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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.
| 551. |
\[m\] and \[n\] are integers and\[\sqrt{mn}=10\]. Which of the following cannot be a value of\[m+n\]? |
| A. | \[25\] |
| B. | \[52\] |
| C. | \[101\] |
| D. | \[50\] |
| Answer» E. | |
| 552. |
Find the value of\[\frac{{{(0.6)}^{0}}-{{(0.1)}^{-1}}}{{{\left( \frac{3}{8} \right)}^{-1}}{{\left( \frac{3}{2} \right)}^{3}}+{{\left( \frac{-1}{3} \right)}^{-1}}}\]. |
| A. | \[\frac{-2}{3}\] |
| B. | \[\frac{3}{2}\] |
| C. | \[-\frac{3}{2}\] |
| D. | \[\frac{2}{3}\] |
| Answer» D. \[\frac{2}{3}\] | |
| 553. |
Identify the simplest form of\[\frac{5\sqrt{3}+3\sqrt{5}}{5\sqrt{3}-3\sqrt{5}}\]. |
| A. | \[6+\sqrt{15}\] |
| B. | \[4+\sqrt{15}\] |
| C. | \[4+\sqrt{3}\] |
| D. | \[6+\sqrt{5}\] |
| Answer» C. \[4+\sqrt{3}\] | |
| 554. |
Find the rational number for\[0.\overline{5}\]. |
| A. | \[\frac{9}{5}\] |
| B. | \[\frac{5}{10}\] |
| C. | \[\frac{5}{9}\] |
| D. | \[\frac{10}{5}\] |
| Answer» D. \[\frac{10}{5}\] | |
| 555. |
Find the value of\[\frac{1}{\sqrt{5}-\sqrt{4}}\]. |
| A. | \[\sqrt{5}-\sqrt{4}\] |
| B. | \[\sqrt{5}+\sqrt{4}\] |
| C. | \[\frac{\sqrt{5}+\sqrt{4}}{9}\] |
| D. | \[\sqrt{4}-\sqrt{5}\] |
| Answer» C. \[\frac{\sqrt{5}+\sqrt{4}}{9}\] | |
| 556. |
If\[p=3\]and\[q=5\], find the value of\[{{\left( \frac{1}{p}+\frac{1}{q} \right)}^{p}}\]. |
| A. | \[\frac{3375}{512}\] |
| B. | \[\frac{512}{3375}\] |
| C. | \[\frac{512}{225}\] |
| D. | \[\frac{64}{225}\] |
| Answer» C. \[\frac{512}{225}\] | |
| 557. |
If\[a=3\]and\[b=5\], find the value of\[{{a}^{a}}+{{b}^{b}}\]. |
| A. | \[512\] |
| B. | \[251\] |
| C. | \[513\] |
| D. | \[152\] |
| Answer» E. | |
| 558. |
If\[x=2+{{2}^{1/3}}+{{2}^{2/3}}\], find the value of\[({{x}^{3}}-6{{x}^{2}}+6x)\]. |
| A. | \[2\] |
| B. | \[4\] |
| C. | \[8\] |
| D. | \[6\] |
| Answer» B. \[4\] | |
| 559. |
Express the mixed recurring decimal 4.32 in the form \[\frac{p}{q}.\] |
| A. | \[\frac{389}{90}\] |
| B. | \[\frac{329}{90}\] |
| C. | \[\frac{29}{90}\] |
| D. | \[\frac{233}{990}\] |
| Answer» B. \[\frac{329}{90}\] | |
| 560. |
Which is an irrational number between \[\sqrt{2}\]and\[\sqrt{3}\]? |
| A. | \[{{2}^{\frac{1}{2}}}\] |
| B. | \[{{3}^{\frac{1}{4}}}\] |
| C. | \[{{6}^{\frac{1}{4}}}\] |
| D. | \[{{6}^{\frac{1}{8}}}\] |
| Answer» D. \[{{6}^{\frac{1}{8}}}\] | |
| 561. |
Which of the following numbers is an irrational number? |
| A. | \[\sqrt{16}-4\] |
| B. | \[\left( 3-\sqrt{3} \right)\left( 3+\sqrt{3} \right)\] |
| C. | \[\sqrt{5}+3\] |
| D. | \[-\sqrt{25}\] |
| Answer» D. \[-\sqrt{25}\] | |
| 562. |
Which of the following is an irrational number? |
| A. | \[\sqrt{9}\] |
| B. | \[\pi \] |
| C. | \[\frac{22}{7}\] |
| D. | \[2.5151515...\] |
| Answer» C. \[\frac{22}{7}\] | |
| 563. |
If \[\sqrt{a}\] is an irrational number, what is\[a\]? |
| A. | Rational |
| B. | Irrational |
| C. | 0 |
| D. | Real |
| Answer» B. Irrational | |
| 564. |
Find the difference between \[1.\overline{4}\] and\[0.\overline{2}\]. |
| A. | \[0.\overline{2}\] |
| B. | \[1.\overline{3}\] |
| C. | \[\frac{11}{9}\] |
| D. | \[\frac{12}{9}\] |
| Answer» D. \[\frac{12}{9}\] | |
| 565. |
Match the following, Column -I Column -II (a) If \[\frac{3}{x+8}=\frac{4}{6-x},\]then \[x\]is ______. (i) 3 (b) if, \[\frac{{{2}^{x-1}}{{.4}^{2x+1}}}{{{8}^{x-1}}}=64,\] (ii) \[-2\] (c) if \[{{4}^{x}}-{{4}^{x}}^{-1}=24\] (iii)\[-2\] (d) \[{{4}^{x+1}}=256,\]then \[x\]is (iv) 1 |
| A. | \[(a)\to (i);(b)\to (ii);(c)\to (iii);(d)\to (iv)\] |
| B. | \[(a)\to (iii);(b)\to (iv);(c)\to (i);(d)\to (ii)\] |
| C. | \[(a)\to (i);(b)\to (iv);(c)\to (ii);(d)\to (iii)\] |
| D. | \[(a)\to (iii);(b)\to (iv);(c)\to (iii);(d)\to (i)\] |
| Answer» E. | |
| 566. |
The sum of the digits of a number is subtracted from the number, the resulting number is always divisible by which of the following numbers? |
| A. | \[2\] |
| B. | \[5\] |
| C. | \[8\] |
| D. | \[9\] |
| Answer» E. | |
| 567. |
Read the statements carefully. Statement 1: Every point on the number line represent a unique real number. Statement 2: Irrational numbers cannot be represented on a number line. Which of the following options hold? |
| A. | Both Statement-1 and Statement-2 are true. |
| B. | Statement-1 is true but Statement-2 is false. |
| C. | Statement-1 is false but Statement-2 is true. |
| D. | Both Statement-1 and Statement-2 are false. |
| Answer» C. Statement-1 is false but Statement-2 is true. | |
| 568. |
Identify a rational number between \[-5\] and\[5\]. |
| A. | \[0\] |
| B. | \[-7.3\] |
| C. | \[-5.7\] |
| D. | \[1.101100110001\]. |
| Answer» B. \[-7.3\] | |
| 569. |
Fill in the blanks. (i) The decimal form of an irrational number is neither P nor Q. (ii) There are R rational numbers between any two consecutive integers. (iii) Every rational number is S. |
| A. | P Q R S non-repeating terminating zero real |
| B. | P Q R S non-repeating non-terminating infinite zero real |
| C. | P Q R S non-repeating non-terminating zero integer |
| D. | P Q R S repeating terminating inifinite integer |
| Answer» C. P Q R S non-repeating non-terminating zero integer | |
| 570. |
If\[x=7+4\sqrt{3}\]and\[xy=1\], what is the value of\[\frac{1}{{{x}^{2}}}+\frac{1}{{{y}^{2}}}\]? |
| A. | \[64\] |
| B. | \[134\] |
| C. | \[194\] |
| D. | \[1/49\] |
| Answer» D. \[1/49\] | |
| 571. |
The value of \[\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+\frac{1}{\sqrt{4}+\sqrt{5}}+\]\[\frac{1}{\sqrt{5}+\sqrt{6}}+\frac{1}{\sqrt{6}+\sqrt{7}}+\frac{1}{\sqrt{7}+\sqrt{8}}+\frac{1}{\sqrt{8}+\sqrt{9}}\]is _____. |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 4 |
| Answer» D. 4 | |
| 572. |
If\[x=\frac{2}{3-\sqrt{7}}\], find the value of\[{{(x-3)}^{2}}\]. |
| A. | \[1\] |
| B. | \[3\] |
| C. | \[6\] |
| D. | \[7\] |
| Answer» E. | |
| 573. |
If \[x=1-\sqrt{2},\]then find the value of \[{{\left( x-\frac{1}{x} \right)}^{2}}.\] |
| A. | 2 |
| B. | 3 |
| C. | 4 |
| D. | 5 |
| Answer» D. 5 | |
| 574. |
If\[x=\sqrt{5}+2\], find the value of\[x-\frac{1}{x}\]. |
| A. | \[2\sqrt{5}\] |
| B. | \[4\] |
| C. | \[2\] |
| D. | \[\sqrt{5}\] |
| Answer» C. \[2\] | |
| 575. |
Of which of the following is the set of natural numbers a subset? |
| A. | The set of even numbers. |
| B. | The set of odd numbers. |
| C. | The set of composite numbers. |
| D. | The set of real numbers. |
| Answer» E. | |
| 576. |
If \[x\]and y are positive real numbers, then which of the following is CORRECT? |
| A. | \[x>y\Rightarrow -x>-y\] |
| B. | \[x>y\Rightarrow -x<-y\] |
| C. | \[x>y\Rightarrow \frac{1}{x}>\frac{1}{y}\] |
| D. | \[x>y\Rightarrow \frac{1}{x}<\frac{-1}{y}\] |
| Answer» C. \[x>y\Rightarrow \frac{1}{x}>\frac{1}{y}\] | |
| 577. |
If\[{{4}^{x}}-{{4}^{x-1}}=24\], what is the value of\[{{(2x)}^{x}}\]? |
| A. | \[5\sqrt{5}\] |
| B. | \[\sqrt{5}\] |
| C. | \[25\sqrt{5}\] |
| D. | \[125\] |
| Answer» D. \[125\] | |
| 578. |
The number \[x=1.242424....\]can be expressed in the form \[x=\frac{p}{q},\]where p and q q are positive integers having no common factors. Then p + q equals ____. |
| A. | 72 |
| B. | 74 |
| C. | 41 |
| D. | 53 |
| Answer» C. 41 | |
| 579. |
If \[\frac{x}{{{x}^{1.5}}}=8{{x}^{-1}}\]and\[x>0\], find\[x\]. |
| A. | \[\frac{\sqrt{2}}{4}\] |
| B. | \[2\sqrt{2}\] |
| C. | \[4\] |
| D. | \[125\] |
| Answer» E. | |
| 580. |
Which of the following numbers has the terminating decimal representation? |
| A. | \[\frac{5}{12}\] |
| B. | \[\frac{8}{35}\] |
| C. | \[\frac{7}{24}\] |
| D. | \[\frac{13}{80}\] |
| Answer» E. | |
| 581. |
If\[{{10}^{x}}=64\], what is the value of\[{{10}^{\frac{x}{2}+1}}\]? |
| A. | \[18\] |
| B. | \[42\] |
| C. | \[80\] |
| D. | \[81\] |
| Answer» D. \[81\] | |
| 582. |
Which expression is equal to\[{{({{x}^{-1}}+{{y}^{-1}})}^{1}}\]? |
| A. | \[xy\] |
| B. | \[x+y\] |
| C. | \[\frac{xy}{x+y}\] |
| D. | \[\frac{x+y}{xy}\] |
| Answer» D. \[\frac{x+y}{xy}\] | |
| 583. |
Which of the following statements is INCORRECT? |
| A. | Every integer is a rational number. |
| B. | Every natural number is an integer. |
| C. | Every natural number is a real number. |
| D. | Every real number is a rational number. |
| Answer» E. | |
| 584. |
Find the value of \[x-{{y}^{x-y}}\] when \[x=2\] and\[y=-2\]. |
| A. | \[18\] |
| B. | \[-18\] |
| C. | \[14\] |
| D. | \[-14\] |
| Answer» E. | |
| 585. |
If \[x=2-\sqrt{3}\]then the value of \[{{x}^{2}}+\frac{1}{{{x}^{2}}}\] and \[{{x}^{2}}-\frac{1}{{{x}^{2}}}\]respectively, are____. |
| A. | \[14,8\sqrt{3}\] |
| B. | \[-14,-8\sqrt{3}\] |
| C. | \[14,-8\sqrt{3}\] |
| D. | \[-14,\,8\sqrt{3}\] |
| Answer» D. \[-14,\,8\sqrt{3}\] | |
| 586. |
The value of \[\frac{1}{3}\] of \[{{15}^{27}}\] is ____. |
| A. | \[{{5}^{27}}\] |
| B. | \[~{{15}^{9}}\] |
| C. | \[~5\times {{15}^{26}}\] |
| D. | \[~5\times {{3}^{9}}\] |
| Answer» D. \[~5\times {{3}^{9}}\] | |
| 587. |
If\[\frac{-4}{7}=\frac{-32}{x}\], what is the value of\[x\]? |
| A. | \[-56\] |
| B. | \[56\] |
| C. | \[-65\] |
| D. | \[65\] |
| Answer» C. \[-65\] | |
| 588. |
The value of \[x,\]if \[{{5}^{x-3}}{{.3}^{2x-8}}=225\] is______. |
| A. | 3 |
| B. | 4 |
| C. | 2 |
| D. | 5 |
| Answer» E. | |
| 589. |
What is the quotient when \[\sqrt[6]{12}\] is divided by\[\sqrt{3}\sqrt[3]{2}\]? |
| A. | \[\frac{1}{\sqrt[2]{3}}\] |
| B. | \[\frac{1}{\sqrt[3]{3}}\] |
| C. | \[\frac{1}{\sqrt[4]{3}}\] |
| D. | \[\frac{1}{\sqrt[5]{3}}\] |
| Answer» C. \[\frac{1}{\sqrt[4]{3}}\] | |
| 590. |
The greater number among \[\sqrt{17}-\sqrt{12}\] and \[\sqrt{11}-\sqrt{6}\]is_____. |
| A. | \[\sqrt{17}-\sqrt{12}\] |
| B. | \[\sqrt{11}-\sqrt{6}\] |
| C. | Both are equal |
| D. | Can't be compared |
| Answer» C. Both are equal | |
| 591. |
What is the product of\[\sqrt[3]{4}\]and\[\sqrt[3]{22}\]? |
| A. | \[2\sqrt[3]{11}\] |
| B. | \[\left( 3\sqrt{11} \right)\] |
| C. | \[4\sqrt{11}\] |
| D. | \[8\sqrt[3]{11}\] |
| Answer» B. \[\left( 3\sqrt{11} \right)\] | |
| 592. |
The ascending order of the surds \[\sqrt[3]{2},\sqrt[6]{3},\sqrt[9]{4},\] is ____. |
| A. | \[\sqrt[9]{4},\sqrt[6]{3},\sqrt[3]{2}\] |
| B. | \[\sqrt[9]{4},\sqrt[3]{2},\sqrt[6]{3}\] |
| C. | \[\sqrt[3]{2},\sqrt[6]{3},\sqrt[9]{4}\] |
| D. | \[\sqrt[6]{3},\sqrt[9]{4},\sqrt[3]{2}\] |
| Answer» B. \[\sqrt[9]{4},\sqrt[3]{2},\sqrt[6]{3}\] | |
| 593. |
Find the value of\[{{\left( \sqrt[6]{27}-\sqrt{6\frac{3}{4}} \right)}^{2}}\] |
| A. | \[\frac{\sqrt{3}}{2}\] |
| B. | \[\frac{3}{2}\] |
| C. | \[\frac{\sqrt{3}}{4}\] |
| D. | \[\frac{3}{4}\] |
| Answer» E. | |
| 594. |
If \[{{2}^{x-3}}{{.3}^{2x-8}}=36,\] then the value of \[x\]is______. |
| A. | 2 |
| B. | 5 |
| C. | 3 |
| D. | 1 |
| Answer» C. 3 | |
| 595. |
If \[a=\frac{x}{x+y}\] and \[b=\frac{x}{x-y}\], then \[\frac{ab}{a+b}\] is equal to: |
| A. | \[\frac{xy}{{{x}^{2}}+{{y}^{2}}}\] |
| B. | \[\frac{{{x}^{2}}+{{y}^{2}}}{xy}\] |
| C. | \[\frac{x}{x+y}\] |
| D. | \[{{\left( \frac{y}{x+y} \right)}^{2}}\] |
| E. | None of these |
| Answer» B. \[\frac{{{x}^{2}}+{{y}^{2}}}{xy}\] | |
| 596. |
The value of\[\frac{1}{\sqrt{6.25}+\sqrt{5.25}}+\frac{1}{\sqrt{4.25}+\sqrt{3.25}}+\frac{1}{\sqrt{5.25}+\sqrt{4.25}}+\frac{1}{\sqrt{3.25}+\sqrt{2.25}}\]is |
| A. | 1.00 |
| B. | 1.25 |
| C. | 1.50 |
| D. | 2.25 |
| Answer» B. 1.25 | |
| 597. |
A boy has enough money to buy 20 exercise books. If each book cost 25 paise less, he could buy two more books and still have 70 paise left. How much money had he originally? |
| A. | 45 |
| B. | 48 |
| C. | 50 |
| D. | 52 |
| E. | None of these |
| Answer» C. 50 | |
| 598. |
The value of: \[\sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{7+4\sqrt{3}}}}\]is |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 8 |
| Answer» C. 3 | |
| 599. |
If the sum of a number and its square is 182, then what is the number? |
| A. | 15 |
| B. | 26 |
| C. | 28 |
| D. | 13 |
| E. | None of these |
| Answer» E. None of these | |
| 600. |
\[\frac{{{\mathbf{x}}^{\mathbf{-1}}}}{{{\mathbf{x}}^{\mathbf{-1}}}\mathbf{+}{{\mathbf{y}}^{\mathbf{-1}}}}\mathbf{+}\frac{{{\mathbf{x}}^{\mathbf{-1}}}}{{{\mathbf{x}}^{\mathbf{-1}}}\mathbf{+}{{\mathbf{y}}^{\mathbf{-1}}}}\mathbf{=?}\] |
| A. | \[\frac{2{{y}^{2}}}{{{y}^{2}}-{{x}^{2}}}\] |
| B. | \[\frac{2{{x}^{2}}}{{{y}^{2}}-{{x}^{2}}}\] |
| C. | \[\frac{2{{y}^{2}}}{{{y}^{2}}+{{z}^{2}}}\] |
| D. | \[\frac{2{{x}^{2}}}{{{y}^{2}}+{{x}^{2}}}\] |
| Answer» B. \[\frac{2{{x}^{2}}}{{{y}^{2}}-{{x}^{2}}}\] | |