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.
| 51. |
If the sum and difference of two angles are 135° and $$\frac{\pi }{{12}}$$respectively, then the value of the angles in degree measure are? |
| A. | 0°, 65° |
| B. | 5°, 60° |
| C. | 5°, 90° |
| D. | 0°, 55° |
| Answer» C. 5°, 90° | |
| 52. |
If θ is positive acute angle and 3(sec2θ + tan2θ) = 5, then the value of cos2θ is? |
| A. | $\frac{1}{2}$$ |
| B. | $\frac{{\sqrt 3 }}{2}$$ |
| C. | $\frac{1}{{\sqrt 2 }}$$ |
| Answer» B. $\frac{{\sqrt 3 }}{2}$$ | |
| 53. |
If secα + tanα = 2, then the value of sinα is (assume that 0 < α < 90°) |
| A. | 0.4 |
| B. | 0.5 |
| C. | 0.6 |
| D. | 0.8 |
| Answer» D. 0.8 | |
| 54. |
If secθ + tanθ = 2 + $$\sqrt 5 {\text{,}}$$then the value of sinθ + cosθ is? |
| A. | $\frac{3}{{\sqrt 5 }}$$ |
| B. | $\sqrt 5 $$ |
| C. | $\frac{7}{{\sqrt 5 }}$$ |
| D. | $\frac{1}{{\sqrt 5 }}$$ |
| Answer» B. $\sqrt 5 $$ | |
| 55. |
If $$sec\theta= x + \frac{1}{{4x}}$$$$\left( {{0^ \circ } < \theta< {{90}^ \circ }} \right)$$then $$sec\theta $$+ $${\text{tan}}\theta $$is equal to? |
| A. | $\frac{x}{2}$$ |
| B. | x |
| C. | |
| Answer» C. | |
| 56. |
If sinθ = $$\frac{a}{b}$$then the value of secθ - cosθ is? (where 0° < θ < 90°) |
| A. | $\frac{a}{{b\sqrt {{b^2} - {a^2}} }}$$ |
| B. | $\frac{{{b^2}}}{{a\sqrt {{b^2} - {a^2}} }}$$ |
| C. | $\frac{{{a^2}}}{{b\sqrt {{b^2} - {a^2}} }}$$ |
| D. | $\frac{{\sqrt {{b^2} + {a^2}} }}{{\sqrt {{b^2} - {a^2}} }}$$ |
| Answer» D. $\frac{{\sqrt {{b^2} + {a^2}} }}{{\sqrt {{b^2} - {a^2}} }}$$ | |
| 57. |
If sin21° = $$\frac{x}{y}{\text{,}}$$then sec21° - sin69° is equal to? |
| A. | $\frac{{{x^2}}}{{y\sqrt {{y^2} - {x^2}} }}$$ |
| B. | $\frac{{{y^2}}}{{x\sqrt {{y^2} - {x^2}} }}$$ |
| C. | $\frac{{{x^2}}}{{y\sqrt {{x^2} - {y^2}} }}$$ |
| D. | $\frac{{{y^2}}}{{x\sqrt {{x^2} - {y^2}} }}$$ |
| Answer» B. $\frac{{{y^2}}}{{x\sqrt {{y^2} - {x^2}} }}$$ | |
| 58. |
In ΔABC, ∠B = 90° and AB : BC = 2 : 1, then value of (sinA + cotC) = ? |
| A. | $3 + \sqrt 5 $$ |
| B. | $\frac{{2 + \sqrt 5 }}{{2\sqrt 5 }}$$ |
| C. | $2 + \sqrt 5 $$ |
| D. | $3\sqrt 5 $$ |
| Answer» C. $2 + \sqrt 5 $$ | |
| 59. |
If a right-angled triangle XYZ right-angled at Y. If XY = $${\text{2}}\sqrt 6 $$and XZ - YZ = 2, then secX + tanX is? |
| A. | $\frac{1}{{\sqrt 6 }}$$ |
| B. | $\sqrt 6 $$ |
| C. | $2\sqrt 6 $$ |
| D. | $\frac{{\sqrt 6 }}{2}$$ |
| Answer» C. $2\sqrt 6 $$ | |
| 60. |
If $$\theta $$ be acute angle and $$\cos \theta= \frac{{15}}{{17}}{\text{,}}$$then the value of $${\text{cot}}\left( {{{90}^ \circ } - \theta } \right)$$is? |
| A. | $\frac{{2\sqrt 8 }}{{15}}$$ |
| B. | $\frac{8}{{15}}$$ |
| C. | $\frac{{\sqrt 2 }}{{17}}$$ |
| D. | $\frac{{8\sqrt 2 }}{{17}}$$ |
| Answer» C. $\frac{{\sqrt 2 }}{{17}}$$ | |
| 61. |
In a triangle ABC, ∠ABC = 75° and ∠ACB = $$\frac{{{\pi ^c}}}{4},$$the circular measure of ∠BAC is? |
| A. | $\frac{{5\pi }}{{12}}$$radian |
| B. | $\frac{\pi }{3}$$radian |
| C. | $\frac{\pi }{6}$$radian |
| D. | $\frac{\pi }{2}$$radian |
| Answer» C. $\frac{\pi }{6}$$radian | |
| 62. |
In circular measure, the value of the angle 11° 15' is? |
| A. | $\frac{{{\pi ^c}}}{{16}}$$ |
| B. | $\frac{{{\pi ^c}}}{8}$$ |
| C. | $\frac{{{\pi ^c}}}{4}$$ |
| D. | $\frac{{{\pi ^c}}}{{12}}$$ |
| Answer» B. $\frac{{{\pi ^c}}}{8}$$ | |
| 63. |
If A = sin2θ + cos4θ for any value of θ, then the value of A is? |
| A. | ${\text{1}} \leqslant {\text{A}} \leqslant {\text{1}}$$ |
| B. | $\frac{3}{4} \leqslant {\text{A}} \leqslant {\text{1}}$$ |
| C. | $\frac{{13}}{{16}} \leqslant {\text{A}} \leqslant {\text{1}}$$ |
| D. | $\frac{3}{4} \leqslant {\text{A}} \leqslant \frac{{13}}{{16}}$$ |
| Answer» C. $\frac{{13}}{{16}} \leqslant {\text{A}} \leqslant {\text{1}}$$ | |
| 64. |
If sec2θ + tan2θ = 7, then the value of θ when 0° ≤ θ ≤ 90° is? |
| A. | 0° |
| B. | 0° |
| C. | ° |
| D. | 0° |
| Answer» B. 0° | |
| 65. |
If $${\text{2cos}}\theta- \sin \theta= \frac{1}{{\sqrt 2 }},$$$$\left( {{0^ \circ } < \theta< {{90}^ \circ }} \right)$$the value of $$2\sin \theta $$+ $$\cos \theta $$is? |
| A. | $\frac{1}{{\sqrt 2 }}$$ |
| B. | $\sqrt 2 $$ |
| C. | $\frac{3}{{\sqrt 2 }}$$ |
| D. | $\frac{1}{{\sqrt 3 }}$$ |
| Answer» D. $\frac{1}{{\sqrt 3 }}$$ | |
| 66. |
If $$\sin \theta- \cos \theta= \frac{7}{{13}}$$and $${0^ \circ }{\text{ < }}\theta {\text{ < }}{90^ \circ }{\text{,}}$$then the value of $$\sin \theta $$+ $${\text{cos}}\theta $$is? |
| A. | $\frac{{17}}{{13}}$$ |
| B. | $\frac{{13}}{{17}}$$ |
| C. | $\frac{1}{{13}}$$ |
| D. | $\frac{1}{{17}}$$ |
| Answer» B. $\frac{{13}}{{17}}$$ | |
| 67. |
If $${\text{0}} \leqslant \theta\leqslant {90^ \circ }$$and $$4{\cos ^2}\theta $$- $$4\sqrt 3 \cos \theta $$+ 3 = 0 then the value of $$\theta $$ is? |
| A. | 0° |
| B. | 0° |
| C. | 5° |
| D. | 0° |
| Answer» B. 0° | |
| 68. |
If $$\sin \left( {\theta+ {{30}^ \circ }} \right) = \frac{3}{{\sqrt {12} }}{\text{,}}$$then find $${\text{co}}{{\text{s}}^2}\theta ?$$ |
| A. | $\frac{1}{4}$$ |
| B. | $\frac{3}{4}$$ |
| C. | $\frac{{\sqrt 3 }}{2}$$ |
| D. | $\frac{1}{2}$$ |
| Answer» C. $\frac{{\sqrt 3 }}{2}$$ | |
| 69. |
If $${\text{sin A}} - \cos {\text{A}}$$= $$\frac{{\sqrt 3- 1}}{2}{\text{,}}$$then the value of $${\text{sin A}}.{\text{cosA}}$$is? |
| A. | $\frac{1}{{\sqrt 3 }}$$ |
| B. | $\frac{{\sqrt 3 }}{2}$$ |
| C. | $\frac{1}{4}$$ |
| D. | $\frac{{\sqrt 3 }}{4}$$ |
| Answer» E. | |
| 70. |
If $${\text{sin}}\left( {{{90}^ \circ } - \theta } \right)$$+ $${\text{cos}}\theta $$= $$\sqrt 2 {\text{cos}}\left( {{{90}^ \circ } - \theta } \right){\text{,}}$$then the value of $${\text{cosec}}\theta $$is? |
| A. | $\frac{1}{{\sqrt 3 }}$$ |
| B. | $\frac{2}{3}$$ |
| C. | $\sqrt {\frac{3}{2}} $$ |
| D. | $\frac{1}{{\sqrt 2 }}$$ |
| Answer» D. $\frac{1}{{\sqrt 2 }}$$ | |
| 71. |
If $$\frac{{{\text{sec}}\theta+ {\text{tan}}\theta }}{{{\text{sec}}\theta- {\text{tan}}\theta }} = 2\frac{{51}}{{79}}{\text{,}}$$then the value of $$\sin \theta $$is? |
| A. | $\frac{{91}}{{144}}$$ |
| B. | $\frac{{39}}{{72}}$$ |
| C. | $\frac{{65}}{{144}}$$ |
| D. | $\frac{{35}}{{72}}$$ |
| Answer» D. $\frac{{35}}{{72}}$$ | |
| 72. |
If $${\left( {r\cos \theta- \sqrt 3 } \right)^2}$$+ $${\left( {r\sin \theta- 1} \right)^2}$$= 0,then the value of $$\frac{{r\tan \theta+ \sec \theta }}{{r\sec \theta+ \tan \theta }}$$is equal to? |
| A. | $\frac{4}{5}$$ |
| B. | $\frac{3}{5}$$ |
| C. | $\frac{{\sqrt 3 }}{4}$$ |
| D. | $\frac{{\sqrt 5 }}{4}$$ |
| Answer» B. $\frac{3}{5}$$ | |
| 73. |
$$\sqrt {\frac{{1 + {\text{sin }}\theta }}{{1 - {\text{sin }}\theta }}} $$+ $$\sqrt {\frac{{1 - {\text{sin }}\theta }}{{1 + {\text{sin }}\theta }}} $$is equal to? |
| A. | cosθ |
| B. | sinθ |
| C. | cotθ |
| D. | secθ |
| Answer» E. | |
| 74. |
If tanA = n tanB and sinA = m sinB, then the value of cos2A = ? |
| A. | $\frac{{{m^2} + 1}}{{{n^2} + 1}}$$ |
| B. | $\frac{{{m^2} + 1}}{{{n^2} - 1}}$$ |
| C. | $\frac{{{m^2} - 1}}{{{n^2} - 1}}$$ |
| D. | $\frac{{{m^2} - 1}}{{{n^2} + 1}}$$ |
| Answer» D. $\frac{{{m^2} - 1}}{{{n^2} + 1}}$$ | |
| 75. |
If tanθ + cotθ = 5, then tan2θ + cot2θ is? |
| A. | 3 |
| B. | 4 |
| C. | 5 |
| D. | 6 |
| Answer» B. 4 | |
| 76. |
$$\frac{{{\text{cos }}\alpha }}{{{\text{sin }}\beta }} = n$$and $$\frac{{{\text{cos }}\alpha }}{{{\text{cos }}\beta }} = m,$$then the value of $${\text{co}}{{\text{s}}^2}\beta $$is? |
| A. | $\frac{{{m^2} - 1}}{{{n^2} - 1}}$$ |
| B. | $\frac{{{m^2} - 3}}{{{n^2} - 4}}$$ |
| C. | $\frac{{{m^2} + 3}}{{{n^2} + 3}}$$ |
| D. | $\frac{{{n^2}}}{{{m^2} + {n^2}}}$$ |
| Answer» E. | |
| 77. |
sinθ = 0.7 then cosθ, 0 ≤ θ < 90° is? |
| A. | 0.3 |
| B. | $\sqrt {0.49} $$ |
| C. | $\sqrt {0.51} $$ |
| D. | $\sqrt {0.9} $$ |
| Answer» D. $\sqrt {0.9} $$ | |
| 78. |
If $$\frac{{{\text{cos }}\alpha }}{{{\text{cos }}\beta }} = a$$and $$\frac{{{\text{sin }}\alpha }}{{{\text{sin }}\beta }} = b{\text{,}}$$then the value of $${\sin ^2}\beta $$in terms of a and b is? |
| A. | $\frac{{{a^2} + 1}}{{{a^2} - {b^2}}}$$ |
| B. | $\frac{{{a^2} - {b^2}}}{{{a^2} + {b^2}}}$$ |
| C. | $\frac{{{a^2} - 1}}{{{a^2} - {b^2}}}$$ |
| D. | $\frac{{{a^2} - 1}}{{{a^2} + {b^2}}}$$ |
| Answer» D. $\frac{{{a^2} - 1}}{{{a^2} + {b^2}}}$$ | |
| 79. |
If tan2θ = 1 - e2, then the value of secθ + tan3θ.cosecθ is? |
| A. | ${\left( {2 + {e^2}} \right)^2}$$ |
| B. | ${\left( {2 - {e^2}} \right)^{\frac{1}{2}}}$$ |
| C. | ${\left( {2 + {e^2}} \right)^{\frac{1}{2}}}$$ |
| D. | ${\left( {2 - {e^2}} \right)^{\frac{3}{2}}}$$ |
| Answer» E. | |
| 80. |
The value of $$\frac{{{\text{sin A}}}}{{1 + \cos {\text{ A}}}}$$+ $$\frac{{{\text{sin A}}}}{{1 - \cos {\text{ A}}}}$$is $$\left( {{0^ \circ } < {\text{A}} < {{90}^ \circ }} \right)$$ |
| A. | cosec A |
| B. | sec A |
| C. | sin A |
| D. | cos A |
| Answer» B. sec A | |
| 81. |
The elimination of θ from x cosθ - y sinθ = 2 and x sinθ + y cosθ = 4 will give? |
| A. | 2 + y2 = 20 |
| B. | x2 + y2 = 20 |
| C. | 2 - y2 = 20 |
| D. | x2 - y2 = 10 |
| Answer» B. x2 + y2 = 20 | |
| 82. |
If $${\text{se}}{{\text{c}}^2}\theta+ {\text{ta}}{{\text{n}}^2}\theta= \frac{7}{{12}}{\text{,}}$$then $${\text{se}}{{\text{c}}^4}\theta $$- $${\text{ta}}{{\text{n}}^4}\theta $$= ? |
| A. | $\frac{7}{{12}}$$ |
| B. | $\frac{1}{2}$$ |
| C. | $\frac{7}{2}$$ |
| Answer» B. $\frac{1}{2}$$ | |
| 83. |
The expression $$\frac{{\tan {{57}^ \circ } + \cot {{37}^ \circ }}}{{\tan {{33}^ \circ } + \cot {{53}^ \circ }}}$$is equal to? |
| A. | an30° cot57° |
| B. | an57° cot37° |
| C. | an33° cot 53° |
| D. | an33° cot37° |
| Answer» C. an33° cot 53° | |
| 84. |
The angles of a triangle are (x + 5)°, (2x - 3)° and (3x + 4)°. Then the value of x is? |
| A. | 0 |
| B. | 1 |
| C. | 9 |
| D. | 8 |
| Answer» D. 8 | |
| 85. |
If $${\text{tan}}\theta= \frac{4}{3}{\text{,}}$$then the value of $$\frac{{3\sin \theta+ 2{\text{cos}}\theta }}{{3\sin \theta- 2{\text{cos}}\theta }}$$is? |
| A. | 0.5 |
| B. | 0.5 |
| C. | 0 |
| D. | 3 |
| Answer» D. 3 | |
| 86. |
$$\frac{{{\text{tan}}\theta }}{{1 - {\text{cot}}\theta }}{\text{ + }}\frac{{{\text{cot}}\theta }}{{1 - {\text{tan}}\theta }}$$is equal to? |
| A. | - tanθ - cotθ |
| B. | anθ - cotθ +1 |
| C. | otθ - tanθ + 1 |
| D. | anθ + cotθ + 1 |
| Answer» E. | |
| 87. |
If θ be an acute angle and 7sin2θ + 3cos2θ = 4, then the value of tanθ is? |
| A. | $\sqrt 3 $$ |
| B. | $\frac{1}{{\sqrt 3 }}$$ |
| Answer» C. | |
| 88. |
The measure of the angles of a triangle are in the ratio 2 : 7 : 11. Measures of angles are ? |
| A. | 6°, 56°, 88° |
| B. | 8°, 63°, 99° |
| C. | 0°, 70°, 90° |
| D. | 5°, 175°, 105° |
| Answer» C. 0°, 70°, 90° | |
| 89. |
If θ be acute angle and tan(4θ - 50°) = cot(50° - θ), then the value of θ in degrees is? |
| A. | 0° |
| B. | 0° |
| C. | 0° |
| D. | 0° |
| Answer» B. 0° | |
| 90. |
If sin 3A = cos(A - 26°), where 3A is an acute angle then the value of A is? |
| A. | 9° |
| B. | 6° |
| C. | 3° |
| D. | 8° |
| Answer» B. 6° | |
| 91. |
If tan7θ.tan2θ = 1, then the value of tan3θ is? |
| A. | $\sqrt 3 $$ |
| B. | $ - \frac{1}{{\sqrt 3 }}$$ |
| C. | $\frac{1}{{\sqrt 3 }}$$ |
| D. | $ - \sqrt 3 $$ |
| Answer» D. $ - \sqrt 3 $$ | |
| 92. |
If A, B and C be the angles of a triangle, the incorrect relation is ? |
| A. | ${\text{sin }}\left( {\frac{{{\text{A + B}}}}{2}} \right) = {\text{cos}}\frac{{\text{C}}}{2}$$ |
| B. | ${\text{cos }}\left( {\frac{{{\text{A + B}}}}{2}} \right) = {\text{sin}}\frac{{\text{C}}}{2}$$ |
| C. | ${\text{tan }}\left( {\frac{{{\text{A + B}}}}{2}} \right) = \sec \frac{{\text{C}}}{2}$$ |
| D. | ${\text{cot }}\left( {\frac{{{\text{A + B}}}}{2}} \right) = \tan \frac{{\text{C}}}{2}$$ |
| Answer» D. ${\text{cot }}\left( {\frac{{{\text{A + B}}}}{2}} \right) = \tan \frac{{\text{C}}}{2}$$ | |
| 93. |
If cosθ.cosec23° = 1, the value of θ is? |
| A. | 3° |
| B. | 7° |
| C. | 3° |
| D. | 7° |
| Answer» E. | |
| 94. |
sin25° + sin26° + ............. sin284° + sin285° = ? |
| A. | $30\frac{1}{2}$$ |
| B. | $40\frac{1}{2}$$ |
| C. | 0 |
| D. | $39\frac{1}{2}$$ |
| Answer» C. 0 | |
| 95. |
Which one of the following is true for 0° < θ < 90° ? |
| A. | osθ ≤ cos2θ |
| B. | osθ < cos2θ |
| C. | osθ > cos2θ |
| D. | osθ ≥ cos2θ |
| Answer» D. osθ ≥ cos2θ | |
| 96. |
The equation $${\cos ^2}\theta $$= $$\frac{{{{\left( {x + y} \right)}^2}}}{{4xy}}$$is only possible when ? |
| A. | = -y |
| B. | > y |
| C. | = y |
| D. | < y |
| Answer» D. < y | |