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MCQOPTIONS
This section includes 1900 Mcqs, each offering curated multiple-choice questions to sharpen your 9th Class knowledge and support exam preparation. Choose a topic below to get started.
| 901. |
If 4 tan A = 3, then the value of \[\frac{\mathbf{3co}{{\mathbf{s}}^{\mathbf{3}}}\mathbf{ A - 5 si}{{\mathbf{n}}^{\mathbf{3}}}\mathbf{ A}}{\mathbf{2cos A+5}}\] is _______ (where A is an acute angle) |
| A. | \[\frac{18}{275}\] |
| B. | \[\frac{19}{175}\] |
| C. | \[\frac{20}{105}\] |
| D. | \[\frac{19}{275}\] |
| E. | None of these |
| Answer» E. None of these | |
| 902. |
Simplify \[\frac{\mathbf{si}{{\mathbf{n}}^{\mathbf{2}}}\mathbf{30{}^\circ }\mathbf{.co}{{\mathbf{s}}^{\mathbf{2}}}\mathbf{ 30{}^\circ - ta}{{\mathbf{n}}^{\mathbf{2}}}\mathbf{30{}^\circ }\mathbf{.ta}{{\mathbf{n}}^{\mathbf{2}}}\mathbf{60{}^\circ }}{{{\mathbf{(sin 60{}^\circ + cos60{}^\circ )}}^{\mathbf{2}}}}\] |
| A. | \[\frac{-1}{2\sqrt{3}-4}\] |
| B. | \[\frac{-13(\sqrt{3}+2)}{4}\] |
| C. | \[\frac{1}{4+2\sqrt{3}}\] |
| D. | \[\frac{13}{8}(\sqrt{3}-2)\] |
| E. | None of these |
| Answer» E. None of these | |
| 903. |
\[Si{{n}^{\mathbf{4}}}\theta \text{ }+\text{ }Co{{s}^{\mathbf{4}}}\theta \]equals to__________ |
| A. | \[1+2\text{ }si{{n}^{2}}\theta \text{ }co{{s}^{2}}\theta \text{ }\] |
| B. | \[2\text{ }si{{n}^{2}}\theta \text{ }co{{s}^{2}}\theta \text{ }-\text{ }1\] |
| C. | \[1-2\text{ si}{{\text{n}}^{\text{2}}}\theta \text{ co}{{\text{s}}^{\text{2}}}\theta \] |
| D. | \[3+2si{{n}^{2}}\theta \text{ }co{{s}^{2}}\theta \] |
| E. | None of these |
| Answer» D. \[3+2si{{n}^{2}}\theta \text{ }co{{s}^{2}}\theta \] | |
| 904. |
If \[\mathbf{cos}\alpha =\mathbf{sin14}\,\alpha \] (where \[\mathbf{0}{}^\circ \mathbf{< 14}\alpha \mathbf{< 90{}^\circ }\]), then find the value of \[\mathbf{sin5}\alpha \mathbf{+cos}\left( \mathbf{12}\alpha -\mathbf{ 27{}^\circ } \right)\]\[-\,\mathbf{cosec}\left( \mathbf{3}\alpha \mathbf{+ 12{}^\circ } \right).\] |
| A. | \[\sqrt{2}\] |
| B. | \[\sqrt{2}-1\] |
| C. | \[\frac{\sqrt{2}-1}{2}\] |
| D. | \[\sqrt{2}+1\] |
| E. | None of these |
| Answer» D. \[\sqrt{2}+1\] | |
| 905. |
The value of cos\[\theta \] in terms of tan\[\theta \] is |
| A. | \[\frac{1}{\sqrt{1-{{\tan }^{2}}\theta }}\] |
| B. | \[\frac{1}{\sqrt{1+{{\tan }^{2}}\theta }}\] |
| C. | \[\frac{\sqrt{1-{{\tan }^{2}}\theta }}{\sqrt{1+{{\tan }^{2}}\theta }}\] |
| D. | \[\frac{1}{\sqrt{3-3{{\tan }^{2}}\theta }}\] |
| E. | None of these |
| Answer» C. \[\frac{\sqrt{1-{{\tan }^{2}}\theta }}{\sqrt{1+{{\tan }^{2}}\theta }}\] | |
| 906. |
If \[\frac{\mathbf{sin}\theta \mathbf{+cos}\theta }{\mathbf{sin}\theta -\mathbf{cos}\theta }\mathbf{=3}\] then the value of \[\mathbf{si}{{\mathbf{n}}^{\mathbf{4}}}\theta -\mathbf{co}{{\mathbf{s}}^{\mathbf{4}}}\theta \] |
| A. | \[\frac{4}{3}\] |
| B. | \[\frac{3}{4}\] |
| C. | \[\frac{5}{3}\] |
| D. | \[\frac{3}{5}\] |
| E. | None of these |
| Answer» E. None of these | |
| 907. |
If \[\mathbf{sin 2x=}\frac{\mathbf{2tan 30{}^\circ }}{\mathbf{1+ ta}{{\mathbf{n}}^{\mathbf{2}}}\mathbf{ 30}}\] , then the value of \[\frac{\mathbf{1}-\mathbf{ta}{{\mathbf{n}}^{\mathbf{2}}}\mathbf{x}}{\mathbf{1+ta}{{\mathbf{n}}^{\mathbf{2}}}\mathbf{x}}\]is equal to____ (where\[0{}^\circ |
| A. | Sin x |
| B. | Cos 3x |
| C. | 0 |
| D. | 1 |
| E. | None of these |
| Answer» B. Cos 3x | |
| 908. |
If\[\mathbf{cos}\,\mathbf{3}x\mathbf{=4}\,\mathbf{co}{{\mathbf{s}}^{\mathbf{3}}}\mathbf{30{}^\circ }-\mathbf{3co}{{\mathbf{s}}^{\mathbf{3}}}\mathbf{0{}^\circ }\]then the value of x is ________ |
| A. | 0 |
| B. | \[30{}^\circ \] |
| C. | \[20{}^\circ \] |
| D. | \[15{}^\circ \] |
| E. | None of these |
| Answer» C. \[20{}^\circ \] | |
| 909. |
If \[\mathbf{cot}\theta \,(\mathbf{1+sin}\theta )=\mathbf{2}\text{ }\mathbf{m}\] and \[\mathbf{cot}\theta ~\]\[(\mathbf{1}-\mathbf{sin}\theta )=\mathbf{2n}\] then \[{{\left( {{\mathbf{m}}^{\mathbf{2}}}-{{\mathbf{n}}^{\mathbf{2}}} \right)}^{\mathbf{2}}}\]equals to _________. |
| A. | 2 mm |
| B. | mn |
| C. | 4 mn |
| D. | 3mn |
| E. | None of these |
| Answer» D. 3mn | |
| 910. |
\[\frac{\mathbf{Si}{{\mathbf{n}}^{\mathbf{3}}}\theta \mathbf{+co}{{\mathbf{s}}^{\mathbf{3}}}\theta }{\mathbf{Sin}\theta \mathbf{(1-sin}\theta \mathbf{ cos}\theta \mathbf{)}}+\frac{\mathbf{si}{{\mathbf{n}}^{\mathbf{3}}}\theta \mathbf{-co}{{\mathbf{s}}^{\mathbf{3}}}\theta }{\mathbf{sin}\theta \mathbf{(1+sin}\theta \mathbf{cos}\theta \mathbf{)}}\]equals to ________ |
| A. | 2 sin\[\theta \] |
| B. | 2\[cos\,\theta \] |
| C. | 1 |
| D. | 2 |
| E. | None of these |
| Answer» E. None of these | |
| 911. |
\[\frac{{{\mathbf{(sin}\theta \mathbf{+cos}\theta \mathbf{)}}^{\mathbf{2}}}-\mathbf{3sin}\theta \mathbf{cos}\theta }{\mathbf{cos}\theta \mathbf{(sec}\theta -\mathbf{cosec}\theta \mathbf{)}}\], \[\frac{\mathbf{si}{{\mathbf{n}}^{\mathbf{2}}}\theta -\mathbf{co}{{\mathbf{s}}^{\mathbf{2}}}\theta }{\mathbf{si}{{\mathbf{n}}^{\mathbf{3}}}\theta \mathbf{+co}{{\mathbf{s}}^{\mathbf{3}}}\theta }\] is equal to________ |
| A. | \[cos\text{ }\theta\] |
| B. | sin \[\theta\] |
| C. | \[\tan \theta \] |
| D. | \[\cos \theta\] |
| E. | None of these |
| Answer» C. \[\tan \theta \] | |
| 912. |
\[\mathbf{cosec}\theta \left( \mathbf{sec}\theta -\mathbf{1} \right)-\mathbf{cot}\theta \text{ }\left( \mathbf{1}-\mathbf{cos}\,\theta \right)\]equals to _______ |
| A. | \[tan\text{ }\theta \text{ }+\text{ }sin\text{ }\theta \] |
| B. | \[tan\text{ }\theta \text{ }+\text{ }\cot \text{ }\theta \] |
| C. | \[tan\text{ }\theta \text{ }+\text{ }\cos \text{ }\theta \] |
| D. | \[tan\text{ }\theta \text{ }-\sin \text{ }\theta \] |
| E. | None of these |
| Answer» E. None of these | |
| 913. |
If \[\mathbf{sin}\alpha +\text{ }\mathbf{sin}\beta +\mathbf{sin}\gamma =\mathbf{3}\] then the value of \[\mathbf{si}{{\mathbf{n}}^{\mathbf{3}}}\alpha \mathbf{+si}{{\mathbf{n}}^{\mathbf{3}}}\beta \mathbf{+si}{{\mathbf{n}}^{\mathbf{3}}}\gamma -\mathbf{2sin}\alpha \mathbf{.sin}\beta \] \[-\,\mathbf{2sin}\beta \mathbf{sin}\gamma \mathbf{-2sin}\gamma \mathbf{.sin}\alpha \] is ________ |
| A. | \[-\]1 |
| B. | \[-\]2 |
| C. | \[-\]3 |
| D. | 0 |
| E. | None of these |
| Answer» D. 0 | |
| 914. |
The value of \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{sec}\theta }}\mathbf{co}{{\mathbf{s}}^{\mathbf{3}}}\theta \] \[\left[ \left( \mathbf{cos}\theta -\mathbf{sin}\theta {{)}^{\mathbf{2}}}\mathbf{+2sin}\theta \text{ }\mathbf{cos}\text{ }\theta \right) \right]\] is _______ |
| A. | 0 |
| B. | \[-\]1 |
| C. | 2 |
| D. | \[-\]3 |
| E. | None of these |
| Answer» E. None of these | |
| 915. |
If \[\mathbf{sin }\theta \mathbf{ =}\frac{\mathbf{p}}{\mathbf{q}}\] then \[\mathbf{cos}\theta \]equals to _________ |
| A. | \[\mathbf{ }\sqrt{{{q}^{2}}-{{p}^{2}}}\mathbf{ }\] |
| B. | \[\frac{\sqrt{{{q}^{2}}-{{p}^{2}}}}{q}\] |
| C. | \[\sqrt{{{p}^{2}}-{{q}^{2}}}\] |
| D. | \[\frac{\sqrt{{{p}^{2}}+{{q}^{2}}}}{q}\] |
| E. | None of these |
| Answer» C. \[\sqrt{{{p}^{2}}-{{q}^{2}}}\] | |
| 916. |
If \[\mathbf{sin}\theta \text{ }+\text{ }\mathbf{cos}\text{ }\theta =\text{ }\mathbf{p}\], then the value of \[\mathbf{si}{{\mathbf{n}}^{\mathbf{6}}}\theta \mathbf{+co}{{\mathbf{s}}^{\mathbf{6}}}\theta \] equals to _________ |
| A. | \[\frac{4+3({{p}^{2}}-1)}{4}\] |
| B. | \[\frac{4-3{{({{p}^{2}}-1)}^{2}}}{4}\] |
| C. | \[4-3\left( {{p}^{2}}-1 \right)~~~~~~~~~~~~~~~~~\] |
| D. | \[4-3{{\left( {{p}^{2}}-1 \right)}^{2}}\] |
| E. | None of these |
| Answer» C. \[4-3\left( {{p}^{2}}-1 \right)~~~~~~~~~~~~~~~~~\] | |
| 917. |
The value of \[log\,\,\cos 0{}^\circ +\log \,\,\cos 1{}^\circ +\] \[\log \,\,\cos 2{}^\circ +\_\_\_\_\_\_+log\,cos90{}^\circ \] is equal to _________ |
| A. | 1 |
| B. | \[-\]1 |
| C. | 0 |
| D. | Undefined |
| E. | None of these |
| Answer» E. None of these | |
| 918. |
If \[\mathbf{A=}\frac{\mathbf{1}}{\mathbf{1+sin }\theta }\mathbf{+}\frac{\mathbf{1}}{\mathbf{1-sin }\theta }\], then A equals to _________ . |
| A. | \[{{\sec }^{2}}\theta \] |
| B. | \[2{{\sec }^{2}}\theta \] |
| C. | \[{{\cos }^{2}}\theta \] |
| D. | \[2{{\cos }^{2}}\theta \] |
| E. | None of these |
| Answer» C. \[{{\cos }^{2}}\theta \] | |
| 919. |
If \[\mathbf{cosec }\theta \mathbf{-cot }\theta \mathbf{=3}\] then find the positive value of\[\mathbf{cos}\text{ }\theta \]. |
| A. | \[\,\frac{4}{5}\] |
| B. | 1 |
| C. | 0 |
| D. | 2 |
| E. | None of these |
| Answer» C. 0 | |
| 920. |
Which among the following statements is/ are true? |
| A. | The value of \[sin\text{ }\theta \]decreases as \[\theta \] increases. \[(when\text{ }0{}^\circ <\theta <90{}^\circ )\] |
| B. | The value of \[cos\text{ }\theta \] increases \[(when\text{ }0{}^\circ <\theta <90{}^\circ )\] |
| C. | \[Sin\text{ }\left( A\text{ }+\text{ }B \right)\text{ }=\text{ }sin~A.\cos B\] |
| D. | The value of tan \[\theta \]is always greater than \[sin\text{ }\theta .\] |
| E. | None of these |
| Answer» C. \[Sin\text{ }\left( A\text{ }+\text{ }B \right)\text{ }=\text{ }sin~A.\cos B\] | |
| 921. |
Find the value of\[\frac{{{\mathbf{k}}^{\mathbf{2}}}\mathbf{-1}}{{{\mathbf{k}}^{\mathbf{2}}}\mathbf{+1}}\]if\[\mathbf{k}=\mathbf{sec}\theta -\mathbf{tan}\theta \]. |
| A. | \[Sin\text{ }\theta \] |
| B. | \[Cos\text{ }\theta \] |
| C. | \[-Sin\text{ }\theta \] |
| D. | \[-Cos\text{ }\theta \] |
| E. | None of these |
| Answer» D. \[-Cos\text{ }\theta \] | |
| 922. |
In a \[\Delta \,\mathbf{PQR}\], \[\angle Q\] is a right angle and QT is a perpendicular drawn on PR. If PR = 15 cm and QT = 5 cm, then the value of \[\frac{\mathbf{tan}\,\mathbf{P+tan}\,\mathbf{R}}{\mathbf{tan}\,\mathbf{R}\,\mathbf{.}\,\mathbf{tan}\,\mathbf{P}}\] is _________ |
| A. | \[\frac{1}{3}\] |
| B. | 2 |
| C. | \[\frac{1}{2}\] |
| D. | 3 |
| E. | None of these |
| Answer» E. None of these | |
| 923. |
Simplify: \[\frac{\mathbf{3 sin 67{}^\circ }}{\mathbf{5 cos 23{}^\circ }}\mathbf{+}\frac{\mathbf{5}}{\mathbf{2}}\frac{\mathbf{Sec39{}^\circ }\mathbf{.cos51{}^\circ }}{\mathbf{(1+co}{{\mathbf{t}}^{\mathbf{2}}}\mathbf{ 51)}}\mathbf{+}\frac{\mathbf{8}}{\mathbf{9}}\]\[\mathbf{(cose}{{\mathbf{c}}^{\mathbf{2}}}\mathbf{42{}^\circ }-\mathbf{ta}{{\mathbf{n}}^{\mathbf{2}}}\mathbf{48{}^\circ )}\] |
| A. | \[3\frac{89}{90}\] |
| B. | \[2\frac{81}{90}\] |
| C. | \[cos\text{ }67{}^\text{o}+\,sec\text{ }39{}^\text{o}\] |
| D. | \[\frac{3}{5}\cos 67{}^\circ +\frac{5}{2}\sec 51{}^\circ +\frac{8}{9}{{\cot }^{2}}\text{48}{}^\circ \] |
| E. | None of these |
| Answer» B. \[2\frac{81}{90}\] | |
| 924. |
For \[\mathbf{0{}^\circ } |
| A. | \[Sin\text{ }\theta -cos\text{ }\theta =0\] |
| B. | \[Sin\text{ }\theta +cos\text{ }\theta =0\] |
| C. | \[\theta =45{}^\circ \] |
| D. | \[Sin\text{ }2\theta =2\text{ }cos\left( \theta +15 \right)\] |
| E. | None of these |
| Answer» C. \[\theta =45{}^\circ \] | |
| 925. |
The value of \[\mathbf{tan}\,\mathbf{10}{}^\circ .\mathbf{tan}\text{ }\mathbf{20}{}^\circ .\mathbf{tan}\,\mathbf{30}{}^\circ .\mathbf{tan}\,\mathbf{45}{}^\circ .\]\[\mathbf{tan}\,\mathbf{60}{}^\circ .\mathbf{tan}\,\mathbf{70}{}^\circ .\mathbf{tan}\,\mathbf{80}{}^\circ \]is: |
| A. | 0 |
| B. | \[-\]1 |
| C. | 1 |
| D. | 2 |
| E. | None of these |
| Answer» D. 2 | |
| 926. |
If \[\theta \] is an acute angle and 4\[\mathbf{cos}\theta \mathbf{+4}\sqrt{\mathbf{3}}\] \[\mathbf{sin}\theta =\mathbf{8}\text{ }\mathbf{sin}\theta \text{ }\mathbf{cos}\theta +2-\sqrt{3}\], then which one among the following is correct? |
| A. | \[sin \theta =\frac{\sqrt{3}}{2}\] |
| B. | \[\cos \theta =\frac{1}{2}\] |
| C. | \[\theta =30{}^\circ \] |
| D. | \[\tan \theta =\sqrt{3}\] |
| E. | None of these |
| Answer» D. \[\tan \theta =\sqrt{3}\] | |
| 927. |
If \[\left( {{p}^{2}}-{{q}^{2}} \right)~~\] \[\mathbf{sin}\theta +\text{ }\mathbf{2pq}\text{ }\mathbf{cos}\text{ }\theta =\text{ }{{\mathbf{p}}^{\mathbf{2}}}-\text{ }{{\mathbf{q}}^{\mathbf{2}}}\], then the value of tan\[\theta \] is ________ |
| A. | \[\frac{p+q}{2pq}\] |
| B. | \[\frac{p-q}{2pq}\] |
| C. | \[\frac{{{p}^{2}}-{{q}^{2}}}{2pq}\] |
| D. | \[\frac{{{p}^{2}}+{{q}^{2}}}{2pq}\] |
| E. | None of these |
| Answer» D. \[\frac{{{p}^{2}}+{{q}^{2}}}{2pq}\] | |
| 928. |
If \[\mathbf{2 sin }\alpha \mathbf{=}\sqrt{\mathbf{3}}\] then \[\frac{\mathbf{ta}{{\mathbf{n}}^{\mathbf{2}}}\alpha \mathbf{+3}\mathbf{.cot}\alpha }{\mathbf{co}{{\mathbf{t}}^{\mathbf{2}}}\alpha \mathbf{+2tan}\alpha }\] is equal to ______ (where \[\alpha \] is an acute angle) |
| A. | \[\frac{3(\sqrt{3}+1)}{1+6\sqrt{3}}\] |
| B. | \[\frac{-\,45-51\sqrt{3}}{-107}\] |
| C. | \[\frac{50\sqrt{3}+45}{-106}\] |
| D. | \[\frac{-\,51\sqrt{3}}{107}\] |
| E. | None of these |
| Answer» C. \[\frac{50\sqrt{3}+45}{-106}\] | |
| 929. |
In a \[\Delta \text{ }\mathbf{PQR}\], right-angled at Q, and if PR \[-\] QR 2 cm and PQ = 10 cm then _______ |
| A. | \[cosec\text{ }R\text{ }=\frac{13}{12}\] |
| B. | \[sec\text{ }R\text{ }=\frac{13}{5}\] |
| C. | \[\tan \text{ }P\text{ }=\frac{12}{5}\] |
| D. | All the above |
| E. | None of these |
| Answer» E. None of these | |
| 930. |
\[\frac{\mathbf{Sin 75{}^\circ }\mathbf{.cos 25{}^\circ }\mathbf{.tan 50{}^\circ }}{\mathbf{Sin 65{}^\circ }\mathbf{.cos15{}^\circ }\mathbf{.cot40{}^\circ }}\] |
| A. | 1 |
| B. | \[\mathbf{~}\frac{1}{2}\] |
| C. | \[\mathbf{~}\frac{1}{3}\] |
| D. | \[\mathbf{~}\frac{1}{4}\] |
| E. | None of these |
| Answer» B. \[\mathbf{~}\frac{1}{2}\] | |
| 931. |
The value of \[\mathbf{cot 5{}^\circ }\mathbf{.cot 15{}^\circ }\mathbf{.cot}\text{ }\mathbf{25{}^\circ }\mathbf{.cot 35{}^\circ }\mathbf{.cot45}{}^\circ \]\[\mathbf{.cot 55{}^\circ }\mathbf{.cot}\mathbf{.65{}^\circ }\mathbf{.cot 75{}^\circ }\mathbf{.cot 85{}^\circ }\]is _____. |
| A. | \[\sqrt{3}\] |
| B. | \[\frac{1}{\sqrt{3}}\] |
| C. | 1 |
| D. | \[2\sqrt{3}\] |
| E. | None of these |
| Answer» D. \[2\sqrt{3}\] | |
| 932. |
If\[\mathbf{m=sin}\theta \mathbf{+cos}\theta \] and \[\mathbf{n = sin }\theta \mathbf{ -cos }\theta \], then which of the following is true? |
| A. | \[{{m}^{2}}+{{n}^{2}}=2\] |
| B. | \[{{m}^{2}}+{{n}^{2}}=1\] |
| C. | \[{{m}^{2}}-{{n}^{2}}=1\] |
| D. | \[{{m}^{2}}+{{n}^{2}}=3\] |
| E. | None of these |
| Answer» B. \[{{m}^{2}}+{{n}^{2}}=1\] | |
| 933. |
Simplified form of \[\left( \mathbf{1 + co}{{\mathbf{t}}^{\mathbf{2}}}\theta \right)\mathbf{ }\left( \mathbf{1 - cos }\theta \right)\mathbf{ }\left( \mathbf{1 + cos }\theta \right)\]is ______ |
| A. | 1 |
| B. | 0 |
| C. | \[Cosec\text{ }\theta ~~~~~\] |
| D. | \[Sin\text{ }\theta ~~~~~~~~\] |
| E. | None of these |
| Answer» B. 0 | |
| 934. |
If \[\mathbf{tan }\theta \mathbf{=}{{\sqrt{\mathbf{3}}}^{{}}}\]then find the value of\[\mathbf{si}{{\mathbf{n}}^{\mathbf{2}}}\theta \mathbf{-co}{{\mathbf{s}}^{\mathbf{2}}}\theta \], where \[\theta \] is acute angle. |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{-1}{3}\] |
| C. | \[\frac{-1}{2}\] |
| D. | \[\frac{1}{4}\] |
| E. | None of these |
| Answer» B. \[\frac{-1}{3}\] | |
| 935. |
If \[\mathbf{sin}\theta -\mathbf{cos}\theta =\mathbf{0}\], then find the value of \[\mathbf{(si}{{\mathbf{n}}^{\mathbf{4}}}\theta \mathbf{+co}{{\mathbf{s}}^{\mathbf{4}}}\theta \mathbf{)}\], where \[\theta \] is a, acute angle. |
| A. | \[\frac{1}{3}\] |
| B. | \[\frac{\sqrt{2}}{4}\] |
| C. | \[\frac{1}{2}\] |
| D. | \[\frac{\sqrt{2}}{2}\] |
| E. | None of these |
| Answer» D. \[\frac{\sqrt{2}}{2}\] | |
| 936. |
The value of \[\mathbf{sin}\,\mathbf{45}{}^\circ .\,\mathbf{cos}\,\mathbf{30}{}^\circ -\mathbf{cos}\,\mathbf{45}{}^\circ .\,\mathbf{sin}\,\mathbf{30}{}^\circ \] is equal to _________ |
| A. | \[\frac{\sqrt{3}+1}{2}\] |
| B. | \[\frac{\sqrt{6}-\sqrt{2}}{4}\] |
| C. | \[\frac{\sqrt{2}}{4}(\sqrt{3}+\sqrt{2})\] |
| D. | \[\frac{\sqrt{6}-\sqrt{2}}{2\sqrt{2}}\] |
| E. | None of these |
| Answer» C. \[\frac{\sqrt{2}}{4}(\sqrt{3}+\sqrt{2})\] | |
| 937. |
If \[l||m\]and\[l\bot n\], identify the correct option. |
| A. | \[l||n\] |
| B. | \[m\bot n\] |
| C. | \[m||n\] |
| D. | \[m\bot l\] |
| Answer» C. \[m||n\] | |
| 938. |
Which of the following describe a surface? |
| A. | Length and Breadth |
| B. | Length only |
| C. | Breadth only |
| D. | Length and Height |
| Answer» B. Length only | |
| 939. |
How many points does a line contain? |
| A. | Two |
| B. | Three |
| C. | Four |
| D. | Infinitely many |
| Answer» E. | |
| 940. |
In the figure given, if\[AC=BD\], what is the measure of\[AB\]? |
| A. | \[AD\] |
| B. | \[BD\] |
| C. | \[CD\] |
| D. | \[AC\] |
| Answer» D. \[AC\] | |
| 941. |
If \[AC=PQ\] and\[CP=BQ\], find the midpoint of the line segment\[AB\]. |
| A. | \[P\] |
| B. | \[Q\] |
| C. | \[C\] |
| D. | \[B\] |
| Answer» B. \[Q\] | |
| 942. |
If \[C\] is the mid-point of the line segment \[AB,\,\,D\] and \[E\] are the mid-points of the segments \[AC\] and \[BC\] respectively, what is the length of\[AC\]? |
| A. | \[4AD\] |
| B. | \[3AD\] |
| C. | \[2AD\] |
| D. | \[AD\] |
| Answer» D. \[AD\] | |
| 943. |
Which of the following is true about two distinct lines? |
| A. | Always intersect. |
| B. | Always either intersect or are parallel. |
| C. | Always have two common points. |
| D. | Always parallel. |
| Answer» C. Always have two common points. | |
| 944. |
If a point \[A\] lies in between \[B\] and\[C\], which of the following is true? |
| A. | \[BC=\frac{1}{2}AC\] |
| B. | \[BC=\frac{1}{2}AB\] |
| C. | \[AC=BC\] |
| D. | \[AB+AC=BC\] |
| Answer» E. | |
| 945. |
Things which are ________ of the same things are equal to one another. |
| A. | Parallel |
| B. | Not equal |
| C. | Halves |
| D. | Triple |
| Answer» D. Triple | |
| 946. |
If \[C\] is the midpoint of the line segment \[AB,\,\,D\] and \[E\] are midpoints of the segments \[AC\] and \[BC\] respectively, what is the length of\[AB\]? |
| A. | \[2\,\,AD\] |
| B. | \[4\,\,BC\] |
| C. | \[4\,\,BE\] |
| D. | \[2\,\,CD\] |
| Answer» D. \[2\,\,CD\] | |
| 947. |
How many common points do two distinct lines in a plane have? |
| A. | Two points |
| B. | Three points |
| C. | One point |
| D. | Four points |
| Answer» D. Four points | |
| 948. |
Two distinct parallel lines have how many common points? |
| A. | No |
| B. | One |
| C. | Two |
| D. | Three |
| Answer» B. One | |
| 949. |
\[ABCD\] are the four points on a line. If\[AD=BC\], which of the following has its length the same as\[BD\]? |
| A. | \[AD\] |
| B. | \[BC\] |
| C. | \[AC\] |
| D. | \[CD\] |
| Answer» D. \[CD\] | |
| 950. |
If \[X,\,\,Y,\,\,Z\] are the three points on a line and \[Y\] lies between \[X\] and\[Z\], which of the following is true? |
| A. | \[XY+YZ=XZ\] |
| B. | \[XY+XZ=YZ\] |
| C. | \[XZ+YZ=XY\] |
| D. | \[\frac{1}{2}(XY+YZ)=XZ\] |
| Answer» B. \[XY+XZ=YZ\] | |