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MCQOPTIONS
This section includes 657 Mcqs, each offering curated multiple-choice questions to sharpen your Testing Subject knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
If\[{{\left( \frac{m}{n} \right)}^{r-7}}={{\left( \frac{n}{m} \right)}^{r-3}}\], then find the value of r. |
| A. | 12 |
| B. | 10 |
| C. | 5 |
| D. | 9 |
| E. | None of these |
| Answer» D. 9 | |
| 2. |
If p and q are whole numbers such that \[{{p}^{q}}\]= 529 then find the value of \[{{\left[ {{(6-q)}^{p-17}} \right]}^{-1}}\] |
| A. | 1024 |
| B. | 2048 |
| C. | \[\frac{1}{2048}\] |
| D. | \[\frac{1}{4096}\] |
| E. | None of these |
| Answer» E. None of these | |
| 3. |
Find the value of \[{{\left[ {{3}^{-1}}+\text{ }{{4}^{-2}}+\text{ }{{6}^{-4}} \right]}^{-1}}\] |
| A. | 257 |
| B. | 257 |
| C. | 648 |
| D. | 348 |
| E. | None of these |
| Answer» B. 257 | |
| 4. |
Simplify \[{{\left[ {{\left( \frac{2}{17} \right)}^{-6}}\div {{\left( \frac{2}{17} \right)}^{4}} \right]}^{4}}\times {{\left( \frac{2}{17} \right)}^{-18}}\] |
| A. | \[{{\left( \frac{2}{17} \right)}^{-20}}\] |
| B. | \[{{\left( \frac{17}{2} \right)}^{-20}}\] |
| C. | \[{{\left( \frac{2}{17} \right)}^{-28}}\] |
| D. | \[{{\left( \frac{17}{2} \right)}^{-28}}\] |
| E. | None of these |
| Answer» D. \[{{\left( \frac{17}{2} \right)}^{-28}}\] | |
| 5. |
Which one among the following is the reciprocal of\[\frac{{{2}^{5}}\times {{3}^{7}}\times {{\left( \sqrt{7} \right)}^{3/4}}}{{{\left( \sqrt{8} \right)}^{2}}\times \left( \sqrt{7} \right)}\]? |
| A. | \[{{2}^{-2}}\times {{3}^{-7}}\times {{7}^{5/8}}\] |
| B. | \[{{2}^{3}}\times {{3}^{7}}\times {{7}^{-5/8}}\] |
| C. | \[{{2}^{5}}\times 3-7\text{ }\times \text{ }{{7}^{-1/8}}\] |
| D. | \[{{2}^{-4}}\times {{3}^{7}}\times {{7}^{5/8}}\] |
| E. | None of these |
| Answer» B. \[{{2}^{3}}\times {{3}^{7}}\times {{7}^{-5/8}}\] | |
| 6. |
If m and n are whole numbers such that \[{{m}^{n}}\]= 262144 (where m > n) and n is a natural number less than 4, then the value of \[\sqrt[n]{m}\] can be____ |
| A. | 4 |
| B. | 8 |
| C. | 4 and 16\[\sqrt{2}\] |
| D. | 16 and 8\[\sqrt{2}\] |
| E. | None of these |
| Answer» D. 16 and 8\[\sqrt{2}\] | |
| 7. |
Simplify: \[\frac{\sqrt[3]{{{(0.008)}^{2}}}+{{\left( \sqrt[3]{0.000216} \right)}^{2}}-\sqrt[3]{0.001728}}{{{(0.02)}^{3}}+\sqrt{0.0081}}\] |
| A. | 0.0009 |
| B. | \[\frac{2500}{11251}\] |
| C. | \[\frac{2700}{11251}\] |
| D. | 0.0008 |
| E. | None of these |
| Answer» C. \[\frac{2700}{11251}\] | |
| 8. |
Find the number of four digit cubes which end with a non-zero perfect square digit. |
| A. | 2 |
| B. | 4 |
| C. | 6 |
| D. | 7 |
| E. | None of these |
| Answer» C. 6 | |
| 9. |
In a five digit number 1p68q, \[p={{q}^{2}}\,and\,p\ne q\]. If the given number is a perfect cube, then find the difference between the sum of its digits and the cube root of the number. |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 9 |
| E. | None of these |
| Answer» B. 1 | |
| 10. |
If\[\sqrt[3]{a}+\frac{64}{\sqrt[3]{a}}=20\], then the value of a can be |
| A. | 4 and 32 |
| B. | 8 and 4 |
| C. | 16 and 8 |
| D. | 4 and 16 |
| E. | None of these |
| Answer» E. None of these | |
| 11. |
\[\sqrt[3]{1+3+5+7+.......+685}\]= ________ |
| A. | 9 |
| B. | 27 |
| C. | 49 |
| D. | 7 |
| E. | None of these |
| Answer» D. 7 | |
| 12. |
If \[{{3}^{m}}=\text{ }{{\left( 81 \right)}^{n}}=\text{ }{{\left( 729 \right)}^{r}}=\text{ }243\] then find the value of \[{{\left( \frac{3m}{4}+n \right)}^{3}}-{{(4n+6r)}^{3}}\] |
| A. | 1125 |
| B. | 875 |
| C. | -875 |
| D. | -1125 |
| E. | None of these |
| Answer» D. -1125 | |
| 13. |
Simplify: \[\frac{274\times 274+2\times 274\times 126+126\times 126}{1600}\] |
| A. | 400 |
| B. | 200 |
| C. | 100 |
| D. | 300 |
| E. | None of these |
| Answer» D. 300 | |
| 14. |
Which of the following is not a Pythagorean triplets? |
| A. | (8, 15, 17) |
| B. | (20, 99, 101) |
| C. | (5, 36, 41) |
| D. | (12, 35, 37) |
| E. | None of these |
| Answer» D. (12, 35, 37) | |
| 15. |
solve: \[\frac{{{(279)}^{2}}-{{(278)}^{2}}}{557}\] |
| A. | 758 |
| B. | 279 |
| C. | 278 |
| D. | 1 |
| E. | None of these |
| Answer» E. None of these | |
| 16. |
simplify \[\frac{{{\left( -2 \right)}^{24}}\times {{(-3)}^{17}}\times {{847}^{42}}}{{{\left( 12 \right)}^{16}}\times {{(27)}^{6}}}\] |
| A. | \[\frac{-1}{{{2}^{35}}\times {{3}^{17}}}\] |
| B. | \[\frac{1}{{{2}^{35}}\times {{3}^{17}}}\] |
| C. | \[\frac{1}{{{3}^{16}}\times {{2}^{34}}}\] |
| D. | \[\frac{-1}{{{3}^{16}}\times {{2}^{34}}}\] |
| E. | None of these |
| Answer» B. \[\frac{1}{{{2}^{35}}\times {{3}^{17}}}\] | |
| 17. |
By observing the given pattern, find the value of missing number.\[{{\left( 11 \right)}^{2}}\]=121\[{{\left( 101 \right)}^{2}}\]= 10201\[{{\left( 1001 \right)}^{2}}\]= 1002001\[{{\left( 100001 \right)}^{2}}\]= _______ |
| A. | 100002000001 |
| B. | 100020001 |
| C. | 1000200001 |
| D. | 10000020001 |
| E. | None of these |
| Answer» B. 100020001 | |
| 18. |
Which among the following is not a perfect cube? |
| A. | 21952 |
| B. | 3365 |
| C. | 4096 |
| D. | 1331 |
| E. | None of these |
| Answer» C. 4096 | |
| 19. |
Which among the following is not a perfect square? |
| A. | 104329 |
| B. | 7921 |
| C. | 10201 |
| D. | 7579 |
| E. | None of these |
| Answer» E. None of these | |
| 20. |
By what number should \[{{\left( -15 \right)}^{-1}}\]1 be divided so that the quotient may be \[{{\left( \frac{5}{9} \right)}^{-1}}\], |
| A. | \[\frac{1}{9}\] |
| B. | \[\frac{-1}{27}\] |
| C. | \[\frac{1}{27}\] |
| D. | \[\frac{-1}{9}\] |
| E. | None of these |
| Answer» C. \[\frac{1}{27}\] | |
| 21. |
If\[{{p}^{{{q}^{r}}}}^{=}{{2}^{64}}\], then find the maximum possible value of p + q + r where p, q and r are natural numbers. |
| A. | 9 |
| B. | 10 |
| C. | 12 |
| D. | 67 |
| E. | None of these |
| Answer» E. None of these | |
| 22. |
The cube of a number is 324 times the number. Find the cube of \[\frac{4}{9}\] of the number |
| A. | 216 |
| B. | 512 |
| C. | 343 |
| D. | 729 |
| E. | None of these |
| Answer» C. 343 | |
| 23. |
Find the sum of \[1+3+5+7+9+---------+101\] |
| A. | 2601 |
| B. | 2401 |
| C. | 2501 |
| D. | 2701 |
| E. | None of these |
| Answer» B. 2401 | |
| 24. |
The product of two numbers is 4332 and their quotient is\[\frac{3}{4}\]. Find the sum of the numbers. |
| A. | 136 |
| B. | 133 |
| C. | 143 |
| D. | 149 |
| E. | None of these |
| Answer» C. 143 | |
| 25. |
Find the sum of\[{{1}^{3}}\text{ }+\text{ }{{2}^{3}}\text{ }+\text{ }{{3}^{3}}\text{ }+----------+\text{ }{{12}^{3}}\] |
| A. | 6084 |
| B. | 4048 |
| C. | 5082 |
| D. | 5048 |
| E. | None of these |
| Answer» B. 4048 | |
| 26. |
Solve: \[{{\left[ {{\left[ {{17}^{2}}+{{(\sqrt{3})}^{8}}-\sqrt{{{5}^{2}}+{{4}^{3}}-{{2}^{3}}} \right]}^{{1}/{2}\;}} \right]}^{3}}\] |
| A. | 5859 |
| B. | 7869 |
| C. | 6859 |
| D. | 5682 |
| E. | None of these |
| Answer» D. 5682 | |
| 27. |
The volume of a cubical box is\[456.533c{{m}^{3}}\]. Find the side of the cubical box in cm. |
| A. | \[7.7\text{ }cm\] |
| B. | \[8.3\text{ }cm\] |
| C. | \[7.27\text{ }cm\] |
| D. | \[6.7\text{ }cm\] |
| E. | None of these |
| Answer» B. \[8.3\text{ }cm\] | |
| 28. |
Three numbers are in the ratio \[1:3:2\]and sum of their cubes is equal to\[2.304\]. Find the sum of the numbers. |
| A. | \[~2.4\] |
| B. | \[3.6\] |
| C. | \[2.8\] |
| D. | \[4.2\] |
| E. | None of these |
| Answer» B. \[3.6\] | |
| 29. |
The smallest number, which when multiplied with 123768 will make the product a perfect cube, is ________ |
| A. | 12321 |
| B. | 36481 |
| C. | 328329 |
| D. | 111475 |
| E. | None of these |
| Answer» D. 111475 | |
| 30. |
Solve :\[\sqrt{8+\sqrt{773+\sqrt{116+\sqrt{2+\sqrt{520+\sqrt{81}}}}}}\] |
| A. | 2 |
| B. | 3 |
| C. | 7 |
| D. | 6 |
| E. | None of these |
| Answer» E. None of these | |
| 31. |
Find the value of \[\sqrt{\frac{4}{1+{{x}^{p-q}}}+\frac{4}{1+{{x}^{q-p}}}}\] |
| A. | -2 |
| B. | 4 |
| C. | 1 |
| D. | -4 |
| E. | None of these |
| Answer» B. 4 | |
| 32. |
If \[{{7}^{2a-b}}=\text{ }70\times 30+15\times 20+1\]then find the value of \[{{\left( \frac{2a}{4+b} \right)}^{-212}}\]. |
| A. | -212 |
| B. | -1 |
| C. | 1 |
| D. | 0 |
| E. | None of these |
| Answer» D. 0 | |
| 33. |
If m = 11 + 6\[\sqrt{2}\] , then find the value of \[{{\left( \sqrt{m}+\sqrt{2} \right)}^{{1}/{2}\;}}\] |
| A. | \[\sqrt{2}\] |
| B. | \[1+\sqrt{2}\] |
| C. | \[1-\sqrt{2}\] |
| D. | \[-\sqrt{2}\] |
| E. | None of these |
| Answer» C. \[1-\sqrt{2}\] | |
| 34. |
By what number should\[{{\left( \frac{1}{8} \right)}^{-1/2\ }}\] be multiplied so that its product becomes \[{{\left( \frac{5}{7} \right)}^{-1/2\ }}\] ? |
| A. | \[{{\left( \frac{7}{40} \right)}^{-1/2\ }}\] |
| B. | \[\frac{\sqrt{7}}{2\sqrt{2}}\] |
| C. | \[\frac{\sqrt{70}}{20}\] |
| D. | \[\frac{\sqrt{70}}{40}\] |
| E. | None of these |
| Answer» D. \[\frac{\sqrt{70}}{40}\] | |
| 35. |
dWhich among the following is a perfect square? 455562, 323761, 675487, 897568, 347860 |
| A. | 455562 |
| B. | 323761 |
| C. | 675487 |
| D. | 897568 |
| E. | None of these |
| Answer» C. 675487 | |
| 36. |
If \[\frac{10}{3}\times {{3}^{x}}-{{3}^{x-1}}=81\], then the value of x is____. |
| A. | 2 |
| B. | 1 |
| C. | 3 |
| D. | 0 |
| Answer» D. 0 | |
| 37. |
If \[{{a}^{x}}={{b}^{y}}={{c}^{z}}\] and \[{{b}^{2}}=ac\], then y equals |
| A. | \[\frac{2xz}{x+z}\] |
| B. | \[\frac{xz}{2(x-z)}\] |
| C. | \[\frac{xz}{2(z-x)}\] |
| D. | \[\frac{2xz}{(x-z)}\] |
| Answer» B. \[\frac{xz}{2(x-z)}\] | |
| 38. |
Evaluate \[\frac{{{(5)}^{0.25}}\times {{(125)}^{0.25}}}{{{(256)}^{0.10}}\times {{(256)}^{0.15}}}\]. |
| A. | \[\frac{\sqrt{5}}{2}\] |
| B. | \[\frac{5}{4}\] |
| C. | \[\frac{25}{2}\] |
| D. | \[\frac{25}{16}\] |
| Answer» C. \[\frac{25}{2}\] | |
| 39. |
If \[{{x}^{y}}={{y}^{x}},\]find the value of \[{{\left( \frac{x}{y} \right)}^{\frac{x}{y}}}\]. |
| A. | \[{{x}^{\frac{x}{y}}}\] |
| B. | \[{{x}^{\frac{x}{y}-1}}\] |
| C. | \[{{x}^{\frac{y}{x}}}\] |
| D. | \[{{x}^{\frac{y}{x}-1}}\] |
| Answer» C. \[{{x}^{\frac{y}{x}}}\] | |
| 40. |
Find the value of\[{{\text{(0}\text{.000064)}}^{\frac{5}{6}}}\div {{\text{(0}\text{.00032)}}^{\frac{6}{5}}}\]. |
| A. | 0.2 |
| B. | 0.4 |
| C. | 5 |
| D. | 2.5 |
| Answer» D. 2.5 | |
| 41. |
Simplify \[{{(32)}^{\frac{-2}{5}}}\div {{(125)}^{\frac{-2}{3}}}\]. |
| A. | \[\frac{4}{25}\] |
| B. | \[\frac{25}{4}\] |
| C. | \[\frac{2}{5}\] |
| D. | \[\frac{5}{2}\] |
| Answer» C. \[\frac{2}{5}\] | |
| 42. |
If (\[{{(6x)}^{6}}={{6}^{{{2}^{3}}}}\], then find the value of x. |
| A. | 1 |
| B. | \[\sqrt{6}\] |
| C. | \[\sqrt[3]{6}\] |
| D. | \[\sqrt[6]{6}\] |
| Answer» D. \[\sqrt[6]{6}\] | |
| 43. |
What is the value of \[{{(512)}^{\frac{-2}{9}}}\]? |
| A. | \[\frac{1}{2}\] |
| B. | \[2\] |
| C. | \[4\] |
| D. | \[\frac{1}{4}\] |
| Answer» E. | |
| 44. |
If \[\sqrt{5}=x-2,\] what is the value of\[{{(x-2)}^{3}}\]? |
| A. | \[\sqrt{25}\] |
| B. | \[\sqrt{65}\] |
| C. | \[5\sqrt{5}\] |
| D. | \[2\sqrt{5}\] |
| Answer» D. \[2\sqrt{5}\] | |
| 45. |
If \[{{x}^{2}}=16\]and \[{{y}^{2}}=4,\]what is the greatest possible value of\[{{(x-y)}^{2}}\]? |
| A. | \[4\] |
| B. | \[-36\] |
| C. | \[-4\] |
| D. | \[36\] |
| Answer» E. | |
| 46. |
If \[x>0,\]which of the following is equal to \[\sqrt{{{x}^{3}}}\]? (i) \[x+{{x}^{1/2}}\] (ii) \[{{({{x}^{\frac{1}{2}}})}^{3}}\] (iii) \[({{x}^{2}})\,{{(x)}^{\frac{-1}{2}}}\] |
| A. | (ii) and (iii) only |
| B. | (i) and (ii) only |
| C. | (i) and (iii) only |
| D. | (i), (ii) and (iii) |
| Answer» B. (i) and (ii) only | |
| 47. |
What is the value of 'x' if \[\frac{{{a}^{x}}}{{{a}^{y}}}={{a}^{10}}\] and \[{{({{a}^{y}})}^{3}}={{a}^{x}}\] for \[a>1\]? |
| A. | \[25\] |
| B. | \[5\] |
| C. | \[20\] |
| D. | \[15\] |
| Answer» E. | |
| 48. |
If \[{{(25)}^{7.5}}\times {{(5)}^{2.5}}\div {{(125)}^{1.5}}={{5}^{x}},\] find 'x'. |
| A. | \[8.5\] |
| B. | \[13\] |
| C. | \[16\] |
| D. | \[17.5\] |
| Answer» C. \[16\] | |
| 49. |
What is the value of \[\left( {{8}^{-25}}-{{8}^{-26}} \right)\] ? |
| A. | \[7\times {{8}^{-25}}\] |
| B. | \[8\times {{8}^{-26}}\] |
| C. | \[7\times {{8}^{-26}}\] |
| D. | \[8\times {{8}^{-25}}\] |
| Answer» D. \[8\times {{8}^{-25}}\] | |
| 50. |
The value of \[\frac{1}{2}\left[ \frac{-7}{4}+\frac{5}{3}+\frac{-5}{6}+\frac{1}{3}+\frac{-1}{2} \right]\]\[+\frac{1}{3}\left[ \frac{-12}{5}+\frac{-7}{20}+\frac{3}{14}+\frac{1}{7}+\frac{-1}{10} \right]\] is |
| A. | \[\frac{1153}{840}\] |
| B. | \[\frac{128}{105}\] |
| C. | \[\frac{128}{105}\] |
| D. | \[\frac{-125}{256}\] |
| Answer» B. \[\frac{128}{105}\] | |