## Lakshya Education MCQs

Question: If $$\sin \alpha + \cos \beta = 2;$$   $$\left( {{0^ \circ } \leqslant \beta < \alpha \leqslant {{90}^ \circ }} \right){\text{,}}$$     then $${\text{sin}}\,{\left( {\frac{{2\alpha + \beta }}{3}} \right)^ \circ }$$   is?
Options:
 A. $${\text{sin }}\frac{\alpha }{2}$$ B. $$\cos \frac{\alpha }{3}$$ C. $${\text{sin }}\frac{\alpha }{3}$$ D. $$\cos \frac{{2\alpha }}{3}$$

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## More Questions on This Topic :

Question 1. If $$2\sin \left( {\frac{{\pi x}}{2}} \right) = {x^2} + \frac{1}{{{x^2}}}{\text{,}}$$     then the value of $$\left( {x - \frac{1}{x}} \right)$$   is?
1.    -1
2.    2
3.    1
4.    0
Question 2. The value of 152(sin30° + 2cos245° + 3sin30° + 4cos245° + ...... + 17sin30° + 18cos245°) is?
1.    An integer but not perfect square
2.    A rational number but not an integer
3.    A perfect square of an integer
4.    Irrational
Question 3. If $$x\sin {45^ \circ }$$  = $$y\operatorname{cosec} {30^ \circ },$$   then $$\frac{{{x^4}}}{{{y^4}}}$$  is equal to?
1.    43
2.    63
3.    23
4.    83
Question 4. Sin2θ - 3sinθ +2 = 0, will be true if ?
1.    0 ≤ θ ≤ 90°
2.    0 < θ < 90°
3.    θ = 0°
4.    θ = 90°
Question 5. If 2(cos2θ - sin2θ) = 1, (θ is positive acute angle), then cotθ is equal to?
1.    $$- \sqrt 3$$
2.    $$\frac{1}{{\sqrt 3 }}$$
3.    1
4.    $$\sqrt 3$$
Question 6. In sin(A - B) = $$\frac{1}{2}$$ and cos(A + B) =$$\frac{1}{2}$$ where A > B > 0 and A + B is an acute angle, then the value of B is?
1.    $$\frac{\pi }{6}$$
2.    $$\frac{\pi }{{12}}$$
3.    $$\frac{\pi }{4}$$
4.    $$\frac{\pi }{2}$$