MCQOPTIONS
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MCQOPTIONS
This section includes 133 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 101. |
cos(α + β)-cos(α - β) = |
| A. | 2sinαcosβ |
| B. | 2cosαsinβ |
| C. | 2cosαcosβ |
| D. | −2sinαsinβ |
| Answer» E. | |
| 102. |
cosec(-α) = |
| A. | −cosα |
| B. | −secα |
| C. | cosecα |
| D. | −cosecα |
| Answer» E. | |
| 103. |
tan(α + β) = |
| A. | tanα-tanβ/1 + tanαtanβ |
| B. | tanα+tanβ/1 - tanαtanβ |
| C. | cotα+cotβ/1-cotαcotβ |
| D. | cotα-cotβ/1 + cotαcotβ |
| Answer» C. cotα+cotβ/1-cotαcotβ | |
| 104. |
cot(π+α) = |
| A. | tanα |
| B. | −tanα |
| C. | cotα |
| D. | −cotα |
| Answer» D. −cotα | |
| 105. |
If tanθ < 0, sinθ < 0, then the terminal arm of the angle lies in the quadrant |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» B. 2 | |
| 106. |
Cos(α - β) = |
| A. | cosαcosβ+sinαsinβ |
| B. | cosαcosβ+sinαsinβ |
| C. | sinαcosβ-cosαsinβ |
| D. | sinαcosβ+cosαsinβ |
| Answer» B. cosαcosβ+sinαsinβ | |
| 107. |
Sin(α - β) = |
| A. | cosαcosβ+sinαsinβ |
| B. | cosαcosβ+sinαsinβ |
| C. | sinαcosβ-cosαsinβ |
| D. | sinαcosβ+cosαsinβ |
| Answer» D. sinαcosβ+cosαsinβ | |
| 108. |
If \[\sin x+\sin y=3(\cos y-\cos x),\] then the value of \[\frac{\sin 3x}{\sin 3y}\] is |
| A. | 1 |
| B. | -1 |
| C. | 0 |
| D. | None of these |
| Answer» C. 0 | |
| 109. |
If \[\text{cosec }A+\cot A=\frac{11}{2},\] then \[\tan A=\] [Roorkee 1995] |
| A. | \[\frac{21}{22}\] |
| B. | \[\frac{15}{16}\] |
| C. | \[\frac{44}{117}\] |
| D. | \[\frac{117}{43}\] |
| Answer» D. \[\frac{117}{43}\] | |
| 110. |
If \[x+\frac{1}{x}=2\,\cos \theta ,\] then \[{{x}^{3}}+\frac{1}{{{x}^{3}}}=\] [MP PET 2004] |
| A. | \[\cos \,\,3\theta \] |
| B. | \[2\,\cos \,3\theta \] |
| C. | \[\frac{1}{2}\cos \,3\theta \] |
| D. | \[\frac{1}{3}\cos \,3\theta \] |
| Answer» C. \[\frac{1}{2}\cos \,3\theta \] | |
| 111. |
If \[\sin A=n\sin B,\] then \[\frac{n-1}{n+1}\tan \,\frac{A+B}{2}=\] |
| A. | \[\sin \frac{A-B}{2}\] |
| B. | \[\tan \frac{A-B}{2}\] |
| C. | \[\cot \frac{A-B}{2}\] |
| D. | None of these |
| Answer» C. \[\cot \frac{A-B}{2}\] | |
| 112. |
The value of \[\frac{\tan x}{\tan \,3x}\]whenever defined never lie between [Kurukshetra CEE 1998; IIT 1992] |
| A. | 1/3 and 3 |
| B. | 1/4and 4 |
| C. | 1/5 and 5 |
| D. | 5 and 6 |
| Answer» B. 1/4and 4 | |
| 113. |
\[{{\left( \frac{\cos A+\cos B}{\sin A-\sin B} \right)}^{n}}+{{\left( \frac{\sin A+\sin B}{\cos A-\cos B} \right)}^{n}}\](n even or odd) = |
| A. | \[2{{\tan }^{n}}\frac{A-B}{2}\] |
| B. | \[2{{\cot }^{n}}\frac{A-B}{2}\] |
| C. | \[0\] |
| D. | None of these |
| Answer» C. \[0\] | |
| 114. |
\[\sin 15{}^\circ +\cos 105{}^\circ =\] [MP PET 1992] |
| A. | 0 |
| B. | \[2\sin 15{}^\circ \] |
| C. | \[\cos 15{}^\circ +\sin 15{}^\circ \] |
| D. | \[\sin 15{}^\circ -\cos 15{}^\circ \] |
| Answer» B. \[2\sin 15{}^\circ \] | |
| 115. |
If \[\tan \theta -\cot \theta =a\] and \[\sin \theta +\cos \theta =b,\] then \[{{({{b}^{2}}-1)}^{2}}({{a}^{2}}+4)\] is equal to [WB JEE 1979] |
| A. | 2 |
| B. | -4 |
| C. | ± 4 |
| D. | 4 |
| Answer» E. | |
| 116. |
\[\cot x-\tan x=\] [MP PET 1986] |
| A. | \[\cot \,2x\] |
| B. | \[2{{\cot }^{2}}x\] |
| C. | \[2\,\,\cot \,2x\] |
| D. | \[{{\cot }^{2}}\,2x\] |
| Answer» D. \[{{\cot }^{2}}\,2x\] | |
| 117. |
If \[\tan A+\cot A=4,\]then \[{{\tan }^{4}}A+{{\cot }^{4}}A\] is equal to [Kerala (Engg.) 2002] |
| A. | 110 |
| B. | 191 |
| C. | 80 |
| D. | 194 |
| Answer» E. | |
| 118. |
The radius of the circle whose arc of length \[15cm\] makes an angle of 3/4 radian at the centre is [Karnataka CET 2002] |
| A. | \[10cm\] |
| B. | \[20\,cm\] |
| C. | \[11\frac{1}{4}cm\] |
| D. | \[22\frac{1}{2}cm\] |
| Answer» C. \[11\frac{1}{4}cm\] | |
| 119. |
If \[\sin \theta +\text{cosec}\theta =2,\] the value of \[{{\sin }^{10}}\theta +\text{cose}{{\text{c}}^{10}}\theta \] is [MP PET 2004] |
| A. | 10 |
| B. | \[{{2}^{10}}\] |
| C. | \[{{2}^{9}}\] |
| D. | 2 |
| Answer» E. | |
| 120. |
If \[\sin x+\text{cosec}\,x=2,\] then \[4\sin A\,\,\sin B\,\,\sin C\] is equal to [UPSEAT 2002] |
| A. | 2 |
| B. | \[{{2}^{n}}\] |
| C. | \[{{2}^{n-1}}\] |
| D. | \[{{2}^{n-2}}\] |
| Answer» B. \[{{2}^{n}}\] | |
| 121. |
If \[\left| \cos \,\theta \,\left\{ \sin \theta +\sqrt{{{\sin }^{2}}\theta +{{\sin }^{2}}\alpha } \right\}\, \right|\,\le k,\] then the value of k is |
| A. | \[\sqrt{1+{{\cos }^{2}}\alpha }\] |
| B. | \[\sqrt{1+{{\sin }^{2}}\alpha }\] |
| C. | \[\sqrt{2+{{\sin }^{2}}\alpha }\] |
| D. | \[\sqrt{2+{{\cos }^{2}}\alpha }\] |
| Answer» C. \[\sqrt{2+{{\sin }^{2}}\alpha }\] | |
| 122. |
If \[A+C=B,\] then \[\tan A\,\tan B\,\tan C=\] [EAMCET 1986] |
| A. | \[\tan A\,\tan B+\tan \,C\] |
| B. | \[\tan \,B-\tan \,C-\tan \,A\] |
| C. | \[\tan A+\tan C-\tan B\] |
| D. | \[-\,(\tan A\tan B+\tan C)\] |
| Answer» C. \[\tan A+\tan C-\tan B\] | |
| 123. |
If \[A+B+C=\pi \] and \[\cos A=\cos B\,\cos C,\] then \[\tan B\,\,\tan C\] is equal to [AMU 2001] |
| A. | \[\frac{1}{2}\] |
| B. | 2 |
| C. | 1 |
| D. | \[-\frac{1}{2}\] |
| Answer» C. 1 | |
| 124. |
If \[f(x)={{\cos }^{2}}x+{{\sec }^{2}}x,\] then[MNR 1986] |
| A. | \[f(x)<1\] |
| B. | \[f(x)=1\] |
| C. | \[1<f(x)<2\] |
| D. | \[f(x)\ge 2\] |
| Answer» E. | |
| 125. |
The value of \[\sin \theta +\cos \theta \] will be greatest when [MNR 1977, 1983; RPET 1995] |
| A. | \[\theta ={{30}^{o}}\] |
| B. | \[\theta ={{45}^{o}}\] |
| C. | \[\theta ={{60}^{o}}\] |
| D. | \[\theta ={{90}^{o}}\] |
| Answer» C. \[\theta ={{60}^{o}}\] | |
| 126. |
\[2\,{{\sin }^{2}}\beta +4\,\,\cos \,(\alpha +\beta )\,\,\sin \,\alpha \,\sin \,\beta +\cos \,2\,(\alpha +\beta )=\] [MNR 1993; IIT 1977] |
| A. | \[\sin \,\,2\alpha \] |
| B. | \[\cos \,\,2\beta \] |
| C. | \[\cos \,\,2\alpha \] |
| D. | \[\sin \,\,2\beta \] |
| Answer» D. \[\sin \,\,2\beta \] | |
| 127. |
If \[\tan \,(A+B)=p,\,\,\tan \,(A-B)=q,\] then the value of \[\tan \,2A\] in terms of p and q is [MP PET 1995, 2002] |
| A. | \[\frac{p+q}{p-q}\] |
| B. | \[\frac{p-q}{1+pq}\] |
| C. | \[\frac{p+q}{1-pq}\] |
| D. | \[\frac{1+pq}{1-p}\] |
| Answer» D. \[\frac{1+pq}{1-p}\] | |
| 128. |
\[\sqrt{2}+\sqrt{3}+\sqrt{4}+\sqrt{6}\] is equal to [IIT 1966, 1975] |
| A. | \[\cot 7\frac{{{1}^{o}}}{2}\] |
| B. | \[\sin 7\frac{{{1}^{o}}}{2}\] |
| C. | \[\sin \,{{15}^{o}}\] |
| D. | \[\cos \,\,{{15}^{o}}\] |
| Answer» B. \[\sin 7\frac{{{1}^{o}}}{2}\] | |
| 129. |
If \[2\sec 2\alpha =\tan \beta +\cot \beta ,\]then one of the values of \[\alpha +\beta \]is [Karnataka CET 2000] |
| A. | \[\frac{\pi }{4}\] |
| B. | \[\frac{\pi }{2}\] |
| C. | \[\pi \] |
| D. | \[2\pi \] |
| Answer» B. \[\frac{\pi }{2}\] | |
| 130. |
If \[\sin \alpha =1/\sqrt{5}\]and \[\sin \beta =3/5\],then \[\beta -\alpha \]lies in the interval [Roorkee Qualifying 1998] |
| A. | \[[0,\,\pi /4]\] |
| B. | \[[\pi /2,\,3\pi /4]\] |
| C. | \[[3\pi /4,\,\pi ]\] |
| D. | \[[\pi ,\,5\pi /4]\] |
| Answer» D. \[[\pi ,\,5\pi /4]\] | |
| 131. |
If \[x=\sin {{130}^{o}}\,\cos {{80}^{o}},\,\,y=\sin \,{{80}^{o}}\,\cos \,{{130}^{o}},\,\,z=1+xy,\]which one of the following is true [AMU 1999] |
| A. | \[x>0,\,\,y>0,\,\,z>0\] |
| B. | \[x>0,\,\,y<0,\,\,0<z<1\] |
| C. | \[x>0,\,\,y<0,\,\,z>1\] |
| D. | \[x<0,\,\,y<0,\,0<z<1\] |
| Answer» C. \[x>0,\,\,y<0,\,\,z>1\] | |
| 132. |
\[1+\cos \,{{56}^{o}}+\cos \,{{58}^{o}}-\cos {{66}^{o}}=\] [IIT 1964] |
| A. | \[2\,\cos {{28}^{o}}\,\cos \,{{29}^{o}}\,\cos \,{{33}^{o}}\] |
| B. | \[4\,\cos {{28}^{o}}\,\cos \,{{29}^{o}}\,\cos \,{{33}^{o}}\] |
| C. | \[4\,\cos {{28}^{o}}\,\cos \,{{29}^{o}}\,\sin {{33}^{o}}\] |
| D. | \[2\,\cos {{28}^{o}}\,\cos \,{{29}^{o}}\,\sin \,{{33}^{o}}\] |
| Answer» D. \[2\,\cos {{28}^{o}}\,\cos \,{{29}^{o}}\,\sin \,{{33}^{o}}\] | |
| 133. |
\[\sqrt{3}\,\text{cosec}\,{{20}^{o}}-\sec \,{{20}^{o}}=\] [IIT 1988] |
| A. | 2 |
| B. | \[\frac{2\,\sin {{20}^{o}}}{\sin {{40}^{o}}}\] |
| C. | 4 |
| D. | \[\frac{4\,\sin {{20}^{o}}}{\sin {{40}^{o}}}\] |
| Answer» D. \[\frac{4\,\sin {{20}^{o}}}{\sin {{40}^{o}}}\] | |