MCQOPTIONS
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MCQOPTIONS
This section includes 62 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
The value of \[\frac{\mathbf{10}{{\mathbf{0}}^{\mathbf{98}}}\mathbf{+10}{{\mathbf{0}}^{\mathbf{100}}}}{\mathbf{10}{{\mathbf{0}}^{\mathbf{98}}}}\]+1 is equal to________. |
| A. | 10001 |
| B. | 10002 |
| C. | 1001 |
| D. | 1002 |
| E. | None of these |
| Answer» C. 1001 | |
| 2. |
If \[\mathbf{m = }{{\mathbf{7}}^{\mathbf{-}}}^{\mathbf{7}}\mathbf{- }{{\mathbf{7}}^{\mathbf{7}}}\mathbf{and n = }{{\mathbf{7}}^{\mathbf{7}}}\mathbf{- }{{\mathbf{7}}^{\mathbf{-}}}^{\mathbf{7}}\], then find the value of \[\frac{\mathbf{m}}{\mathbf{n}}\mathbf{-}\frac{\mathbf{n}}{\mathbf{m}}\]. |
| A. | 1 |
| B. | 2 |
| C. | 0 |
| D. | -1 |
| E. | None of these |
| Answer» D. -1 | |
| 3. |
Find the unit's digit in the product of \[\frac{{{2}^{32}}\times {{3}^{42}}\times {{847}^{42}}}{{{9}^{14}}}\]. |
| A. | 9 |
| B. | 6 |
| C. | 3 |
| D. | 1 |
| E. | None of these |
| Answer» C. 3 | |
| 4. |
Simplify \[{{\left( \frac{{{a}^{-2}}}{{{b}^{-2}}} \right)}^{-3}}\left( \frac{{{a}^{-3}}}{{{b}^{-5}}} \right)\] |
| A. | \[\frac{1}{{{b}^{2}}}\] |
| B. | \[\frac{{{a}^{3}}}{{{b}^{11}}}\] |
| C. | \[\frac{a}{b}\] |
| D. | \[\frac{{{a}^{2}}}{{{b}^{3}}}\] |
| Answer» C. \[\frac{a}{b}\] | |
| 5. |
Evaluate \[{{\left[ {{\left( \sqrt{\frac{2}{3}} \right)}^{2}}-\sqrt[3]{\frac{8}{27}} \right]}^{1000}}\] |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | -1 |
| Answer» B. 1 | |
| 6. |
If \[x={{\left( \frac{3}{2} \right)}^{2}}\times {{\left( \frac{2}{3} \right)}^{-4}}\], find the value of \[{{x}^{2}}\]. |
| A. | \[{{\left( \frac{4}{3} \right)}^{12}}\] |
| B. | \[{{\left( \frac{2}{3} \right)}^{12}}\] |
| C. | \[{{\left( \frac{3}{2} \right)}^{12}}\] |
| D. | \[{{\left( \frac{3}{4} \right)}^{12}}\] |
| Answer» C. \[{{\left( \frac{3}{2} \right)}^{12}}\] | |
| 7. |
Evaluate \[{{\left\{ {{\left( \frac{3}{4} \right)}^{-1}}-{{\left( \frac{1}{4} \right)}^{-1}} \right\}}^{-1}}\]. |
| A. | \[\frac{3}{16}\] |
| B. | \[\frac{-3}{8}\] |
| C. | \[\frac{16}{3}\] |
| D. | \[\frac{-8}{3}\] |
| Answer» C. \[\frac{16}{3}\] | |
| 8. |
Simplify \[\frac{{{(16{{a}^{2}})}^{\frac{1}{2}}}\times {{(36\,{{a}^{4}})}^{\frac{-1}{2}}}}{2{{a}^{\frac{1}{2}}}\times 5{{a}^{\frac{3}{2}}}\times 8{{a}^{\frac{9}{4}}}}\]. |
| A. | \[120\,\,{{a}^{\frac{25}{4}}}\] |
| B. | \[\frac{1}{120\,{{a}^{\frac{25}{4}}}}\] |
| C. | \[24{{a}^{\frac{-25}{4}}}\] |
| D. | \[24{{a}^{\frac{25}{4}}}\] |
| Answer» C. \[24{{a}^{\frac{-25}{4}}}\] | |
| 9. |
Mr Gupta asked two of his students to solve the expression \[{{\left( \frac{9{{a}^{3}}{{b}^{-8}}}{81{{a}^{-5}}{{b}^{2}}} \right)}^{-\frac{1}{2}}}\]and write the answer on blackboard. Aryan wrote the answer as \[3{{a}^{-4}}{{b}^{5}}\] whereas Ayan wrote the answer as \[\frac{3{{b}^{5}}}{{{a}^{4}}}\].Who wrote the correct answer? |
| A. | Aryan |
| B. | Ayan |
| C. | Both of them |
| D. | None of these |
| Answer» D. None of these | |
| 10. |
Find the value of \[{{16}^{\frac{3}{4}}}\times {{4}^{\frac{-1}{2}}}.\] |
| A. | \[8\] |
| B. | \[1\] |
| C. | 4 |
| D. | \[0\] |
| Answer» D. \[0\] | |
| 11. |
If \[x={{\left( \frac{3}{2} \right)}^{2}}\times {{\left( \frac{2}{3} \right)}^{-4}}\]then value of \[{{\mathbf{x}}^{\mathbf{2}}}\]is |
| A. | \[{{\left( \frac{2}{3} \right)}^{11}}\] |
| B. | \[{{\left( \frac{2}{3} \right)}^{12}}\] |
| C. | \[{{\left( \frac{2}{3} \right)}^{7}}\] |
| D. | \[{{\left( \frac{2}{3} \right)}^{3}}\] |
| Answer» C. \[{{\left( \frac{2}{3} \right)}^{7}}\] | |
| 12. |
\[{{\left( \frac{5}{7} \right)}^{5}}\]can be written as |
| A. | \[{{\left( \frac{7}{5} \right)}^{5}}\] |
| B. | \[{{\left( 57 \right)}^{6}}\] |
| C. | \[\frac{{{5}^{5}}}{{{7}^{5}}}\] |
| D. | \[{{\left( {{5}^{5}} \right)}^{7}}\] |
| Answer» D. \[{{\left( {{5}^{5}} \right)}^{7}}\] | |
| 13. |
\[{{\left\{ {{3}^{-2}}+{{\left( \frac{3}{2} \right)}^{-2}} \right\}}^{-1}}=?\] |
| A. | \[{}^{81}/{}_{4}\] |
| B. | \[{}^{5}/{}_{9}\] |
| C. | \[\frac{9}{5}\] |
| D. | \[\frac{4}{81}\] |
| Answer» D. \[\frac{4}{81}\] | |
| 14. |
Simplify and leave the answer in exponent form\[{{\left( \frac{3}{5} \right)}^{-30}}\times {{\left( \frac{5}{3} \right)}^{-30}}\]. |
| A. | \[\frac{3}{5}\] |
| B. | \[{{1}^{1}}\] |
| C. | \[{{\left( \frac{3}{5} \right)}^{-60}}\] |
| D. | \[{{\left( \frac{5}{3} \right)}^{-60}}\] |
| Answer» C. \[{{\left( \frac{3}{5} \right)}^{-60}}\] | |
| 15. |
Simplify\[\frac{{{\left( 9{{m}^{2}} \right)}^{1/3}}}{{{6}^{4}}}\times \frac{{{\left( 4{{n}^{2}} \right)}^{1/3}}}{5m}\]. |
| A. | \[\frac{1}{5}{{\left[ \frac{{{n}^{2}}}{m{{6}^{10}}} \right]}^{1/3}}\] |
| B. | \[\frac{1}{5}{{\left[ \frac{n}{{{m}^{2}}{{6}^{10}}} \right]}^{1/3}}\] |
| C. | \[\frac{1}{5}{{\left[ \frac{{{n}^{2}}}{m{{6}^{-10}}} \right]}^{1/3}}\] |
| D. | \[\frac{1}{5}{{\left[ \frac{{{n}^{2}}}{m{{6}^{10}}} \right]}^{2/3}}\] |
| Answer» B. \[\frac{1}{5}{{\left[ \frac{n}{{{m}^{2}}{{6}^{10}}} \right]}^{1/3}}\] | |
| 16. |
If \[\frac{x}{y}={{\left( \frac{6}{7} \right)}^{3}}\div {{\left( \frac{7}{6} \right)}^{-3}},\] then the value of \[{{\left( \frac{x}{y} \right)}^{-10}}\] is |
| A. | 1 |
| B. | 0 |
| C. | \[-1\] |
| D. | Cannot be determined |
| Answer» B. 0 | |
| 17. |
The value \[\frac{{{\left( -\frac{1}{2} \right)}^{5}}}{{{\left( -\frac{1}{2} \right)}^{4}}}\div \frac{\left( -\frac{1}{8} \right)}{\left( -\frac{1}{4} \right)}\] is |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | \[-1\] |
| Answer» E. | |
| 18. |
Express \[\frac{729\times 64}{270}\] as a product of prime factors in exponential form. |
| A. | \[\frac{{{2}^{6}}\times {{3}^{4}}}{27}\] |
| B. | \[\frac{{{2}^{5}}\times {{3}^{3}}}{5}\] |
| C. | \[\frac{{{2}^{5}}\times {{3}^{3}}}{{{5}^{3}}}\] |
| D. | \[\frac{{{2}^{6}}\times {{3}^{2}}}{{{5}^{2}}}\] |
| Answer» C. \[\frac{{{2}^{5}}\times {{3}^{3}}}{{{5}^{3}}}\] | |
| 19. |
The value \[\frac{{{\left( -\frac{1}{2} \right)}^{5}}}{\left( -\frac{1}{2} \right)}\div \frac{\left( -\frac{1}{8} \right)}{\left( -\frac{1}{4} \right)}\]is |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | \[-1\] |
| Answer» E. | |
| 20. |
Express \[\frac{729\times 64}{270}\] as a product of prime factors in a exponential form. |
| A. | \[\frac{{{2}^{6}}\times {{3}^{4}}}{27}\] |
| B. | \[\frac{{{2}^{5}}\times {{3}^{3}}}{5}\] |
| C. | \[\frac{{{2}^{5}}\times {{3}^{3}}}{{{5}^{3}}}\] |
| D. | \[\frac{{{2}^{6}}\times {{3}^{2}}}{{{5}^{2}}}\] |
| Answer» C. \[\frac{{{2}^{5}}\times {{3}^{3}}}{{{5}^{3}}}\] | |
| 21. |
Simplify and leave the answer in the exponent form\[{{\left( \frac{3}{5} \right)}^{-30}}\times {{\left( \frac{5}{3} \right)}^{-30}}.\] |
| A. | \[\frac{3}{5}\] |
| B. | \[{{1}^{1}}\] |
| C. | \[{{\left( \frac{3}{5} \right)}^{-60}}\] |
| D. | \[{{\left( \frac{5}{3} \right)}^{-60}}\] |
| Answer» C. \[{{\left( \frac{3}{5} \right)}^{-60}}\] | |
| 22. |
What is the result of\[\frac{{{2}^{1}}\times {{3}^{2}}\times {{3}^{3}}}{{{1}^{2}}\times {{4}^{2}}}?\] |
| A. | \[\frac{243}{8}\] |
| B. | \[42\] |
| C. | \[\frac{46}{16}\] |
| D. | \[48\] |
| Answer» B. \[42\] | |
| 23. |
Find the numerical value of\[{{\left( 4096 \right)}^{\frac{-1}{4}}}.\] |
| A. | 16 |
| B. | 8 |
| C. | 4 |
| D. | 1 |
| Answer» E. | |
| 24. |
Find the value of \[{{(16)}^{0.16}}\times {{(16)}^{0.09}}.\] |
| A. | 1 |
| B. | 2 |
| C. | |
| D. | 3 |
| Answer» C. | |
| 25. |
Find the value of \[{{(-1)}^{2013}}.\] |
| A. | 0 |
| B. | -1 |
| C. | |
| D. | 2 |
| Answer» C. | |
| 26. |
What is the value of \[{{20}^{-3}}\times {{25}^{2}}\times {{20}^{3}}\times {{25}^{-4}}?\] |
| A. | \[\frac{1}{625}\] |
| B. | \[\frac{1}{400}\] |
| C. | |
| D. | 625 |
| Answer» B. \[\frac{1}{400}\] | |
| 27. |
Solve for \[\mathbf{x},\text{ }{{\left( \mathbf{243} \right)}^{\mathbf{x+5}}}=\text{ }{{\left( \mathbf{2187} \right)}^{\mathbf{3x-1}}}\] |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| E. | None of these |
| Answer» D. 3 | |
| 28. |
The least integer value of a which satisfies \[{{\mathbf{a}}^{\mathbf{4}}}>\text{ }\mathbf{2400}\] is _________. |
| A. | 7 |
| B. | 6 |
| C. | 5 |
| D. | 8 |
| E. | None of these |
| Answer» B. 6 | |
| 29. |
If\[{{\mathbf{x}}^{{{\mathbf{(3+m)}}^{\mathbf{2}}}}}\mathbf{\times }\,\,{{\mathbf{x}}^{\mathbf{3-m}}}^{^{\mathbf{2}}}\mathbf{ }{{\mathbf{x}}^{\mathbf{24}}}\], then value of m is ___________. |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| E. | None of these |
| Answer» D. 3 | |
| 30. |
Which among the following is the ascending order of\[{{2}^{1024}},\text{ }{{5}^{512}},\text{ }{{7}^{256}}\text{ }and\text{ }{{81}^{128}}.~~~\] |
| A. | \[{{5}^{512}}>\text{ }{{2}^{1024}}>\text{ }{{7}^{256}}>\text{ }{{81}^{128}}\] |
| B. | \[{{7}^{256}}<\text{ }{{81}^{128}}<\text{ }{{2}^{1024}}<\text{ }{{5}^{512}}\] |
| C. | \[{{7}^{256}}<\text{ }{{81}^{128}}<\text{ }{{5}^{512}}<\text{ }{{2}^{1024}}\] |
| D. | \[{{2}^{1024}}>\text{ }{{5}^{512}}>\text{ }{{81}^{128}}>\text{ }{{7}^{256}}\] |
| E. | None of these |
| Answer» C. \[{{7}^{256}}<\text{ }{{81}^{128}}<\text{ }{{5}^{512}}<\text{ }{{2}^{1024}}\] | |
| 31. |
If \[{{8}^{m}}\] = 262144, then find the value of\[{{8}^{m-4}}\]. |
| A. | 32 |
| B. | 96 |
| C. | 512 |
| D. | 64 |
| E. | None of these |
| Answer» E. None of these | |
| 32. |
If \[{{\mathbf{p}}^{\mathbf{q}}}=\text{ }{{\mathbf{q}}^{\mathbf{p}}}\] then find\[{{\mathbf{p}}^{\mathbf{3}}}+\text{ }{{\mathbf{q}}^{\mathbf{3}}}\], where p and q are distinct natural numbers. |
| A. | 72 |
| B. | 152 |
| C. | 208 |
| D. | 728 |
| E. | None of these |
| Answer» B. 152 | |
| 33. |
Write \[a\times a\times a\times c\times c\times c\times c\times d\times d\] in exponential form. |
| A. | \[{{a}^{3}}{{c}^{3}}{{d}^{3}}\] |
| B. | \[{{a}^{3}}{{c}^{3}}d\] |
| C. | \[{{a}^{3}}{{c}^{3}}{{d}^{2}}\] |
| D. | \[{{a}^{3}}{{c}^{4}}{{d}^{2}}\] |
| Answer» E. | |
| 34. |
Simplify \[{{\left( 5a{{n}^{-2}} \right)}^{-1}}\] |
| A. | \[\frac{{{n}^{2}}}{5a}\] |
| B. | \[\frac{n}{5a}\] |
| C. | \[\frac{{{n}^{3}}}{5a}\] |
| D. | \[\frac{{{n}^{4}}}{5a}\] |
| Answer» B. \[\frac{n}{5a}\] | |
| 35. |
How much is \[{{(0.04)}^{-1.5}}\]? |
| A. | \[25\] |
| B. | \[125\] |
| C. | \[250\] |
| D. | \[625\] |
| Answer» C. \[250\] | |
| 36. |
Solve \[{{\left( {{4}^{5}} \right)}^{x}}={{\left( {{4}^{4}} \right)}^{x}}\div {{4}^{2}}\] |
| A. | \[x=4\] |
| B. | \[x=-2\] |
| C. | \[x=-3\] |
| D. | \[x=2\] |
| Answer» C. \[x=-3\] | |
| 37. |
Which is greater \[{{4}^{3}}\] or \[{{3}^{4}}\]? |
| A. | Both are equal |
| B. | \[{{4}^{3}}\] |
| C. | \[{{3}^{4}}\] |
| D. | cannot be determined |
| Answer» D. cannot be determined | |
| 38. |
The speed of light is 300,000,000 \[\mathbf{m}{{\mathbf{s}}^{-1}}\] Express it in standard form. |
| A. | \[3.0\times {{10}^{8}}m{{s}^{-1}}\] |
| B. | \[3.0\times {{10}^{10}}m{{s}^{-1}}\] |
| C. | \[3.0\times {{10}^{6}}m{{s}^{-1}}\] |
| D. | \[3.0\times {{10}^{12}}m{{s}^{-1}}\] |
| Answer» B. \[3.0\times {{10}^{10}}m{{s}^{-1}}\] | |
| 39. |
What is the simplified form of the product given? \[{{(-3p)}^{4}}{{(6q)}^{5}}{{(3r)}^{6}}\] |
| A. | \[{{(-3)}^{15}}{{2}^{5}}{{p}^{4}}{{q}^{5}}{{r}^{6}}\] |
| B. | \[{{p}^{4}}\,{{q}^{5}}\,{{r}^{6}}\] |
| C. | \[{{3}^{15}}\,{{2}^{5}}\,{{p}^{4}}\,{{q}^{5}}\,{{r}^{6}}\] |
| D. | \[{{(-3)}^{15}}\,{{2}^{5}}\,{{p}^{4}}\,{{q}^{4}}\,{{r}^{4}}\] |
| Answer» D. \[{{(-3)}^{15}}\,{{2}^{5}}\,{{p}^{4}}\,{{q}^{4}}\,{{r}^{4}}\] | |
| 40. |
A number in standard form in written as \[\mathbf{6}.\mathbf{6}\times \mathbf{1}{{\mathbf{0}}^{\mathbf{6}}}.\] It can also be written as: |
| A. | 6666666 |
| B. | 66000 |
| C. | 6600000000 |
| D. | 6600000 |
| Answer» E. | |
| 41. |
What is the simplified form of \[{{\left( -6xy \right)}^{6}}\div {{\left( -6xy \right)}^{2}}?\] |
| A. | \[{{\left( -6xy \right)}^{6}}\] |
| B. | \[{{\left( -6xy \right)}^{8}}\] |
| C. | \[\left( -\,6xy \right)\] |
| D. | \[{{\left( -6xy \right)}^{4}}\] |
| Answer» E. | |
| 42. |
Avogadro number is written as 602,000,000,000,000,000,000,000, Express this number in standard form. |
| A. | \[6.02\times {{10}^{23}}\] |
| B. | \[6.02\times {{10}^{21}}\] |
| C. | \[602.0\times {{10}^{21}}\] |
| D. | \[0.602\times {{10}^{23}}\] |
| Answer» B. \[6.02\times {{10}^{21}}\] | |
| 43. |
By what number should \[{{(-8)}^{-1}}\] be divided to get \[{{10}^{-1}}\]? |
| A. | \[\frac{4}{5}\] |
| B. | \[\frac{-5}{4}\] |
| C. | \[\frac{-4}{5}\] |
| D. | \[\frac{5}{4}\] |
| Answer» C. \[\frac{-4}{5}\] | |
| 44. |
Find the value of \[{{\left[ {{(-3)}^{(-2)}} \right]}^{(-3)}}\]. |
| A. | \[729\] |
| B. | \[32\] |
| C. | \[64\] |
| D. | \[-729\] |
| Answer» B. \[32\] | |
| 45. |
What is the standard form of\[6020000000000000\]? |
| A. | \[6.02\times {{10}^{15}}\] |
| B. | \[6.02\times {{10}^{13}}\] |
| C. | \[602\times {{10}^{13}}\] |
| D. | \[602\times {{10}^{-15}}\] |
| Answer» B. \[6.02\times {{10}^{13}}\] | |
| 46. |
If \[{{27}^{x+1}}={{9}^{x+3}}={{3}^{y}},\] find the respective values of ?x' and 'y'. |
| A. | 3 and 12 |
| B. | 12 and 3 |
| C. | 6 and 6 |
| D. | 4 and 9 |
| Answer» B. 12 and 3 | |
| 47. |
When simplified, \[{{\text{(}{{\text{x}}^{-1}}+{{y}^{-1}})}^{-1}}\] is equal to_____. |
| A. | \[x+y\] |
| B. | \[\frac{xy}{x+y}\] |
| C. | \[xy\] |
| D. | \[\frac{1}{xy}\] |
| Answer» C. \[xy\] | |
| 48. |
The size of a red blood cell is 0.000007 m and the size of a plant cell is 0.00001275 m. Find the ratio of the size of red blood cell to that of plant cell. |
| A. | 0.58055555555556 |
| B. | 1.2020833333333 |
| C. | 31 : 39 |
| D. | 22 : 31 |
| Answer» C. 31 : 39 | |
| 49. |
The exponential form of \[\sqrt{\sqrt{2}\times \sqrt{5}}\] is |
| A. | \[{{\left( 10 \right)}^{1/2}}\] |
| B. | \[{{10}^{1/4}}\] |
| C. | 10 |
| D. | \[{{10}^{1/6}}\] |
| Answer» C. 10 | |
| 50. |
The value of \[{{\left[ {{\left( \sqrt[n]{{{x}^{2}}} \right)}^{n/2}} \right]}^{2}}\] |
| A. | 0 |
| B. | \[{{x}^{2}}\] |
| C. | \[x\] |
| D. | \[1/x\] |
| Answer» C. \[x\] | |