((m + n) + \frac{1}{( m + n )}) =$ (1) $2$ (2) $2 m$ (3) $2 n$ (4) $mn$ 184. $\frac{1 - tan ^{2} 15 ^{\circ}}{1 + tan ^{2} 15 ^{\circ}} is equal to$ (1) $1$ (2) $3$ (3) $\frac{3}{2}$ (4) $2$ 185. $If 0 \leq x < 2π, then the number of real values of x, which satisfy the equation cosx + cos2x + cos3x + cos4x = 0, is$ (1) $5$ (2) $7$ (3) $9$ (4) $3$ 186. $If a, b and c are the sides of △ ABC for which r_{1} = 8, r_{2} = 12 and r_{3} = 24, then the ordered triad (a, b, c) =$ (1) $(12, 20, 16)$ (2) $(12, 16, 20)$ (3) $(16, 12, 20)$ (4) $(20, 16, 12)$ 187. $In a triangle A B C, if cos A cos B + sin A sin B sin C = 1, then sin A + sin B + sin C =$ (1) $\frac{2 + 3}{2}$ (2) $1 + 2$ (3) $\frac{2 3 - 1}{2}$ (4) $\frac{3 + 3}{2}$ 188. $If - 1 is a twice repeated root of the equation a x^{3} + a x^{2} + b x + c = 0, then a : b : c =$ (1) $: - 1 : 1$ (2) $- 1 : 1 : 1$ (3) $1 : 1 : - 1$ (4) $1 : 1 : 1$ 189. $cos (2 sin^{- 1} \frac{3}{4} + cos^{- 1} \frac{3}{4}) =$ (1) $\frac{- 3}{4}$ (2) $\frac{3}{5}$ (3) $\frac{3}{4}$ (4) $does not exist$ 190. $If \frac{1}{sin 45 ^{\circ} sin 46 ^{\circ}} + \frac{1}{sin 46 ^{\circ} sin 47 ^{\circ}} + \dots . upto 45 terms = \frac{1}{sin x ^{\circ}}, then sin (\frac{π}{2} x) =$ (1) $0$ (2) $sin 1$ (3) $1$ (4) $cos 1$ 191. $Let P = {θ : sin θ - cos θ = 2 cos θ} and Q = {θ : sin θ + cos θ = 2 sin θ} be two sets. Then$ (1) $P \subset Q and Q - P \neq \emptyset$ (2) $Q \subset P$ (3) $P \subset Q$ (4) $P = Q$ 192. $Internal bisector of ∠A of triangle ABC meets side BC at D. A line drawn through D perpendicular to AD intersects the side AC at E and the side AB at F. If a, b, c represent sides of ΔABC, the$ (1) $AE is HM of b and c$ (2) $AD = \frac{2 b c}{b + c} cos \frac{A}{2}$ (3) $EF = \frac{4 b c}{b + c} sin \frac{A}{2}$ (4) $the triangle AEF is isosceles$ 193. $If one solution of the equation cosh x - \frac{4}{5} sin hx = 1 is x = 0, then the other solution is x =$ (1) $2 log 2$ (2) $2 log 5$ (3) $log (\frac{4}{3})$ (4) $2 log 3$ 194. $If sin x + sin y = \frac{1}{2} and cos x + cos y = 1, then tan (x + y) =$ (1) $- \frac{3}{4}$ (2) $\frac{4}{3}$ (3) $\frac{8}{3}$ (4) $\frac{- 8}{3}$ 195. $In a triangle ABC, a [b cos C - c cos B] =$ (1) $0$ (2) $b^{2} - c^{2}$ (3) $a^{2}$ (4) $b^{2}$ 196. $Let P = {θ : sinθ - cosθ = 2 cosθ} and Q = {θ : sinθ + cosθ = 2 sinθ} be two sets. Then, [JEE (Main) 2016]$ (1) $Q ⊄ P$ (2) $P ⊄ Q$ (3) $P \subset Q and Q-P\neqϕ$ (4) $P = Q$ 197. $In △ ABC, if a sin^{2} \frac{C}{2} + c sin^{2} \frac{A}{2} = \frac{b}{2}, then a + c : b =$ (1) $2 : 1$ (2) $1 : 2$ (3) $3 : 2$ (4) $4 : 3$ 198. $Which of the following equation has no solution?$ (1) $sec θ = 23$ (2) $cos θ = 2$ (3) $tan θ = 2019$ (4) $sin θ = - \frac{1}{5}$ 199. $Let α and β be two real roots of the (k + 1) tan^{2} x - 2 \cdot λ tan x = (1 - k) where k (\neq = - 1) and λ are real numbers. If tan^{2} (α + β) = 50 then a value of λ is:$ (1) $10$ (2) $5$ (3) $7$ (4) $12$ 200. $If \frac{5 sinh 2 x}{7 + 6 cosh 2 x} = \frac{3}{2}, then 3 tan h^{2} x + 20 tan hx =$ (1) $13$ (2) $26$ (3) $39$ (4) $\frac{13}{2}$ 201. $In a ΔPQR, if 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P = 1, then the angle R is equal to$ (1) $\frac{5 π}{6}$ (2) $\frac{π}{6}$ (3) $\frac{π}{4}$ (4) $\frac{3 π}{4}$ 202. $If tan 15° + \frac{1}{tan 75°} + \frac{1}{tan 105°} + tan 195° = 2 a then the value of (a + \frac{1}{a}) is$ (1) $4$ (2) $4 - 23$ (3) $2$ (4) $5 - \frac{3}{2} 3$ 203. $The value of tan (\frac{7 π}{8}) is$ (1) $2 - 1$ (2) $1 - 2$ (3) $1 + 2$ (4) $\frac{1}{1 + 2}$ 204. $The minimum value of 27^{cos 2 x} 81^{sin 2 x} is$ (1) $\frac{1}{243}$ (2) $\frac{1}{27}$ (3) $-5$ (4) $1/5$ 205. $Let f_{k} (x) = \frac{1}{k} (sinkx + coskx) where x \in R and k \geq 1. Then f_{4} (x) - f_{6} (x) equals$ (1) $\frac{1}{4}$ (2) $\frac{1}{12}$ (3) $\frac{1}{6}$ (4) $\frac{1}{3}$ 206. $\frac{1 - cos 2 θ + sin 2 θ}{1 + cos 2 θ + sin 2 θ} is equal to$ (1) $cot θ$ (2) $cos 2 θ$ (3) $tan θ$ (4) $tan 2 θ$ 207. $If α and β are roots of the equation x^{2} + 5 \| x \| - 6 = 0 then the value of (tan^{- 1} α - tan^{- 1} β) is$ (1) $\frac{π}{2}$ (2) $0$ (3) $π$ (4) $\frac{π}{4}$ 208. $The equation sin^{4} x - (K + 3) sin^{2} x - K - 4 = 0 has a solution if$ (1) $K > 4$ (2) $-4\leqK\leq-3$ (3) $K is any positive integer$ (4) $K = 0$ 209. $For some a, b, c \in R, if sin 5 θ = a cos^{4} θsin θ + b cos^{2} θ sin^{3} θ + c sin^{5} θ, then abc =$ (1) $-10$ (2) $10$ (3) $0$ (4) $-50$ 210. $If f^{’} (x) = tan^{- 1} (sec x + tan x), - \frac{π}{2} < x < \frac{π}{2} and f (0) = 0, then f (1) is$ (1) $\frac{π + 1}{4}$ (2) $\frac{π + 2}{4}$ (3) $π + \frac{1}{4}$ (4) $\frac{π - 1}{4}$