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.$$\cos \frac{{2\alpha }}{3}$$
Answer: Option B

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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
Answer: Option D
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
Answer: Option C
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
Answer: Option A
Question 4. Sin2θ - 3sinθ +2 = 0, will be true if ?
  1.    0 ≤ θ ≤ 90°
  2.    0 < θ < 90°
  3.    θ = 0°
  4.    θ = 90°
Answer: Option D
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.    $$\sqrt 3 $$
Answer: Option D
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.    $$\frac{\pi }{2}$$
Answer: Option B

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