Trigonometric Ratios & Identities PYQs Set 5 (PDF)

Back to Trigonometric Ratios & Identities

Set 5 of 18 · Questions 121-150 of 519

In the print window choose “Save as PDF”. The file prints without a web address or date line.

Mere Teacher · Previous Year Questions JEE Main Mathematics · Trigonometric Ratios & Identities · Set 5 (Q121-150)
Scan or visit mereteacher.com for free PYQ practice, timed CBT tests, step-by-step solutions and BroBot AI. Answers and solutions are free with a sign-up.
121. $If cos h 2 x = 241, then cot hx is equal to$ (1) $\frac{7}{30}$ (2) $\frac{11}{30}$ (3) $\frac{7}{2 30}$ (4) $\frac{11}{2 30}$ 122. $If 4 + 6 (e^{2 x} + 1) tanh x = 11 cosh x + 11 sinh x, then x =$ (1) $log 10$ (2) $log 4$ (3) $log 5$ (4) $log 2$ 123. $If sin xcos hy = cos θ, cos xsin hy = sin θ and 4 tan x = 3 . Then, sin h^{2} y =$ (1) $\frac{4}{5}$ (2) $\frac{9}{16}$ (3) $\frac{9}{25}$ (4) $\frac{16}{25}$ 124. $If 10 sin^{4} θ + 15 cos^{4} θ = 6, then the value of \frac{27 cosec ^{6} θ + 8 sec ^{6} θ}{16 sec ^{8} θ} is$ (1) $\frac{2}{5}$ (2) $\frac{3}{5}$ (3) $\frac{1}{5}$ (4) $\frac{3}{4}$ 125. $If tan^{- 1} x + tan^{- 1} y = \frac{4 π}{5}, then cot^{- 1} x + cot^{- 1} y is equal to$ (1) $\frac{π}{5}$ (2) $\frac{3 π}{5}$ (3) $\frac{2 π}{5}$ (4) $π$ 126. $If d_{1}, d_{2}, d_{3} are the diameters of three ex-circles of a △ ABC, then d_{1} d_{2} + d_{2} d_{3} + d_{3} d_{1} =$ (1) $(a + b + c)^{2}$ (2) $ab + bc + ca$ (3) $4 Δ^{2}$ (4) $2 s^{2}$ 127. $sin 20^{\circ} \cdot sin 40^{\circ} \cdot sin 60^{\circ} \cdot sin 80^{\circ} is equal to$ (1) $\frac{- 3}{16}$ (2) $\frac{5}{16}$ (3) $\frac{3}{16}$ (4) $\frac{- 5}{16}$ 128. $In a triangle ABC, 2 (bc cos A + ac cos B + ab cos C) =$ (1) $a + b + c$ (2) $2 (a + b + c)$ (3) $a^{2} + b^{2} + c^{2}$ (4) $2 a^{2} + b^{2} + c^{2}$ 129. $For any real number n \in R, (cosh x + sinh x)^{n} =$ (1) $cosh nx - sinh nx$ (2) $cosh nx + sinh nx$ (3) $cosh^{2} nx + 2 sinh nx$ (4) $2coshnx-sinhnx$ 130. $The value of sin^{2} 51^{\circ} + sin^{2} 39^{\circ} is$ (1) $0$ (2) $sin 12^{\circ}$ (3) $cos 12^{\circ}$ (4) $1$ 131. $The common solution set of the equations 2 sin^{2} x + sin^{2} 2 x = 2 and sin 2 x + cos 2 x = tan x is$ (1) $(x \in R : x = (2 n + 1) \frac{π}{4}, n \in Z)$ (2) $(x \in R : x = (3 n + 1) \frac{π}{4}, n \in Z)$ (3) $(x \in R : x = (4 n + 1) \frac{π}{8}, n \in Z)$ (4) $(x \in R : x = (4 n - 1) \frac{π}{8}, n \in Z)$ 132. $In triangle ABC, if BC is the hypotenuse, then r_{2} + r_{3} =$ (1) $r_{1} + r$ (2) $a$ (3) $r - r_{1}$ (4) $2 (R + r)$ 133. $If x + \frac{1}{x} = 2 cos θ, then x^{6} + x^{- 6} =$ (1) $2 cos 6 θ$ (2) $2 cos 12 θ$ (3) $2 cos 3 θ$ (4) $2 sin 3 θ$ 134. $The value of cos^{4} x is$ (1) $\frac{3}{8} + \frac{1}{2} cos 2 x + \frac{1}{8} cos 4 x$ (2) $\frac{3}{8} - \frac{1}{2} cos 2 x + \frac{1}{8} cos 4 x$ (3) $\frac{3}{8} - \frac{1}{8} cos 4 x + \frac{1}{2} cos 2 x$ (4) $\frac{1}{8} cos 4 x + \frac{1}{2} cos 2 x - \frac{3}{8}$ 135. $I f \frac{cos ( θ _{1} + θ _{2} )}{cos ( θ _{1} - θ _{2} )} + \frac{cos ( θ _{3} - θ _{4} )}{cos ( θ _{3} + θ _{4} )} = 0, then cot θ_{1} \cdot co t θ_{2} cot θ_{3} \cdot cot θ_{4} =$ (1) $1$ (2) $-1$ (3) $2$ (4) $1/2$ 136. $\frac{1 - cos ( 2 x ) + sin ( x )}{sin ( 2 x ) + cos ( x )} =$ (1) $sin (x)$ (2) $cos (x)$ (3) $tan (x)$ (4) $cosec (x)$ 137. $If sin hx = \frac{- 1}{2} then tan h 2 x =$ (1) $\frac{- 5}{2}$ (2) $- 3$ (3) $\frac{- 5}{3}$ (4) $\frac{- 3}{2}$ 138. $The value of cos 1200^{\circ} + tan 1485^{\circ} is$ (1) $\frac{1}{2}$ (2) $\frac{3}{2}$ (3) $- \frac{3}{2}$ (4) $- \frac{1}{2}$ 139. $cot 12^{\circ} cot 102^{\circ} + cot 102^{\circ} cot 66^{\circ} + cot 66^{\circ} cot 12^{\circ} =$ (1) $1$ (2) $-2$ (3) $2$ (4) $-1$ 140. $3 (sin x - cos x)^{4} + 6 (sin x + cos x)^{2} + 4 (sin^{6} x + cos^{6} x) =$ (1) $14$ (2) $11$ (3) $12$ (4) $13$ 141. $Let y = 4 sin^{2} θ - cos 2 θ . If l and m are the minimum and maximum values of y respectively, then$ (1) $lm = \frac{m}{l}$ (2) $lm = \frac{l}{m}$ (3) $l + m = \frac{l}{m}$ (4) $\frac{lm}{l - m} = 1 + m$ 142. $If tan^{- 1} x = \frac{π}{4} - tan^{- 1} (\frac{1}{3}), then x is$ (1) $\frac{1}{3}$ (2) $\frac{1}{2}$ (3) $\frac{1}{4}$ (4) $\frac{1}{6}$ 143. $If cos^{- 1} x = α, (0 < x < 1) and sin^{- 1} (2 x 1 - x^{2}) + sec^{- 1} (\frac{1}{2 x ^{2} - 1}) = \frac{2 π}{3}, then tan^{- 1} (2 x) equals$ (1) $π /6$ (2) $π /4$ (3) $π /3$ (4) $π /2$ 144. $In a triangle ABC, if a \neq = b, \frac{a cos A - b cos B}{a cos B - b cos A} + cos C =$ (1) $0$ (2) $1$ (3) $2$ (4) $-1$ 145. $Let f_{k} (x) = \frac{1}{k} (sin^{k} x + cos^{k} x) where x \in R and k \geq 1 . Then, f_{4} (x) - f_{6} (x) equals [JEE Main) 2014]$ (1) $\frac{1}{4}$ (2) $\frac{1}{12}$ (3) $\frac{1}{6}$ (4) $\frac{1}{3}$ 146. $The value of 2 sin (\frac{π}{8}) sin (\frac{2 π}{8}) sin (\frac{3 π}{8}) sin (\frac{5 π}{8}) sin (\frac{6 π}{8}) sin (\frac{7 π}{8}) is:$ (1) $\frac{1}{4 2}$ (2) $\frac{1}{4}$ (3) $\frac{1}{8}$ (4) $\frac{1}{8 2}$ 147. $If 4 cos x + 3 sin x = 5, then find the value of tan x =$ (1) $\frac{3}{4}$ (2) $\frac{4}{3}$ (3) $\frac{- 3}{4}$ (4) $\frac{- 4}{3}$ 148. $If a > b > 0, then the value of tan^{- 1} (\frac{a}{b}) + tan^{- 1} (\frac{a + b}{a - b}) depends on$ (1) $both a and b$ (2) $a and not b$ (3) $b and not a$ (4) $neither a nor b$ 149. $If s i n^{2} (1 0^{°}) s in (2 0^{°}) s in (4 0^{°}) s in (5 0^{°}) s in (7 0^{°}) = α \frac{1}{16} sin(10°), then 16 + α^{- 1} is equal to__________$ 150. $If \frac{cos ^{2} 48 ^{\circ} - sin ^{2} 12 ^{\circ}}{sin ^{2} 24 ^{\circ} - sin ^{2} 6 ^{\circ}} = \frac{α + β 5}{2}, where α, β \in N, then α + β is equal to____$