01Easy7×since 2019Q5626If 0 ≤\le≤ x < π2{\pi \over 2}2π, then the number of values of x for which sin x −-− sin 2x + sin 3x = 0, is :A3B1C4D2Check answerSkip
02Medium7×since 2019Q5627The number of solutions of the equation 4sin2x−4cos3x+9−4cosx=0;x∈[−2π,2π]4 \sin ^2 x-4 \cos ^3 x+9-4 \cos x=0 ; x \in[-2 \pi, 2 \pi]4sin2x−4cos3x+9−4cosx=0;x∈[−2π,2π] is :A0B3C1D2Check answerSkip
03Medium7×since 2019Q5628If 2tan2θ−5secθ=12 \tan ^2 \theta-5 \sec \theta=12tan2θ−5secθ=1 has exactly 7 solutions in the interval [0,nπ2]\left[0, \frac{n \pi}{2}\right][0,2nπ], for the least value of n∈Nn \in \mathbf{N}n∈N, then \sum_\limits{k=1}^n \frac{k}{2^k} is equal to:A1214(215−15)\frac{1}{2^{14}}\left(2^{15}-15\right)2141(215−15)B1−152131-\frac{15}{2^{13}}1−21315C1215(214−14)\frac{1}{2^{15}}\left(2^{14}-14\right)2151(214−14)D1213(214−15)\frac{1}{2^{13}}\left(2^{14}-15\right)2131(214−15)Check answerSkip
04Easy7×since 2019Q5629If α,−π2<α<π2\alpha,-\frac{\pi}{2}<\alpha<\frac{\pi}{2}α,−2π<α<2π is the solution of 4cosθ+5sinθ=14 \cos \theta+5 \sin \theta=14cosθ+5sinθ=1, then the value of tanα\tan \alphatanα isA10−1012\frac{10-\sqrt{10}}{12}1210−10B10−106\frac{\sqrt{10}-10}{6}610−10C10−1012\frac{\sqrt{10}-10}{12}1210−10D10−106\frac{10-\sqrt{10}}{6}610−10Check answerSkip
05Easy7×since 2019Q5630The sum of the solutions x∈Rx \in \mathbb{R}x∈R of the equation 3cos2x+cos32xcos6x−sin6x=x3−x2+6\frac{3 \cos 2 x+\cos ^3 2 x}{\cos ^6 x-\sin ^6 x}=x^3-x^2+6cos6x−sin6x3cos2x+cos32x=x3−x2+6 isA3B1C0D−-−1Check answerSkip
06Easy7×since 2019Q5631If 2sin3x+sin2xcosx+4sinx−4=02 \sin ^3 x+\sin 2 x \cos x+4 \sin x-4=02sin3x+sin2xcosx+4sinx−4=0 has exactly 3 solutions in the interval [0,nπ2],n∈N\left[0, \frac{\mathrm{n} \pi}{2}\right], \mathrm{n} \in \mathrm{N}[0,2nπ],n∈N, then the roots of the equation x2+nx+(n−3)=0x^2+\mathrm{n} x+(\mathrm{n}-3)=0x2+nx+(n−3)=0 belong to :A(0,∞)(0, \infty)(0,∞)BZC(−172,172)\left(-\frac{\sqrt{17}}{2}, \frac{\sqrt{17}}{2}\right)(−217,217)D(−∞,0)(-\infty, 0)(−∞,0)Check answerSkip
07Easy7×since 2019Q5632Let ∣cosθcos(60−θ)cos(60+θ)∣≤18,θϵ[0,2π]|\cos \theta \cos (60-\theta) \cos (60+\theta)| \leq \frac{1}{8}, \theta \epsilon[0,2 \pi]∣cosθcos(60−θ)cos(60+θ)∣≤81,θϵ[0,2π]. Then, the sum of all θ∈[0,2π]\theta \in[0,2 \pi]θ∈[0,2π], where cos3θ\cos 3 \thetacos3θ attains its maximum value, is :A6π6 \pi6πB9π9 \pi9πC18π18 \pi18πD15π15 \pi15πCheck answerSkip