Trigonometric Ratios & Identities PYQs Set 4 (PDF)

Back to Trigonometric Ratios & Identities

Set 4 of 18 · Questions 91-120 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 4 (Q91-120)
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.
91. $sin^{4} x + 4 cos^{2} x - cos^{4} x + 4 sin^{2} x =$ (1) $1 - cos 2 x$ (2) $tan 2 x$ (3) $sin 2 x$ (4) $cos 2 x$ 92. $Let a and b be non-negative real numbers. If sin x + acos x = b, then \| asin x - cos x \| =$ (1) $a^{2} - b^{2} + 1$ (2) $b^{2} - a^{2} + 1$ (3) $1 + a^{2} + b^{2}$ (4) $a^{2} + b^{2} - 1$ 93. $If the identity cos^{4} θ = acos 4 θ + bcos 2 θ + c holds for some a, b, c \in Q, then (a, b, c) =$ (1) $(\frac{1}{8}, \frac{3}{8}, \frac{1}{2})$ (2) $(\frac{1}{8}, \frac{1}{2}, \frac{3}{8})$ (3) $(\frac{1}{2}, \frac{1}{8}, \frac{3}{8})$ (4) $(\frac{1}{2}, \frac{3}{8}, \frac{1}{8})$ 94. $△ ABC, if \frac{cos A}{a} = \frac{cos B}{b} = \frac{cos C}{c} and side a = 2, then area of the △ ABC (in sq. units) is$ (1) $82$ (2) $43$ (3) $\frac{3}{2}$ (4) $3$ 95. $In the triangle ABC, if a = 7, b = 6 and A = 120^{\circ}, then the approximate value of B is$ (1) $47.9^{\circ}$ (2) $44.9^{\circ}$ (3) $59.9^{\circ}$ (4) $61.9^{\circ}$ 96. $cos (cot^{- 1} (- 3) + \frac{π}{6}) =$ (1) $0$ (2) $1$ (3) $\frac{1}{2}$ (4) $-1$ 97. $In △ ABC, \frac{1 + cos C}{r _{1} + r _{2}} + \frac{1 + cos A}{r _{2} + r _{3}} + \frac{1 + cos B}{r _{1} + r _{3}} =$ (1) $\frac{2}{3 R}$ (2) $\frac{R}{2}$ (3) $\frac{3}{2 R}$ (4) $\frac{6 R}{5}$ 98. $If θ = \frac{17 π}{3} then tan θ - cot θ =$ (1) $\frac{1}{2 3}$ (2) $\frac{- 1}{2 3}$ (3) $\frac{2}{3}$ (4) $- \frac{2}{3}$ 99. $In △ ABC, if ∠ A = 90^{\circ}, then (r_{2} - r_{1}) (r_{3} - r_{1}) =$ (1) $r_{2} r_{3}$ (2) $2 r_{2} r_{3}$ (3) $4 r_{2} r_{3}$ (4) $2$ 100. $tan^{- 1} (\frac{1}{3} sin \frac{5 π}{2}) + sin^{- 1} (cos (sin^{- 1} \frac{3}{2})) =$ (1) $0$ (2) $\frac{π}{6}$ (3) $\frac{π}{3}$ (4) $π$ 101. $The value of cot^{- 1} (\frac{1 - sin x + 1 + sin x}{1 - sin x - 1 + sin x}) where x \in (0, \frac{π}{4}) is$ (1) $π - \frac{x}{3}$ (2) $\frac{x}{2}$ (3) $π - \frac{x}{2}$ (4) $\frac{x}{2} - π$ 102. $The value of 2 sin^{- 1} (\frac{1}{2}) + cot^{- 1} (\frac{1}{3}) is$ (1) $2 π /3$ (2) $π /4$ (3) $π /6$ (4) $π /3$ 103. $\frac{sin x}{1 + cos x} + \frac{1 + cos x}{sin x} =$ (1) $2 sec x$ (2) $2 cosec x$ (3) $tan 2 x$ (4) $sin 2 x$ 104. $sin (2 sin^{- 1} \frac{63}{65}) =$ (1) $\frac{8 63}{65}$ (2) $\frac{63}{65}$ (3) $\frac{2 126}{65}$ (4) $\frac{4 65}{65}$ 105. $If a > b > 0, sec^{- 1} (\frac{a + b}{a - b}) = 2 sin^{- 1} x, then x =$ (1) $\frac{b}{a + b}$ (2) $- \frac{b}{a + b}$ (3) $\frac{a}{a + b}$ (4) $- \frac{a}{a + b}$ 106. $If cos x + cos y = p, sin x + sin y = q, then cos (\frac{x - y}{2}) =$ (1) $\pm \frac{p ^{2} + q ^{2}}{2}$ (2) $\pm \frac{pq}{2}$ (3) $\pm (\frac{p + q}{2})$ (4) $\pm \frac{p ^{2} + q ^{2}}{4}$ 107. $If cos^{- 1} x + cos^{- 1} y + cos^{- 1} z = 3 π, then the value of x^{2025} + x^{2026} + x^{2027} is$ (1) $-1$ (2) $0$ (3) $1$ (4) $3$ 108. $If for θ \in (- \frac{π}{3}, 0), the points (x, y) = (3 tan (θ + \frac{π}{3}), 2 tan (θ + \frac{π}{6})) lie on xy + αx + βy + γ = 0, then α^{2} + β^{2} + γ^{2} is equal to:$ (1) $75$ (2) $96$ (3) $80$ (4) $72$ 109. $For α, β \in (0, \frac{π}{2}), let 3 sin (α + β) = 2 sin (α - β) and a real number k be such that tan α = ktan β . Then the value of k is equal to :$ (1) $- \frac{2}{3}$ (2) $-5$ (3) $\frac{2}{3}$ (4) $5$ 110. $\frac{cot A}{1 - tan A} + \frac{tan A}{1 - cot A} =$ (1) $tan A + cot A$ (2) $sec A + cosec A$ (3) $sin Acos A + 1$ (4) $sec Acosec A + 1$ 111. $(sin θ + cos θ) (tan θ + cot θ) =$ (1) $1$ (2) $sin θ \cdot cos θ$ (3) $sec θ \cdot cosec θ$ (4) $sec θ + cosec θ$ 112. $Considering only the principal values of inverse functions, the set A = (x \geq 0/ tan^{- 1} (2 x) + tan^{- 1} (3 x) = \frac{π}{4})$ (1) $is a singleton set$ (2) $contains more than two elements$ (3) $contains two elements$ (4) $is an empty set$ 113. $If cos α + cos β = \frac{1}{3} and sin α + sin β = \frac{1}{4}, then cos (α + β) =$ (1) $\frac{24}{25}$ (2) $\frac{7}{25}$ (3) $\frac{13}{25}$ (4) $\frac{12}{13}$ 114. $If tan 20^{\circ} = λ, then \frac{tan 160 ^{\circ} - tan 110 ^{\circ}}{1 + ( tan 160 ^{\circ} ) ( tan 110 ^{\circ} )} =$ (1) $\frac{1 + λ ^{2}}{2 λ}$ (2) $\frac{1 + λ ^{2}}{λ}$ (3) $\frac{1 - λ ^{2}}{λ}$ (4) $\frac{1 - λ ^{2}}{2 λ}$ 115. $If 3 tan^{- 1} x + cot^{- 1} x = π then x equal to$ (1) $0$ (2) $1$ (3) $-1$ (4) $\frac{1}{2}$ 116. $The value of cosec 10^{\circ} - 3 sec 10^{\circ} is equal to:$ (1) $8$ (2) $6$ (3) $2$ (4) $4$ 117. $If sin θ + cos θ = p and tan θ + cot θ = q, then q (p^{2} - 1) is equal to$ (1) $\frac{1}{2}$ (2) $2$ (3) $1$ (4) $3$ 118. $The number of principal solutions of tan 2 θ = 1 is$ (1) $One$ (2) $Two$ (3) $Three$ (4) $Four$ 119. $If \frac{sin ^{4} x}{2} + \frac{cos ^{4} x}{3} = \frac{1}{5}, then [JEE (Main) 2009]$ (1) $tan^{2} x = \frac{2}{3}$ (2) $\frac{sin ^{8} x}{8} + \frac{cos ^{8} x}{27} = \frac{1}{125}$ (3) $tan^{2} x = \frac{1}{3}$ (4) $\frac{sin ^{8} x}{8} + \frac{cos ^{8} x}{27} = \frac{2}{125}$ 120. $The function f (x) = 3 sin 2 x - cos 2 x + 4 is one-one in the interval$ (1) $(\frac{- π}{6}, \frac{π}{3})$ (2) $(\frac{π}{6}, \frac{- π}{3})$ (3) $(\frac{- π}{2}, \frac{π}{2})$ (4) $(\frac{- π}{6}, \frac{- π}{3})$