91Ó°ÊÓ

Solve the following equations and tick the correct one. The number of solutions of the cquation \(2\left(\sin ^{4} 2 x+\cos ^{4} 2 x\right)+3 \sin 2 x \cos 2 x=0\) is (a) 0 (b) 1 (c) 2 (d) 3

Solve the following equations and tick the correct one. \(\cos 2 x+a \sin x=2 a-7\) possesses a solution for (a) all \(a\) (b) \(a>6\) (c) \(a \leq 2\) (d) \(a \in[2,6]\)

Solve the following equations and tick the correct one. If \(0

Solve the following equations and tick the correct one. If \(1+\sin \theta+\sin ^{2} \theta+\ldots \ldots\) to \(\infty=4+2 \sqrt{3}\), \(0<\theta<\pi, \theta \neq \frac{\pi}{2}\), then (a) \(\theta=\frac{\pi}{6}\) (b) \(\theta=\frac{\pi}{3}\) (c) \(\theta=\frac{\pi}{3}\) or \(\frac{\pi}{6}\) (d) \(\frac{\pi}{3}\) or \(\frac{2 \pi}{3}\)

Solve the following equations and tick the correct one. If \(\tan (\pi \cos \theta)=\cot (\pi \sin \theta)\), then the value of \(\cos \left(\theta-\frac{\pi}{4}\right)\) is (a) \(\frac{1}{2}\) (b) \(\frac{1}{\sqrt{2}}\) (c) \(\frac{1}{2 \sqrt{2}}\) (d) None

Solve the following equations and tick the correct one. The most general values of \(x\) for which \(\sin x+\cos x=\min _{a \in R}\left\\{1, a^{2}-4 a+6\right\\}\) are given by (a) \(2 n \pi, n \in N\) (b) \(2 n \pi+\frac{\pi}{2}, n \in N\) (c) \(n \pi+(-1)^{n} \frac{\pi}{4}-\frac{\pi}{4}, n \in N\) (d) None

Solve the following equations and tick the correct one. The number of roots of the equation \(x+2 \tan x=\frac{\pi}{2}\) in the interval \([0,2 \pi]\) is (a) 1 (b) 2 (c) 3 (d) \(\infty\)

Solve the following equations and tick the correct one. The number of solutions of the equation \(\cos (\pi \sqrt{x-4})\) \(\cos (\pi \sqrt{x})=1\) is (a) None (b) 1 (c) 2 (d) \(>2\)

Solve the following equations and tick the correct one. The number of solutions of the equation \(\sin \left(\frac{\pi x}{2 \sqrt{3}}\right)=x^{2}-2 \sqrt{3} x+4\) (a) forms an empty set (b) only one (c) is only two (d) is greater then two

Solve the following equations and tick the correct one. Number of real roots of the equation \(\sec \theta+\operatorname{cosec} \theta=\sqrt{15}\) lying between 0 and \(2 \pi\) is (a) \(\underline{8}\) (b) 4 (c) 2 (d) 0