MCQOPTIONS
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MCQOPTIONS
This section includes 96 Mcqs, each offering curated multiple-choice questions to sharpen your BITSAT knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
The expression of $$\frac{{\cot \theta+ \operatorname{cosec} \theta- 1}}{{\cot \theta+ \operatorname{cosec} \theta+ 1}}$$is equal to? |
| A. | $\frac{{1 + \cos \theta }}{{\sin \theta }}$$ |
| B. | $\frac{{1 - \cos \theta }}{{\sin \theta }}$$ |
| C. | $\frac{{\cot \theta+ 1}}{{\operatorname{cosec} \theta }}$$ |
| D. | $\frac{{\cot \theta- 1}}{{\sin \theta }}$$ |
| Answer» C. $\frac{{\cot \theta+ 1}}{{\operatorname{cosec} \theta }}$$ | |
| 2. |
If secθ + tanθ = m(>1), then the value of sinθ is (0° < θ < 90°) |
| A. | $\frac{{1 - {m^2}}}{{1 + {m^2}}}$$ |
| B. | $\frac{{{m^2} - 1}}{{{m^2} + 1}}$$ |
| C. | $\frac{{{m^2} + 1}}{{{m^2} - 1}}$$ |
| D. | $\frac{{1 + {m^2}}}{{1 - {m^2}}}$$ |
| Answer» C. $\frac{{{m^2} + 1}}{{{m^2} - 1}}$$ | |
| 3. |
If $$\cot \theta= 4{\text{,}}$$then the value of $$\frac{{5\sin \theta+ 3\cos \theta }}{{5\sin \theta- 3\cos \theta }}$$is? |
| A. | $ - \frac{{17}}{7}$$ |
| B. | $\frac{1}{3}$$ |
| Answer» B. $\frac{1}{3}$$ | |
| 4. |
If 7sin2θ + 3cos2θ = 4, then the value of secθ + cosecθ is? |
| A. | $\frac{2}{{\sqrt 3 }} - 2$$ |
| B. | $\frac{2}{{\sqrt 3 }} + 2$$ |
| C. | $\frac{2}{{\sqrt 3 }}$$ |
| D. | one of these |
| Answer» C. $\frac{2}{{\sqrt 3 }}$$ | |
| 5. |
If tanθ = tan30° .tan60° and θ is an acute angle, then 2θ is equal to? |
| A. | 0° |
| B. | 5° |
| C. | 0° |
| D. | ° |
| Answer» D. ° | |
| 6. |
If sec15θ = cosec15θ (0° < θ < 10°) then the value of θ is? |
| A. | ° |
| B. | ° |
| C. | ° |
| D. | ° |
| Answer» E. | |
| 7. |
If $$\frac{{\cos \theta }}{{1 - \sin \theta }}$$+ $$\frac{{\cos \theta }}{{1 + {\text{sin }}\theta }}$$= 4, then the value of $$\theta \left( {{0^ \circ } < \theta< {{90}^ \circ }} \right)$$is? |
| A. | 0° |
| B. | 5° |
| C. | 0° |
| D. | 5° |
| Answer» B. 5° | |
| 8. |
If $${\text{tan}}\theta= \frac{4}{3}{\text{,}}$$then the value of $$\frac{{3\sin \theta+ 2\cos \theta }}{{3\sin \theta- 2\cos \theta }}$$is? |
| A. | $\frac{1}{2}$$ |
| B. | ${\text{1}}\frac{2}{3}$$ |
| C. | |
| Answer» D. | |
| 9. |
If cos27° = x, then the value of tan63° is? |
| A. | $\frac{x}{{\sqrt {1 - {x^2}} }}$$ |
| B. | $\frac{x}{{\sqrt {1 + {x^2}} }}$$ |
| C. | $\frac{{\sqrt {1 - {x^2}} }}{x}$$ |
| D. | $\frac{{\sqrt {1 + {x^2}} }}{x}$$ |
| Answer» B. $\frac{x}{{\sqrt {1 + {x^2}} }}$$ | |
| 10. |
If θ is positive acute angle and 7cos2θ + 3sin2θ = 4, then value of θ is? |
| A. | 0° |
| B. | 0° |
| C. | 5° |
| D. | 0° |
| Answer» B. 0° | |
| 11. |
If sec(4x - 50°) = cosec(50° - x), then the value of x is? |
| A. | 5° |
| B. | 0° |
| C. | 0° |
| D. | 0° |
| Answer» D. 0° | |
| 12. |
If α + β = 90° and α : β = 2 : 1, then the ratio of cosα to cosβ is? |
| A. | : $$\sqrt 3 $$ |
| B. | : 3 |
| C. | : $$\sqrt 2 $$ |
| D. | : 2 |
| Answer» B. : 3 | |
| 13. |
If sin31° = $$\frac{x}{y}{\text{,}}$$ then the value of sec31° - sin59° is? |
| A. | $\frac{{{x^2}}}{{y\sqrt {{y^2} + {x^2}} }}$$ |
| B. | $\frac{{{x^2}}}{{y\sqrt {{y^2} - {x^2}} }}$$ |
| C. | $ - \frac{{{y^2}}}{{\sqrt {{y^2} - {x^2}} }}$$ |
| D. | $ - \frac{{{x^2}}}{{\sqrt {{y^2} - {x^2}} }}$$ |
| Answer» C. $ - \frac{{{y^2}}}{{\sqrt {{y^2} - {x^2}} }}$$ | |
| 14. |
If θ is a acute angle and sin(θ + 18°) = $$\frac{1}{2}{\text{,}}$$ then the value of θ in circular measure is? |
| A. | $\frac{\pi }{{12}}$$ Radians |
| B. | $\frac{\pi }{{15}}$$ Radians |
| C. | $\frac{{2\pi }}{5}$$ Radians |
| D. | $\frac{{3\pi }}{{13}}$$ Radians |
| Answer» C. $\frac{{2\pi }}{5}$$ Radians | |
| 15. |
In a ΔABC, if 4∠A = 3∠B = 12∠C, find ∠A? |
| A. | 2.5° |
| B. | 0° |
| C. | 7.5° |
| D. | 12.5° |
| Answer» D. 12.5° | |
| 16. |
If $$\tan \theta= \frac{3}{4}{\text{,}}$$find the value of $${\text{cos2}}\theta $$? |
| A. | $\frac{{24}}{{25}}$$ |
| B. | $\frac{{16}}{{25}}$$ |
| C. | $\frac{7}{{25}}$$ |
| D. | $\frac{9}{{30}}$$ |
| Answer» D. $\frac{9}{{30}}$$ | |
| 17. |
$$\frac{{2\sin \theta }}{{\cos \theta \left( {1 + {\text{ta}}{{\text{n}}^2}\theta } \right)}}$$simplifies to? |
| A. | osθ |
| B. | os2θ |
| C. | in2θ |
| D. | inθ |
| Answer» D. inθ | |
| 18. |
The value of 8(sin6θ + cos6θ) - 12(sin4θ + cos4θ) is equal to? |
| A. | 0 |
| B. | 20 |
| C. | 4 |
| Answer» D. | |
| 19. |
If a2 sec2x - b2 tan2x = c2, then the value of sec2x + tan2x is equal to (assume b2 ≠ a2) |
| A. | $\frac{{{b^2} - {a^2} + 2{c^2}}}{{{b^2} + {a^2}}}$$ |
| B. | $\frac{{{b^2} + {a^2} - 2{c^2}}}{{{b^2} - {a^2}}}$$ |
| C. | $\frac{{{b^2} - {a^2} - 2{c^2}}}{{{b^2} + {a^2}}}$$ |
| D. | $\frac{{{b^2} - {a^2}}}{{{b^2} + {a^2} + 2{c^2}}}$$ |
| Answer» C. $\frac{{{b^2} - {a^2} - 2{c^2}}}{{{b^2} + {a^2}}}$$ | |
| 20. |
x, y be two acute angles, x + y < 90° and sin(2x - 20°) = cos(2y + 20°), the value of tan(x + y) is? |
| A. | $\sqrt 3 $$ |
| B. | $\frac{1}{{\sqrt 3 }}$$ |
| C. | |
| Answer» D. | |
| 21. |
If xtan60° + cos45° = sec45°, then the value of x2 + 1 is? |
| A. | $\frac{6}{7}$$ |
| B. | $\frac{7}{6}$$ |
| C. | $\frac{5}{6}$$ |
| D. | $\frac{6}{5}$$ |
| Answer» C. $\frac{5}{6}$$ | |
| 22. |
If $${\text{A}} \times {\text{tan}}\left( {\theta+ {{150}^ \circ }} \right)$$= $${\text{B}} \times \tan $$ $$\left( {\theta- {{60}^ \circ }} \right){\text{,}}$$the value of $$\frac{{{\text{A}} - {\text{B}}}}{{{\text{A}} + {\text{B}}}}$$is? |
| A. | $ - \frac{{\sin \theta }}{2}$$ |
| B. | $\frac{{\sin 2\theta }}{2}$$ |
| C. | $\frac{{\cos 2\theta }}{2}$$ |
| Answer» B. $\frac{{\sin 2\theta }}{2}$$ | |
| 23. |
The numerical value of $$\frac{{{\text{co}}{{\text{s}}^2}{{45}^ \circ }}}{{{{\sin }^2}{{60}^ \circ }}}$$+ $$\frac{{{\text{co}}{{\text{s}}^2}{{60}^ \circ }}}{{{{\sin }^2}{{45}^ \circ }}}$$- $$\frac{{{\text{ta}}{{\text{n}}^2}{{30}^ \circ }}}{{{\text{co}}{{\text{t}}^2}{{45}^ \circ }}}$$- $$\frac{{{{\sin }^2}{{30}^ \circ }}}{{{\text{co}}{{\text{t}}^2}{{30}^ \circ }}}$$is? |
| A. | $\frac{3}{4}$$ |
| B. | $\frac{1}{4}$$ |
| C. | $\frac{1}{2}$$ |
| D. | ${\text{1}}\frac{1}{4}$$ |
| Answer» B. $\frac{1}{4}$$ | |
| 24. |
If x = cosecθ - sinθ and y = secθ - cosθ, then the relation between x and y is? |
| A. | 2 + y2 + 3 = 1 |
| B. | 2y2(x2 + y2 + 3) = 1 |
| C. | 2(x2 + y2 - 5) = 1 |
| D. | 2(x2 + y2 - 5) = 1 |
| Answer» C. 2(x2 + y2 - 5) = 1 | |
| 25. |
If $${\text{cos}}\theta= \frac{{{x^2} - {y^2}}}{{{x^2} + {y^2}}}$$then the value of$${\text{cot}}\theta $$is equal to $$\left[ {{\text{if }}{0^ \circ } \leqslant \theta\leqslant {{90}^ \circ }} \right]$$ |
| A. | $\frac{{2xy}}{{{x^2} - {y^2}}}$$ |
| B. | $\frac{{2xy}}{{{x^2} + {y^2}}}$$ |
| C. | $\frac{{{x^2} + {y^2}}}{{2xy}}$$ |
| D. | $\frac{{{x^2} - {y^2}}}{{2xy}}$$ |
| Answer» E. | |
| 26. |
If secA + tanA = a, then the value of cosA is? |
| A. | $\frac{{{a^2} + 1}}{{2a}}$$ |
| B. | $\frac{{2a}}{{{a^2} + 1}}$$ |
| C. | $\frac{{{a^2} - 1}}{{2a}}$$ |
| D. | $\frac{{2a}}{{{a^2} - 1}}$$ |
| Answer» C. $\frac{{{a^2} - 1}}{{2a}}$$ | |
| 27. |
If $${\text{tan }}\alpha= 2,$$then the value of $$\frac{{{\text{cose}}{{\text{c}}^2}\alpha- {\text{se}}{{\text{c}}^2}\alpha }}{{{\text{cose}}{{\text{c}}^2}\alpha+ se{c^2}\alpha }}$$is? |
| A. | $ - \frac{5}{9}$$ |
| B. | $\frac{3}{5}$$ |
| C. | $ - \frac{3}{5}$$ |
| D. | $\frac{{17}}{5}$$ |
| Answer» D. $\frac{{17}}{5}$$ | |
| 28. |
a, b, c are the lengths of three sides of a triangle ABC. If a, b, c are related by the relation a2 + b2 + c2 = ab + bc + ca, then the value of (sin2A + sin2B + sin2C) is? |
| A. | $\frac{3}{4}$$ |
| B. | $\frac{3}{2}$$ |
| C. | $\frac{{3\sqrt 3 }}{2}$$ |
| D. | $\frac{9}{4}$$ |
| Answer» E. | |
| 29. |
The value of θ(0 ≤ θ ≤ 90°) satisfying 2sin2θ = 3cosθ is? |
| A. | 0° |
| B. | 0° |
| C. | 0° |
| D. | 5° |
| Answer» B. 0° | |
| 30. |
If $$\sec \theta- \tan \theta= \frac{1}{{\sqrt 3 }}{\text{,}}$$the value of $$\sec \theta $$ . $$\tan \theta $$= ? |
| A. | $\frac{4}{{\sqrt 3 }}$$ |
| B. | $\frac{2}{{\sqrt 3 }}$$ |
| C. | $\frac{2}{3}$$ |
| D. | $\frac{1}{{\sqrt 3 }}$$ |
| Answer» D. $\frac{1}{{\sqrt 3 }}$$ | |
| 31. |
The value of $$\frac{{{\text{co}}{{\text{s}}^2}{{60}^ \circ } + 4{\text{se}}{{\text{c}}^2}{{30}^ \circ } - {\text{ta}}{{\text{n}}^2}{{45}^ \circ }}}{{{{\sin }^2}{{30}^ \circ } + {\text{co}}{{\text{s}}^2}{{30}^ \circ }}}$$is? |
| A. | $\frac{{64}}{{\sqrt 3 }}$$ |
| B. | $\frac{{55}}{{12}}$$ |
| C. | $\frac{{67}}{{12}}$$ |
| D. | $\frac{{67}}{{10}}$$ |
| Answer» C. $\frac{{67}}{{12}}$$ | |
| 32. |
0 < θ < 90°, tanθ + sinθ =m and tanθ - sinθ = n, where m ≠ n, then the value of m2 - n2 is? |
| A. | (tan2θ + sin2θ) |
| B. | mn |
| C. | $$\sqrt {\text{mn}} $$ |
| D. | (m2 + n2) |
| Answer» D. (m2 + n2) | |
| 33. |
If $$\frac{{\sin \theta+ \cos \theta }}{{\sin \theta- \cos \theta }} = 3{\text{,}}$$then the value of $${\sin ^4}\theta $$is? |
| A. | $\frac{{16}}{{25}}$$ |
| B. | $\frac{2}{5}$$ |
| C. | $\frac{1}{5}$$ |
| D. | $\frac{3}{5}$$ |
| Answer» B. $\frac{2}{5}$$ | |
| 34. |
If sinθ + cosθ= $$\sqrt 2 $$ sin(90° - θ) then the value of cotθ is? |
| A. | $$\sqrt 2 $$ - 1 |
| B. | $\sqrt 2 $$ + 1 |
| C. | $\sqrt 2 $$ - 1 |
| D. | $$\sqrt 2 $$ + 1 |
| Answer» C. $\sqrt 2 $$ - 1 | |
| 35. |
If cos2θ - sin2θ = $$\frac{1}{3}{\text{,}}$$ where 0 ≤ θ ≤ $$\frac{\pi }{2}{\text{,}}$$ then the value of cos4θ - sin4θ is? |
| A. | $\frac{1}{3}$$ |
| B. | $\frac{2}{3}$$ |
| C. | $\frac{1}{9}$$ |
| D. | $\frac{2}{9}$$ |
| Answer» B. $\frac{2}{3}$$ | |
| 36. |
If $$x\cos \theta- y\sin \theta $$= $$\sqrt {{x^2} + {y^2}} $$and $$\frac{{{{\cos }^2}\theta }}{{{a^2}}}$$+ $$\frac{{{{\sin }^2}\theta }}{{{b^2}}}$$= $$\frac{1}{{{x^2} + {y^2}}}{\text{,}}$$then the correct relation is? |
| A. | $\frac{{{x^2}}}{{{b^2}}} - \frac{{{y^2}}}{{{a^2}}} = 1$$ |
| B. | $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$$ |
| C. | $\frac{{{x^2}}}{{{b^2}}} + \frac{{{y^2}}}{{{a^2}}} = 1$$ |
| D. | $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$$ |
| Answer» C. $\frac{{{x^2}}}{{{b^2}}} + \frac{{{y^2}}}{{{a^2}}} = 1$$ | |
| 37. |
If $$x{\sin ^2}{60^ \circ }$$- $$\frac{3}{2}{\text{sec}}{60^ \circ }$$ . $${\text{ta}}{{\text{n}}^2}{30^ \circ }$$+ $$\frac{4}{5}{\sin ^2}{45^ \circ }$$ . $${\text{ta}}{{\text{n}}^2}{60^ \circ }$$= 0, then x is? |
| A. | $ - \frac{1}{{15}}$$ |
| B. | 4 |
| C. | $ - \frac{4}{{15}}$$ |
| D. | 2 |
| Answer» D. 2 | |
| 38. |
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? |
| A. | ${\text{sin }}\frac{\alpha }{2}$$ |
| B. | $\cos \frac{\alpha }{3}$$ |
| C. | ${\text{sin }}\frac{\alpha }{3}$$ |
| D. | $\cos \frac{{2\alpha }}{3}$$ |
| Answer» C. ${\text{sin }}\frac{\alpha }{3}$$ | |
| 39. |
sin2θ - 3sinθ +2 = 0, will be true if ? |
| A. | ≤ θ ≤ 90° |
| B. | < θ < 90° |
| C. | = 0° |
| D. | = 90° |
| Answer» E. | |
| 40. |
In sin(A - B) = $$\frac{1}{2}$$ and cos(A + B) =$$\frac{1}{2}$$ where A > B > 0 and A + B is an acute angle,then the value of B is? |
| A. | $\frac{\pi }{6}$$ |
| B. | $\frac{\pi }{{12}}$$ |
| C. | $\frac{\pi }{4}$$ |
| D. | $\frac{\pi }{2}$$ |
| Answer» C. $\frac{\pi }{4}$$ | |
| 41. |
If $$x\sin {45^ \circ }$$= $$y\operatorname{cosec} {30^ \circ },$$then $$\frac{{{x^4}}}{{{y^4}}}$$is equal to? |
| A. | 3 |
| B. | 3 |
| C. | 3 |
| D. | 3 |
| Answer» B. 3 | |
| 42. |
The value of 152(sin30° + 2cos245° + 3sin30° + 4cos245° + ...... + 17sin30° + 18cos245°) is? |
| A. | n integer but not perfect square |
| B. | rational number but not an integer |
| C. | perfect square of an integer |
| D. | rrational |
| Answer» D. rrational | |
| 43. |
If tan(2θ + 45°) = cot3θ, where (2θ + 45°) and 3θ are acute angles, then the value of θ is? |
| A. | ° |
| B. | ° |
| C. | 2° |
| D. | 5° |
| Answer» C. 2° | |
| 44. |
If 7sin2θ + 3cos2θ = 4, (0° ≤ θ ≤ 90°), then the value of θ is? |
| A. | $\frac{\pi }{2}$$ |
| B. | $\frac{\pi }{3}$$ |
| C. | $\frac{\pi }{6}$$ |
| D. | $\frac{\pi }{4}$$ |
| Answer» D. $\frac{\pi }{4}$$ | |
| 45. |
The value of following is, cos24° + cos55° + cos125° + cos204° + cos300° ? |
| A. | $ - \frac{1}{2}$$ |
| B. | $\frac{1}{2}$$ |
| Answer» C. | |
| 46. |
If A = tan11°. tan29°, B = 2cot61°. cot79° then - |
| A. | = 2B |
| B. | = -2B |
| C. | A = B |
| D. | A = -B |
| Answer» D. A = -B | |
| 47. |
If tan15° = 2 - $$\sqrt 3 ,$$then the value of tan15° cot75° + tan75° cot15° is? |
| A. | 4 |
| B. | 2 |
| C. | 0 |
| Answer» B. 2 | |
| 48. |
$$\frac{{\sin \theta+ \cos \theta }}{{{\text{sin}}\theta- \cos \theta }} = 3,$$then the value of $${\sin ^4}\theta- {\text{co}}{{\text{s}}^4}\theta $$is? |
| A. | $\frac{1}{5}$$ |
| B. | $\frac{3}{5}$$ |
| C. | $\frac{2}{5}$$ |
| D. | $\frac{4}{5}$$ |
| Answer» C. $\frac{2}{5}$$ | |
| 49. |
$$\frac{{{\text{tan}}\theta+ \cot \theta }}{{{\text{tan}}\theta- \cot \theta }} = 2,$$$$\left( {0 \leqslant \theta\leqslant {{90}^ \circ }} \right),$$then the value of $$\sin \theta $$is? |
| A. | $\frac{2}{{\sqrt 3 }}$$ |
| B. | $\frac{{\sqrt 3 }}{2}$$ |
| C. | $\frac{1}{2}$$ |
| Answer» C. $\frac{1}{2}$$ | |
| 50. |
If cosθ + sinθ = $$\sqrt 2 $$ cosθ, then cosθ - sinθ is? |
| A. | $\sqrt 2 $$ tanθ |
| B. | $$\sqrt 2 $$ cosθ |
| C. | $$\sqrt 2 $$ sinθ |
| D. | $\sqrt 2 $$ sinθ |
| Answer» E. | |