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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.
| 1801. |
What are the factors of\[{{x}^{3}}+{{x}^{2}}-\frac{1}{{{x}^{2}}}+\frac{1}{{{x}^{3}}}\]? |
| A. | \[\left( {{x}^{2}}+1 \right)\left( x+\frac{1}{x}-1+\frac{1}{{{x}^{2}}} \right)\] |
| B. | \[\left( x+1 \right)\left( {{x}^{2}}+\frac{1}{{{x}^{2}}}-1+\frac{1}{x}-x \right)\] |
| C. | \[\left( x+\frac{1}{x} \right)\left( {{x}^{2}}+x-1-\frac{1}{x}+\frac{1}{{{x}^{2}}} \right)\] |
| D. | \[\left( {{x}^{2}}+\frac{1}{{{x}^{2}}} \right)\left( x+\frac{1}{x}-1 \right)\] |
| Answer» D. \[\left( {{x}^{2}}+\frac{1}{{{x}^{2}}} \right)\left( x+\frac{1}{x}-1 \right)\] | |
| 1802. |
What is the product of\[\left( y-\frac{1}{y} \right)\left( y+\frac{1}{y} \right)\left( {{y}^{2}}+\frac{1}{{{y}^{2}}} \right)\]? |
| A. | \[{{y}^{4}}+\frac{1}{{{y}^{4}}}\] |
| B. | \[{{y}^{2}}+\frac{1}{{{y}^{2}}}+2\] |
| C. | \[{{y}^{4}}-\frac{1}{{{y}^{4}}}\] |
| D. | \[{{y}^{3}}+\frac{1}{{{y}^{3}}}-2\] |
| Answer» D. \[{{y}^{3}}+\frac{1}{{{y}^{3}}}-2\] | |
| 1803. |
If \[\mathbf{x=3+2}\sqrt{\mathbf{2}}\] and \[\mathbf{xy=1}\], then the value of \[\frac{{{\mathbf{x}}^{\mathbf{2}}}\mathbf{-3xy+}{{\mathbf{y}}^{\mathbf{2}}}}{{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+3xy+}{{\mathbf{y}}^{\mathbf{2}}}}\] is |
| A. | \[\frac{30}{31}\] |
| B. | \[\frac{70}{31}\] |
| C. | \[\frac{35}{31}\] |
| D. | \[\frac{31}{37}\] |
| Answer» E. | |
| 1804. |
If \[\mathbf{x+y+z}=0\] then \[\mathbf{3}\left[ \frac{{{\mathbf{x}}^{\mathbf{2}}}}{\mathbf{yz}}\mathbf{+}\frac{{{\mathbf{y}}^{\mathbf{2}}}}{\mathbf{zx}}\mathbf{+}\frac{{{\mathbf{z}}^{\mathbf{2}}}}{\mathbf{xy}} \right]\mathbf{=?}\] |
| A. | \[{{\left( xyz \right)}^{2}}\] |
| B. | \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}\] |
| C. | 9 |
| D. | 3 |
| Answer» D. 3 | |
| 1805. |
If\[{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+}{{\mathbf{y}}^{\mathbf{2}}}\mathbf{+}{{\mathbf{z}}^{\mathbf{2}}}\mathbf{+}\frac{\mathbf{1}}{{{\mathbf{x}}^{\mathbf{2}}}}\mathbf{+}\frac{\mathbf{1}}{{{\mathbf{y}}^{\mathbf{2}}}}\mathbf{+}\frac{\mathbf{1}}{{{\mathbf{z}}^{\mathbf{2}}}}\mathbf{=6}\], then the valve of \[{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+}{{\mathbf{y}}^{\mathbf{2}}}\mathbf{+}{{\mathbf{z}}^{\mathbf{2}}}\]is |
| A. | 3 |
| B. | 4 |
| C. | 8 |
| D. | 16 |
| Answer» B. 4 | |
| 1806. |
Find the coefficient of \[{{x}^{2}}\] in the product of\[(x-1)(1-2x)\]. |
| A. | \[-3\] |
| B. | \[3\] |
| C. | \[-2\] |
| D. | \[1\] |
| Answer» B. \[3\] | |
| 1807. |
If polynomials \[\mathbf{2}{{\mathbf{x}}^{\mathbf{3}}}\mathbf{+a}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+3x-5}\] and \[{{\mathbf{x}}^{\mathbf{3}}}\mathbf{+}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{-2x+a}\] are divided by\[\left( \mathbf{x-2} \right)\], the same remainders are obtained. Find the value of a. |
| A. | -3 |
| B. | 3 |
| C. | -4 |
| D. | -9 |
| Answer» B. 3 | |
| 1808. |
When the polynomial \[\mathbf{f(x)=}{{\mathbf{x}}^{\mathbf{4}}}\mathbf{+3}{{\mathbf{x}}^{\mathbf{3}}}\mathbf{-2}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+x-1}\] is divided by \[\left( \mathbf{x-2} \right)\] what will be the remainder? |
| A. | 17 |
| B. | 33 |
| C. | 23 |
| D. | 29 |
| Answer» C. 23 | |
| 1809. |
he factors of the expression \[\mathbf{4}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+4xy+}{{\mathbf{y}}^{\mathbf{2}}}\] is |
| A. | \[\left( 2x+y \right)\left( 2x+y \right)\] |
| B. | \[\left( 2x+y \right)\left( 2x-y \right)\] |
| C. | \[\left( 2x-y \right)(2x-y)\] |
| D. | \[\left( 2x+x \right)\left( 2y+x \right)\] |
| Answer» B. \[\left( 2x+y \right)\left( 2x-y \right)\] | |
| 1810. |
If \[{{\mathbf{x}}^{\mathbf{2}}}+\frac{1}{{{\mathbf{x}}^{\mathbf{2}}}}=\mathbf{123}.\]Then the value of \[{{\mathbf{x}}^{3}}-\frac{1}{{{\mathbf{x}}^{3}}}\] is |
| A. | 1340 |
| B. | 1364 |
| C. | 1358 |
| D. | 1360 |
| Answer» C. 1358 | |
| 1811. |
Factorise:\[ab{{(a+b)}^{2}}-3ab(a+b)\] |
| A. | \[(a+b)(a-b)ab\] |
| B. | \[(a+b-5)(2a+b)(a-b)\] |
| C. | \[ab(a+b)(a+b-3)\] |
| D. | \[ab(2a-b)(2a+b-6)\] |
| Answer» D. \[ab(2a-b)(2a+b-6)\] | |
| 1812. |
The factors of the expression \[{{\mathbf{x}}^{\mathbf{4}}}+{{\mathbf{x}}^{\mathbf{2}}}+\mathbf{1}\]is |
| A. | \[\left( {{x}^{2}}+1-x \right)\left( {{x}^{2}}-1+x \right)\] |
| B. | \[\left( {{x}^{2}}-1-x \right)\left( {{x}^{2}}-1-x \right)\] |
| C. | \[\left( {{x}^{2}}+1-x \right)\left( {{x}^{2}}-1-x \right)\] |
| D. | \[({{x}^{2}}+1-x)({{x}^{2}}+1+x)\] |
| Answer» E. | |
| 1813. |
If \[\mathbf{a}+\mathbf{b}+\mathbf{c}=\mathbf{12}\]and a2 + b2 + c2 = 50, then the value of \[\mathbf{ab}+\mathbf{be}+\mathbf{ca},\]is |
| A. | 44 |
| B. | 22 |
| C. | 23 |
| D. | 47 |
| Answer» E. | |
| 1814. |
The value of \[{{\left( \mathbf{-a+b+c} \right)}^{\mathbf{2}}}\] is |
| A. | \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}-2ab+2bc-2ca\] |
| B. | \[~{{a}^{2}}-{{b}^{2}}-{{c}^{2}}-2ab+2bc-2ca\] |
| C. | \[{{x}^{2}}-{{y}^{2}}+{{z}^{2}}-2xy+3yz-4xz\] |
| D. | \[{{a}^{2}}+{{b}^{2}}-{{c}^{2}}-2ab-2bc-2ac\] |
| Answer» B. \[~{{a}^{2}}-{{b}^{2}}-{{c}^{2}}-2ab+2bc-2ca\] | |
| 1815. |
What is the value of \[\frac{0.96\times 0.96\times 0.96+0.04\times 0.04\times 0.04}{0.96\times 0.96-0.96\times 0.04+0.04\times 0.04}\]? |
| A. | \[0\] |
| B. | \[2\] |
| C. | \[1\] |
| D. | Not defined |
| Answer» D. Not defined | |
| 1816. |
The remainder when \[{{x}^{4}}-{{y}^{4}}\]is divided by \[x-y\]is ____. |
| A. | 0 |
| B. | \[x+y\] |
| C. | \[{{x}^{2}}-{{y}^{2}}\] |
| D. | \[2{{y}^{4}}\] |
| Answer» B. \[x+y\] | |
| 1817. |
If \[\mathbf{(x+2)}\] and \[\left( \mathbf{x+3} \right)\] are two factors of \[{{\mathbf{x}}^{\mathbf{3}}}+\mathbf{9}{{\mathbf{x}}^{\mathbf{2}}}+\mathbf{26x}+\mathbf{24},\]then the third factor is |
| A. | \[x+7\] |
| B. | \[x+9\] |
| C. | \[x+4\] |
| D. | \[~x+8\] |
| Answer» D. \[~x+8\] | |
| 1818. |
If the area of rectangle is 3x2 + 6xy + 3y2 and its breadth is \[\mathbf{x+y,}\]then its length is |
| A. | \[x-2y\] |
| B. | \[-x+2y\] |
| C. | \[3x+3y\] |
| D. | \[x+y\] |
| Answer» D. \[x+y\] | |
| 1819. |
If \[\mathbf{x}+\mathbf{1}\text{ }\mathbf{and}\text{ }\mathbf{x}-\mathbf{1}\] are factors of \[\mathbf{f}\left( \mathbf{x} \right)\mathbf{=}{{\mathbf{x}}^{\mathbf{4}}}\mathbf{+3ax+b,}\] then the value of \[\mathbf{3a}+\mathbf{2b}\] is |
| A. | 5 |
| B. | -1 |
| C. | 4 |
| D. | -6 |
| Answer» C. 4 | |
| 1820. |
Identify the degree of the polynomial\[4-{{x}^{2}}-{{x}^{3}}+\frac{5{{x}^{7}}}{3}\]. |
| A. | \[2\] |
| B. | \[7\] |
| C. | \[0\] |
| D. | \[3\] |
| Answer» C. \[0\] | |
| 1821. |
Find the remainder when the expression \[3{{x}^{3}}+8{{x}^{2}}-6x+1\] is divided by \[x+3.\] |
| A. | 1 |
| B. | 10 |
| C. | 6 |
| D. | 0 |
| Answer» C. 6 | |
| 1822. |
Factorise:\[{{a}^{4}}+4\] |
| A. | \[({{a}^{2}}+2a-2)({{a}^{2}}+2a+2)\] |
| B. | \[({{a}^{2}}-2a-2)({{a}^{2}}+2a-2)\] |
| C. | \[({{a}^{2}}+2a-2)({{a}^{2}}-2a+2)\] |
| D. | \[({{a}^{2}}+2a+2)({{a}^{2}}-2a+2)\] |
| Answer» E. | |
| 1823. |
If \[\mathbf{x+}\frac{\mathbf{1}}{\mathbf{x}}\mathbf{=3}\], then the value of \[\frac{{{\mathbf{x}}^{\mathbf{4}}}\mathbf{+3}{{\mathbf{x}}^{\mathbf{3}}}\mathbf{+5}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+3x+1}}{{{\mathbf{x}}^{\mathbf{4}}}\mathbf{+1}}\] |
| A. | 3 |
| B. | 5 |
| C. | 7 |
| D. | 9 |
| Answer» B. 5 | |
| 1824. |
If \[{{\left( \mathbf{a+}\frac{\mathbf{1}}{\mathbf{a}}\mathbf{~} \right)}^{\mathbf{2}}}\mathbf{=3}\], then the value of \[{{\mathbf{a}}^{\mathbf{206}}}\mathbf{+}{{\mathbf{a}}^{\mathbf{200}}}\mathbf{+}{{\mathbf{a}}^{\mathbf{90}}}\mathbf{+}{{\mathbf{a}}^{\mathbf{84}}}\mathbf{+}{{\mathbf{a}}^{\mathbf{18}}}\mathbf{+}{{\mathbf{a}}^{\mathbf{12}}}\mathbf{+}{{\mathbf{a}}^{\mathbf{6}}}\mathbf{+1}\]is |
| A. | 0 |
| B. | 1 |
| C. | 84 |
| D. | 206 |
| Answer» B. 1 | |
| 1825. |
If \[\mathbf{xy}\left( \mathbf{x}-\mathbf{y} \right)=\mathbf{1}\], then the value of \[\frac{\mathbf{1}}{{{\mathbf{x}}^{\mathbf{3}}}{{\mathbf{y}}^{\mathbf{3}}}}\mathbf{-}{{\mathbf{x}}^{\mathbf{3}}}\mathbf{+}{{\mathbf{y}}^{\mathbf{3}}}\]is: |
| A. | 0 |
| B. | 1 |
| C. | 3 |
| D. | -3 |
| Answer» D. -3 | |
| 1826. |
In how many ways 4 rings of different types can be worn in 3 fingers? |
| A. | 49 |
| B. | 12 |
| C. | 24 |
| D. | 81 |
| Answer» E. | |
| 1827. |
How many numbers of 5 digits can be formed with the digits 0,2,3,4 and 5 if the digits may repeat? |
| A. | 2500 |
| B. | 250 |
| C. | 120 |
| D. | 2400 |
| Answer» B. 250 | |
| 1828. |
Given \[X\]: Every fraction is a rational number and \[Y\]: Every rational number is a fraction. Which of the following is correct? |
| A. | \[X\] is False and \[Y\] is True. |
| B. | \[X\] is True and \[Y\] is False. |
| C. | Both \[X\] and \[Y\] are True. |
| D. | Both \[X\] and \[Y\] are False. |
| Answer» C. Both \[X\] and \[Y\] are True. | |
| 1829. |
If\[2.5252525...=\frac{p}{q}\](in the lowest form) what is the value of\[\frac{q}{p}\]? |
| A. | \[0.4\] |
| B. | \[0.42525\] |
| C. | \[0.0396\] |
| D. | \[0.396\] |
| Answer» E. | |
| 1830. |
If\[x=\frac{1}{2-\sqrt{3}}\], find the value of\[{{x}^{3}}-2{{x}^{2}}-7x+10\]. |
| A. | \[14\] |
| B. | \[8\] |
| C. | \[4\] |
| D. | \[16\] |
| Answer» C. \[4\] | |
| 1831. |
If\[\sqrt{5}=2.236\]and\[\sqrt{3}=1.732\], find the value of\[\frac{1}{\sqrt{5}-\sqrt{3}}\]. |
| A. | \[3.968\] |
| B. | \[\frac{1}{3.968}\] |
| C. | \[1.984\] |
| D. | \[\sqrt{0.504}\] |
| Answer» D. \[\sqrt{0.504}\] | |
| 1832. |
If \[N=\frac{\sqrt{\sqrt{5}+2}+\sqrt{5-2}}{\sqrt{\sqrt{5}+1}}-\sqrt{3-2\sqrt{2}},\] then N equals ____. |
| A. | 1 |
| B. | \[2\sqrt{2}-1\] |
| C. | \[\frac{\sqrt{5}}{2}\] |
| D. | \[\frac{2}{\sqrt{\sqrt{5}+1}}\] |
| Answer» B. \[2\sqrt{2}-1\] | |
| 1833. |
If \[\frac{(\sqrt{3}-1)}{(\sqrt{3}+1)}=(a-b\sqrt{3}),\] find the values of a and b. |
| A. | \[a=1,b=2\] |
| B. | a = 2,b = 1 |
| C. | a = 2, b = 3 |
| D. | a = 3, b = 2 |
| Answer» C. a = 2, b = 3 | |
| 1834. |
If\[{{9}^{x+2}}=240+{{9}^{x}}\], find\[x\]. |
| A. | \[0.5\] |
| B. | \[0.2\] |
| C. | \[0.4\] |
| D. | \[0.1\] |
| Answer» B. \[0.2\] | |
| 1835. |
Which of the following is not a rational number? |
| A. | \[\sqrt{2}\] |
| B. | \[\sqrt{4}\] |
| C. | \[\sqrt{9}\] |
| D. | \[\sqrt{16}\] |
| Answer» B. \[\sqrt{4}\] | |
| 1836. |
If \[m=\sqrt{3+\sqrt{3+\sqrt{3+.....}}}\] \[n=\sqrt{3-\sqrt{3-\sqrt{3-.........}}}\] Then among the following the relation between m and n holds is |
| A. | \[m-n+1=0\] |
| B. | \[~m+n-1=0\] |
| C. | \[m+n+1=0\] |
| D. | \[m-n-1=0\] |
| Answer» E. | |
| 1837. |
The value of\[\sqrt{4\sqrt[3]{16\sqrt{4\sqrt[3]{16}\sqrt{4\sqrt[3]{16}}}}}......\]is |
| A. | 2 |
| B. | \[{{2}^{2}}\] |
| C. | 23 |
| D. | \[{{2}^{5}}\] |
| Answer» C. 23 | |
| 1838. |
\[\frac{1}{3-\sqrt{8}}-\frac{1}{\sqrt{8}-\sqrt{7}}+\frac{1}{\sqrt{7}-\sqrt{6}}-\frac{1}{\sqrt{6}-\sqrt{5}}+\frac{1}{\sqrt{5}-2}=\] |
| A. | 5 |
| B. | 4 |
| C. | 3 |
| D. | 2 |
| Answer» B. 4 | |
| 1839. |
\[({{5}^{61}}+{{5}^{62}}+{{5}^{63}})\]is divisible by |
| A. | 31 |
| B. | 11 |
| C. | 13 |
| D. | 17 |
| Answer» B. 11 | |
| 1840. |
If \[x=\sqrt[3]{2+\sqrt{3}}\],then \[{{\mathbf{x}}^{\mathbf{3}}}+\frac{1}{{{\mathbf{x}}^{\mathbf{3}}}},=\] |
| A. | 2 |
| B. | 4 |
| C. | 8 |
| D. | 9 |
| Answer» C. 8 | |
| 1841. |
If the sum of five consecutive integers is S, then the largest of those integers in terms of S is |
| A. | \[\frac{S-10}{5}\] |
| B. | \[\frac{S-4}{4}\] |
| C. | \[\frac{S+5}{4}\] |
| D. | \[\frac{S+10}{5}\] |
| Answer» E. | |
| 1842. |
The smallest of \[\sqrt{6}+\sqrt{3},\] \[\sqrt{7}+\sqrt{2},\]\[\sqrt{8}+\sqrt{1},\] \[\sqrt{5}+\sqrt{4}\] is |
| A. | \[\sqrt{6}+\sqrt{3}\] |
| B. | \[\sqrt{7}+\sqrt{2}\] |
| C. | \[\sqrt{8}+\sqrt{1}\] |
| D. | \[\sqrt{5}+\sqrt{4}\] |
| Answer» D. \[\sqrt{5}+\sqrt{4}\] | |
| 1843. |
The greatest among \[\sqrt{\mathbf{11}}\mathbf{-}\sqrt{\mathbf{9}}\mathbf{,}\sqrt{\mathbf{5}}\mathbf{-}\sqrt{\mathbf{3}}\mathbf{,}\sqrt{\mathbf{7}}\mathbf{-}\sqrt{\mathbf{5}}\mathbf{,}\sqrt{\mathbf{13}}\mathbf{-}\sqrt{\mathbf{11}}\]is |
| A. | \[\sqrt{11}-\sqrt{9}\] |
| B. | \[\sqrt{5}-\sqrt{3}\] |
| C. | \[\sqrt{7}-\sqrt{5}\] |
| D. | \[\sqrt{13}-\sqrt{11}\] |
| Answer» C. \[\sqrt{7}-\sqrt{5}\] | |
| 1844. |
\[\frac{{{\left( {{\mathbf{a}}^{\mathbf{x+y}}} \right)}^{\mathbf{2}}}{{\left( {{\mathbf{a}}^{\mathbf{y+z}}} \right)}^{\mathbf{2}}}{{\left( {{\mathbf{a}}^{\mathbf{z+x+}}} \right)}^{\mathbf{2}}}}{\left( {{\mathbf{a}}^{\mathbf{4x}}}\mathbf{.}{{\mathbf{a}}^{\mathbf{4y}}}\mathbf{.}{{\mathbf{a}}^{\mathbf{4z}}} \right)}\mathbf{=?}\] |
| A. | 2a |
| B. | \[x+y+z\] |
| C. | 1 |
| D. | 0 |
| Answer» D. 0 | |
| 1845. |
\[\mathbf{0}.\mathbf{142857}-\mathbf{0}.\mathbf{285714}\]is equal to |
| A. | 2 |
| B. | 1 |
| C. | 0 |
| D. | \[\frac{1}{2}\] |
| Answer» E. | |
| 1846. |
The product of \[\left( 0.\overline{\mathbf{09}}\times \mathbf{7}.\overline{\mathbf{3}} \right)\] is equal to |
| A. | 1 |
| B. | 0 |
| C. | 0 |
| D. | \[\frac{1}{2}\] |
| Answer» D. \[\frac{1}{2}\] | |
| 1847. |
If\[{{\mathbf{2}}^{\mathbf{x-1}}}\mathbf{+}{{\mathbf{2}}^{\mathbf{x+1}}}\mathbf{=640}\], the value of x is |
| A. | 7 |
| B. | 8 |
| C. | 9 |
| D. | 6 |
| Answer» C. 9 | |
| 1848. |
If \[x=\frac{1}{2+\sqrt{3}}\], then the value of \[{{x}^{3}}-2{{x}^{2}}-7x+5\]is |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» D. 4 | |
| 1849. |
The two irrational numbers lying between \[\sqrt{\mathbf{3}}\]and \[\sqrt{5}\] are |
| A. | \[{{15}^{\frac{1}{4}}},\frac{{{3}^{\frac{1}{4}}}}{1}\times {{15}^{\frac{1}{8}}}\] |
| B. | \[{{6}^{\frac{1}{2}}},{{2}^{\frac{1}{8}}}\times {{6}^{\frac{1}{4}}}\] |
| C. | \[{{6}^{\frac{1}{8}}},{{2}^{\frac{1}{6}}}\times {{6}^{\frac{1}{6}}}\] |
| D. | \[{{3}^{\frac{1}{8}}},{{2}^{\frac{1}{8}}}\times {{6}^{\frac{1}{8}}}\] |
| Answer» B. \[{{6}^{\frac{1}{2}}},{{2}^{\frac{1}{8}}}\times {{6}^{\frac{1}{4}}}\] | |
| 1850. |
If \[7\sqrt[4]{162}-5\sqrt[4]{32}+\sqrt[4]{1250}\] is simplified, then the resultant value is |
| A. | \[6\sqrt[3]{2}\] |
| B. | \[6\sqrt[4]{2}\] |
| C. | \[6\sqrt[5]{2}\] |
| D. | \[16\sqrt[4]{2}\] |
| Answer» E. | |