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MCQOPTIONS
This section includes 53 Mcqs, each offering curated multiple-choice questions to sharpen your Arithmetic Ability knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
The value of log2 16 is: |
| A. | 4 |
| B. | 1 |
| C. | 16 |
| D. | 8 |
| Answer» C. 16 | |
| 2. |
If log10 2 = 0.3010, the value of log10 80 is: |
| A. | 1.602 |
| B. | 1.903 |
| C. | 3.903 |
| D. | None of these |
| Answer» C. 3.903 | |
| 3. |
The value of log2 16 is: |
| A. | (1/8) |
| B. | 4 |
| C. | 8 |
| D. | 16 |
| Answer» C. 8 | |
| 4. |
If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 512 is: |
| A. | 2.87 |
| B. | 2.967 |
| C. | 3.876 |
| D. | 3.912 |
| Answer» D. 3.912 | |
| 5. |
If log 2 = 0.30103, the number of digits in 264 is: |
| A. | 18 |
| B. | 19 |
| C. | 20 |
| D. | 21 |
| Answer» D. 21 | |
| 6. |
\eqalign{ & {\text{If}}\,{\log _{10}}a = p,\,\,\,{\log _{10}}b = q, \cr & {\text{then}}\,{\text{what}}\,\,{\text{is}}\,\,{\log _{10}}\left( {{a^p}{b^q}} \right)\,\,{\text{equal}}\,\,{\text{to}}? \cr} $$%! |
| A. | p2 + q2 |
| B. | p2 - q2 |
| C. | p2q2 |
| D. | p2/q2 |
| Answer» B. p2 - q2 | |
| 7. |
\eqalign{ & {\text{If}}\,\log 3\log \left( {{3^x} - 2} \right)\,{\text{and}}\,\log \left( {{3^x} + 4} \right)\, \cr & {\text{are}}\,{\text{in}}\,{\text{arithmetic}}\,\,{\text{progression}}\,{\text{,}} \cr & {\text{then}}\,x\,{\text{is}}\,{\text{equal}}\,{\text{to}} - \cr} $$%! |
| A. | 8/3 |
| B. | log 38 |
| C. | log 23 |
| D. | 8 |
| Answer» D. 8 | |
| 8. |
\eqalign{ & {\text{The number of digits in }}{{\text{4}}^9} \times {{\text{5}}^{17}}{\text{,}} \cr & {\text{when expressed in usual form, is - }} \cr} $$%! |
| A. | 16 |
| B. | 17 |
| C. | 18 |
| D. | 19 |
| Answer» D. 19 | |
| 9. |
{\rm{If}}\log {a \over b} + \log {b \over a} = \log \left( {a + b} \right),{\rm{then:}}$$%! |
| A. | a + b = 1 |
| B. | a - b = 1 |
| C. | a = b |
| D. | a2 - b2 = 1 |
| Answer» B. a - b = 1 | |
| 10. |
*$_$$\eqalign{ & {\text{If}}\log 2 = 0.30103, \cr & {\text{the}}\,{\text{number}}\,{\text{of}}\,{\text{digits}}\,{\text{in}}\,{4^{50}}{\text{is}} - \cr} $$? |
| A. | 30 |
| B. | 31 |
| C. | 100 |
| D. | 200 |
| Answer» C. 100 | |
| 11. |
*$_$$\eqalign{ & {\text{If}}\,{\log _3}x + {\log _{\underline 9 }}{x^2} + {\log _{27}}{x^3} = 9, \cr & {\text{then}}\,\,x\,\,{\text{equals - }} \cr} $$? |
| A. | 3 |
| B. | 9 |
| C. | 27 |
| D. | None of these |
| Answer» D. None of these | |
| 12. |
*$_The value of log2 16 is:? |
| A. | 1/8 |
| B. | 4 |
| C. | 8 |
| D. | 16 |
| Answer» C. 8 | |
| 13. |
*$_$$\eqalign{ & {\text{The}}{\kern 1pt} {\text{value}}{\kern 1pt} {\text{of}} \cr & \left( {\frac{1}{{{{\log }_3}60}} + \frac{1}{{{{\log }_4}60}} + \frac{1}{{{{\log }_5}60}}} \right){\text{is}}: \cr} $$? |
| A. | 0 |
| B. | 1 |
| C. | 5 |
| D. | 60 |
| Answer» C. 5 | |
| 14. |
*$_$$\eqalign{ & \frac{1}{{{{\log }_a}b}} \times \frac{1}{{{{\log }_b}c}} \times \frac{1}{{{{\log }_c}a}} \cr & {\text{is}}\,{\text{equal}}\,{\text{to - }} \cr} $$? |
| A. | a+b+c |
| B. | abc |
| C. | 0 |
| D. | 1 |
| Answer» E. | |
| 15. |
*$_$$\eqalign{ & {\text{If }}{\log _5}\left( {{x^2} + x} \right) - {\log _5}\left( {x + 1} \right) = 2, \cr & {\text{then the value of }}x{\text{ is - }} \cr} $$? |
| A. | 5 |
| B. | 10 |
| C. | 25 |
| D. | 32 |
| Answer» D. 32 | |
| 16. |
*$_What is the value of the following expression?$$\log \left( {\frac{8}{{14}}} \right) - \log \left( {\frac{{15}}{{16}}} \right) + \log \left( {\frac{{35}}{{24}}} \right)$$? |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| Answer» B. 1 | |
| 17. |
*$_$${\text{If }}\,\,{\text{lo}}{{\text{g}}_8}{\text{p}} = 25\,\,{\text{and lo}}{{\text{g}}_2}{\text{q}} = 5\,,{\text{then - }}$$? |
| A. | p = q15 |
| B. | p2 = q3 |
| C. | p = q5 |
| D. | p3 = q |
| Answer» B. p2 = q3 | |
| 18. |
*/*_$${\rm{If}}\log {a \over b} + \log {b \over a} = \log \left( {a + b} \right),{\rm{then:}}$$? |
| A. | a + b = 1 |
| B. | a - b = 1 |
| C. | a = b |
| D. | a2 - b2 = 1 |
| Answer» B. a - b = 1 | |
| 19. |
%_$$\eqalign{ & {\text{If the logarithm of a number is - 3}}{\text{.153,}} \cr & {\text{what are characteristic and mantisa?}} \cr} $$_% |
| A. | characteristic = -4, mantisa = 0.847 |
| B. | characteristic = -3, mantisa = -0.153 |
| C. | characteristic = 4, mantisa = -0.847 |
| D. | characteristic = 3, mantisa = -0.153 |
| Answer» B. characteristic = -3, mantisa = -0.153 | |
| 20. |
%_$$\eqalign{ & {\text{If }}a = {b^2} = {c^3} = {d^4}, \cr & {\text{then}}\,{\text{the}}\,{\text{value}}\,{\text{of}}\,{\log _a}\left( {abcd} \right)\,{\text{would be - }} \cr} $$_% |
| A. | loga1 + loga2 + loga3 + loga4 |
| B. | log124 |
| C. | 1 + 1/2 + 1/3 + 1/4 |
| D. | 1 + 1/2! + 1/3! + 1/4! |
| Answer» D. 1 + 1/2! + 1/3! + 1/4! | |
| 21. |
%_If logx y = 100 and log2 x = 10, then the value of y is:_% |
| A. | 210 |
| B. | 2100 |
| C. | 21000 |
| D. | 210000 |
| Answer» D. 210000 | |
| 22. |
%_$$\eqalign{ & {\text{If}} \Rightarrow {\log _{10}}5 + {\log _{10}}\left( {5x + 1} \right) = {\log _{10}}\left( {x + 5} \right) + 1, \cr & {\text{then}}\,x\,{\text{is}}\,{\text{equal}}\,{\text{to}}: \cr} $$_% |
| A. | 1 |
| B. | 3 |
| C. | 5 |
| D. | 10 |
| Answer» C. 5 | |
| 23. |
%_$$\eqalign{ & \left[ {\log \left( {\frac{{{a^2}}}{{bc}}} \right) + \log \left( {\frac{{{b^2}}}{{ac}}} \right) + \log \left( {\frac{{{c^2}}}{{ab}}} \right)} \right] \cr & {\text{is}}\,{\text{equal}}\,{\text{to - }} \cr} $$_% |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | abc |
| Answer» B. 1 | |
| 24. |
%_$$\eqalign{ & {\text{If}}\,{\log _{10}}125 + {\log _{10}}8 = x, \cr & {\text{then }}x\,{\text{is equel to}} - \cr} $$_% |
| A. | 1/3 |
| B. | 0.064 |
| C. | -3 |
| D. | 3 |
| Answer» E. | |
| 25. |
%_$$\eqalign{ & {\text{If }}{\log _2}\left[ {{\text{ }}{{\log }_3}\left( {{\text{ }}{{\log }_2}x} \right)} \right] = 1, \cr & {\text{then }}x\,\,{\text{is equal to = ?}} \cr} $$_% |
| A. | 0 |
| B. | 12 |
| C. | 128 |
| D. | 512 |
| Answer» E. | |
| 26. |
%_$$\eqalign{ & {\text{What is the value of}} \cr & {\left[ {{\text{lo}}{{\text{g}}_{10}}\left( {{\text{5lo}}{{\text{g}}_{10}}100} \right)\,} \right]^2} = ? \cr} $$_% |
| A. | 1 |
| B. | 2 |
| C. | 10 |
| D. | 25 |
| Answer» B. 2 | |
| 27. |
_ If log 27 = 1.431, then the value of log 9 is:$? |
| A. | 0.934 |
| B. | 0.945 |
| C. | 0.954 |
| D. | 0.958 |
| Answer» D. 0.958 | |
| 28. |
_$$\eqalign{ & {\text{If}}\,\log 2 = 0.3010\,and\,\log 3 = 0.4771, \cr & the\,value\,of\,{\log _5}512 = ? \cr} $$$? |
| A. | 2.870 |
| B. | 2.967 |
| C. | 3.876 |
| D. | 3.912 |
| Answer» D. 3.912 | |
| 29. |
_$$\eqalign{ & {\text{If}}\,\,\log x - 5\log 3 = - 2, \cr & {\text{then }}x{\text{ equals - }} \cr} $$$? |
| A. | 0.8 |
| B. | 0.81 |
| C. | 1.25 |
| D. | 2.43 |
| Answer» E. | |
| 30. |
_If ax = by, then:$? |
| A. | log a/b = x/y |
| B. | log a/log b = x/y |
| C. | log a/log b = y/x |
| D. | None of these |
| Answer» D. None of these | |
| 31. |
_If log10 2 = 0.3010, the value of log10 80 is:$? |
| A. | 1.6020 |
| B. | 1.9030 |
| C. | 3.9030 |
| D. | None of these |
| Answer» C. 3.9030 | |
| 32. |
_$${\text{If}}\,\,\,\log \frac{a}{b} + \log \frac{b}{a} = \log \left( {a + b} \right),\,\,{\text{then}} - $$$? |
| A. | a + b = 1 |
| B. | a - b = 1 |
| C. | a = b |
| D. | a2 - b2 = 1 |
| Answer» B. a - b = 1 | |
| 33. |
_$$\eqalign{ & {\text{If}}\,\,{\log _{10}}2 = a\,{\text{and}} \cr & {\log _{10}}3 = b,\,{\text{then}} \cr & {\log _5}12 = ? \cr} $$$? |
| A. | (a+b)/(1+a) |
| B. | (2a+b)/(1+a) |
| C. | (a+2b)/(1+a) |
| D. | (2a+b)/(1-a) |
| Answer» E. | |
| 34. |
_$$\eqalign{ & {\text{The value of }} \cr & \,\frac{{6{\text{ }}{{\log }_{10}}1000}}{{3{\text{ }}{{\log }_{10}}100}}\,\,{\text{is equal to - }} \cr} $$$? |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| Answer» E. | |
| 35. |
_$$\eqalign{ & {\text{The value of }} \cr & {\text{lo}}{{\text{g}}_{10}}\left( {0.0001} \right)\,\,{\text{is }} = ? \cr} $$$? |
| A. | 1/4 |
| B. | -1/4 |
| C. | -4 |
| D. | 4 |
| Answer» D. 4 | |
| 36. |
_$${{\log \sqrt 8 } \over {\log 8}}$$ is equal to:$? |
| A. | 1/6 |
| B. | 1/4 |
| C. | 1/2 |
| D. | 1/8 |
| Answer» D. 1/8 | |
| 37. |
\eqalign{ & {\text{If}}\,{\text{a = lo}}{{\text{g}}_{\text{8}}}{\text{225}}\,{\text{and}}\,{\text{b = lo}}{{\text{g}}_{\text{2}}}{\text{15}}, \cr & {\text{then}}\,a\,{\text{in}}\,{\text{terms}}\,{\text{of}}\,b\,{\text{is}} - \cr} $$? |
| A. | b/2 |
| B. | 2b/3 |
| C. | b |
| D. | 3b/2 |
| Answer» C. b | |
| 38. |
\eqalign{ & {\text{If}}\,\,{\log _{10}}7 = a,{\text{then}}\,\,{\log _{10}}\left( {\frac{1}{{70}}} \right)\,\, \cr & {\text{is}}\,\,{\text{equal}}\,\,{\text{to}} - \cr} $$? |
| A. | -(1 + a) |
| B. | (1 + a)-1 |
| C. | a/10 |
| D. | 1/10a |
| Answer» B. (1 + a)-1 | |
| 39. |
{\rm{If}}\,{\log _x}\left( {{9 \over {16}}} \right) = - {1 \over 2},\,{\rm{then}}\,x\,{\rm{is}}\,{\rm{equal}}\,{\rm{to:}}$$? |
| A. | - 3/4 |
| B. | 3/4 |
| C. | 81/256 |
| D. | 256/81 |
| Answer» E. | |
| 40. |
If log10 2 = 0.3010, then log2 10 is equal to:? |
| A. | 699/301 |
| B. | 1000/301 |
| C. | 0.3010 |
| D. | 0.6990 |
| Answer» C. 0.3010 | |
| 41. |
\eqalign{ & {\text{The}}\,{\text{value}}\,{\text{of}}\,\, \cr & \,\left( {\frac{1}{{{{\log }_3}60}} + \frac{1}{{{{\log }_4}60}} + \frac{1}{{{{\log }_5}60}}} \right)\,\,{\text{is}} - \cr} $$? |
| A. | 0 |
| B. | 1 |
| C. | 5 |
| D. | 60 |
| Answer» C. 5 | |
| 42. |
{\text{If }}{\log _a}\left( {ab} \right){\text{ }} = {\text{ }}x{\text{, then }}{\log _b}\left( {ab} \right){\text{ is - }}$$? |
| A. | 1/x |
| B. | x/(x+1) |
| C. | x/(1-x) |
| D. | x/(x-1) |
| Answer» E. | |
| 43. |
\frac{{\log \sqrt 8 }}{{\log 8}}\,\,{\text{is equal to = ?}}$$? |
| A. | 1/‚à ö8 |
| B. | 1/4 |
| C. | 1/2 |
| D. | 1/8 |
| Answer» D. 1/8 | |
| 44. |
\eqalign{ & {\text{Determine the value of }} \cr & {\text{lo}}{{\text{g}}_{3\sqrt 2 }}\left( {\frac{1}{{18}}} \right)\,{\text{ is = ?}} \cr} $$? |
| A. | 2 |
| B. | -2 |
| C. | ‚à ö2 |
| D. | ‚à ö3 |
| Answer» C. ‚Äö√ √∂2 | |
| 45. |
If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 512 is: |
| A. | 2.870 |
| B. | 2.967 |
| C. | 3.876 |
| D. | 3.912 |
| Answer» D. 3.912 | |
| 46. |
\eqalign{ & {\text{If}}\,\,{\log _7}{\log _5}\left( {\sqrt {x + 5} + \sqrt x } \right) = 0, \cr & {\text{what}}\,\,{\text{is}}\,\,{\text{the}}\,\,{\text{value}}\,\,{\text{of}}\,\,x? \cr} $$ |
| A. | 2 |
| B. | 3 |
| C. | 4 |
| D. | 5 |
| Answer» D. 5 | |
| 47. |
\eqalign{ & \left[ {\frac{1}{{\left( {{{\log }_a}bc} \right) + 1}} + \frac{1}{{\left( {{{\log }_b}ca} \right) + 1}} + \frac{1}{{\left( {{{\log }_c}ab} \right) + 1}}} \right] \cr & {\text{is}}\,\,{\text{equal}}\,{\text{to - }} \cr} $$ |
| A. | 1 |
| B. | 3/2 |
| C. | 2 |
| D. | 3 |
| Answer» B. 3/2 | |
| 48. |
If log 2 = 0.30103, the number of digits in 264 is: |
| A. | 18 |
| B. | 19 |
| C. | 20 |
| D. | 21 |
| Answer» D. 21 | |
| 49. |
{\rm{If}}{\kern 1pt} \,{\kern 1pt} {\log _{10}}7 = a,{\kern 1pt} {\kern 1pt} {\rm{then}}\,{\kern 1pt} {\kern 1pt} {\log _{10}}\left( {{1 \over {70}}} \right){\rm{is}}\,{\kern 1pt} {\rm{equal}}\,{\kern 1pt} {\rm{to}}$$ |
| A. | - (1 + a) |
| B. | (1 + a)-1 |
| C. | a/10 |
| D. | 1/10a |
| Answer» B. (1 + a)-1 | |
| 50. |
\eqalign{ & \frac{1}{2}\left( {\log x + \log y} \right)\,\,{\text{will}}\,{\text{equal}}\,{\text{to}} \cr & \log \left( {\frac{{x + y}}{2}} \right)\,\,{\text{if - }} \cr} $$ |
| A. | y = 0 |
| B. | x = ‚à öy |
| C. | x = y |
| D. | x = y/2 |
| Answer» D. x = y/2 | |