MCQOPTIONS
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MCQOPTIONS
This section includes 33 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Factorize \[{{x}^{2}}+\frac{1}{{{x}^{2}}}+2-2x-\frac{2}{x}\] |
| A. | \[\left( x+\frac{1}{x} \right)\left( x+\frac{1}{x}-2 \right)\] |
| B. | \[\left( x-\frac{1}{x} \right)\left( x+\frac{1}{x}-2 \right)\] |
| C. | \[\left( x-\frac{1}{x} \right)\left( x-\frac{1}{x}+2 \right)\] |
| D. | \[\left( x+\frac{1}{x} \right)\left( x-\frac{1}{x}+2 \right)\] |
| Answer» B. \[\left( x-\frac{1}{x} \right)\left( x+\frac{1}{x}-2 \right)\] | |
| 2. |
Which two binomials when multiplied give \[5ct-5c+6-6t?\] |
| A. | \[(5c-6)\]and \[(t-1)\] |
| B. | \[(5c+6)\]and \[(t+1)\] |
| C. | |
| D. | \[(6c-1)\]and \[(t-5)\] |
| Answer» B. \[(5c+6)\]and \[(t+1)\] | |
| 3. |
\[9{{x}^{2}}+12xy+4{{y}^{2}}-25{{z}^{2}}\]is expressed as a product of two trinomials. Identify it. |
| A. | \[(3x+2y-5z)(3x-2y-5z)\] |
| B. | \[(3x+2y+5z)(3x-2y-5z)\] |
| C. | |
| D. | \[(3x-2y-5z)(3x-2y+5z)\] |
| Answer» D. \[(3x-2y-5z)(3x-2y+5z)\] | |
| 4. |
Identify the four binomials whose product is \[{{({{x}^{2}}-2x)}^{2}}\]\[11({{x}^{2}}+2x)+24.\] |
| A. | \[(x-4),(x+2),(x-3)\] and\[(x+1)\] |
| B. | \[(x+6),(x-2),(x+3)\] and\[(x-1)\] |
| C. | |
| D. | \[(x-6),(x+2),(x-3)\] and\[(x+1)\] |
| Answer» D. \[(x-6),(x+2),(x-3)\] and\[(x+1)\] | |
| 5. |
If one of the factors of \[12-4x-5{{x}^{2}}\]is \[x+2,\]find the other. |
| A. | \[5x+6\] |
| B. | \[5x-6\] |
| C. | |
| D. | \[-5x-6\] |
| Answer» D. \[-5x-6\] | |
| 6. |
Find the factors of \[25{{x}^{2}}-60xy+36{{y}^{2}}.\] |
| A. | \[(5x-3y)\]and\[(5x-12y)\] |
| B. | \[(6x-5y)\]and\[(6x-2y)\] |
| C. | |
| D. | \[(5x-3y)\]and\[(5x-3y)\] |
| Answer» E. | |
| 7. |
Factorization: \[\mathbf{6}{{\mathbf{x}}^{\mathbf{2}}}+11\mathbf{x}-\mathbf{10}\] |
| A. | \[\left( 2x+5 \right)\left( 3x-2 \right)\] |
| B. | \[\left( 2x+5 \right)\left( 2x+2 \right)\] |
| C. | \[\left( 2x+5 \right)\] |
| D. | \[\left( 2x+2 \right)\left( x-2 \right)\] |
| Answer» B. \[\left( 2x+5 \right)\left( 2x+2 \right)\] | |
| 8. |
Solve \[{{\left( \mathbf{a}+\mathbf{b} \right)}^{\mathbf{2}}}-{{\left( \mathbf{a}-\mathbf{b} \right)}^{\mathbf{2}}}\] |
| A. | \[2ab\] |
| B. | \[{{a}^{2}}+{{b}^{2}}\] |
| C. | \[2{{a}^{2}}+2{{b}^{2}}\] |
| D. | \[4ab\] |
| Answer» E. | |
| 9. |
Factorization: \[{{\mathbf{x}}^{\mathbf{2}}}-\mathbf{3x}-\mathbf{54}\] |
| A. | \[\left( x-9 \right)\left( x-6 \right)\] |
| B. | \[\left( x-9 \right)\left( x+6 \right)\] |
| C. | \[\left( x+9 \right)\left( x+6 \right)\] |
| D. | \[\left( x-4 \right)\left( x+3 \right)\] |
| Answer» C. \[\left( x+9 \right)\left( x+6 \right)\] | |
| 10. |
Factorize \[\mathbf{36}{{\mathbf{x}}^{\mathbf{3}}}\mathbf{y}-\mathbf{60}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{yz}\] |
| A. | \[12{{x}^{2}}y\left( 3x-5z \right)\] |
| B. | \[12{{x}^{2}}y(3x+5z)\] |
| C. | \[12{{x}^{2}}\left( 5z-3x \right)\] |
| D. | \[6{{x}^{2}}y\left( 6x-2z \right)\] |
| Answer» B. \[12{{x}^{2}}y(3x+5z)\] | |
| 11. |
The value of \[\left( x-y \right)\left( x+y \right)\left( {{x}^{2}}+{{y}^{^{2}}} \right)\left\{ {{\left( {{x}^{2}}+{{y}^{^{2}}} \right)}^{2}}-2{{x}^{2}}{{y}^{2}} \right\}\]is |
| A. | \[{{x}^{8}}-{{y}^{8}}\] |
| B. | \[{{x}^{8}}+{{y}^{8}}\] |
| C. | \[{{x}^{6}}-{{y}^{6}}\] |
| D. | \[{{x}^{6}}+{{y}^{6}}\] |
| Answer» B. \[{{x}^{8}}+{{y}^{8}}\] | |
| 12. |
Factorize \[\mathbf{16}{{\mathbf{x}}^{\mathbf{2}}}-\mathbf{25}{{\mathbf{y}}^{\mathbf{2}}}\] |
| A. | \[{{(4x-5y)}^{2}}\] |
| B. | \[{{(4x+5y)}^{2}}\] |
| C. | \[\frac{4x+5y}{4x-5y}\] |
| D. | \[\left( 4x+5y \right)(4x-5y)\] |
| Answer» E. | |
| 13. |
Factorize the given expression \[~\mathbf{mn}({{\mathbf{u}}^{\mathbf{2}}}+{{\mathbf{v}}^{\mathbf{2}}})-\mathbf{uv}\left( {{\mathbf{m}}^{\mathbf{2}}}+{{\mathbf{n}}^{\mathbf{2}}} \right)\] |
| A. | \[\left( un+vm \right)\left( um-vn \right)\] |
| B. | \[\left( un+vm \right)\left( um+vn \right)\] |
| C. | \[\left( un-vm \right)\left( um-vn \right)\] |
| D. | \[\left( un-vm \right)\left( um+vn \right)\] |
| Answer» D. \[\left( un-vm \right)\left( um+vn \right)\] | |
| 14. |
Factorize \[\left( p+q \right)\left( 2p+5 \right)-\left( p+q \right)\left( p+3 \right)\] |
| A. | \[\left( p-q \right)\left( p+2 \right)\] |
| B. | \[\left( p-q \right)\left( p-2 \right)\] |
| C. | \[\left( p-q \right)\left( p+2 \right)\] |
| D. | \[\left( p+q \right)\left( p+2 \right)\] |
| Answer» E. | |
| 15. |
Factorize the expression given by \[18{{x}^{3}}{{y}^{3}}-27{{x}^{2}}{{y}^{3}}+36{{x}^{3}}{{y}^{2}}\] |
| A. | \[9{{x}^{2}}{{y}^{2}}(2xy-3y+4x)\] |
| B. | \[9{{x}^{2}}{{y}^{2}}(2xy+3y+4x)\] |
| C. | \[~9{{x}^{2}}{{y}^{2}}(2xy+3y-4x)\] |
| D. | \[9{{x}^{2}}{{y}^{2}}(2xy-3y-4x)\] |
| Answer» B. \[9{{x}^{2}}{{y}^{2}}(2xy+3y+4x)\] | |
| 16. |
The degree of \[-3{{x}^{3}}+5{{x}^{2}}+4\] is |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» D. 4 | |
| 17. |
Factorization: \[{{x}^{2}}{{y}^{2}}-12xy-45\] |
| A. | \[\left( xy-15 \right)\left( xy+3 \right)\] |
| B. | \[\left( xy+15 \right)\left( xy+3 \right)\] |
| C. | \[\left( xy-15 \right)\left( xy-3 \right)\] |
| D. | \[\left( x-15 \right)\left( y+3 \right)\] |
| Answer» B. \[\left( xy+15 \right)\left( xy+3 \right)\] | |
| 18. |
Factorization: \[2{{x}^{3}}+5x-12x{{y}^{2}}\] |
| A. | \[x\left( x+2y \right)\left( 2x+3y \right)\] |
| B. | \[x~\left( x+4y \right)\left( 2x-3y \right)\] |
| C. | \[~x\left( x-4y \right)\left( 2x-3y \right)\] |
| D. | \[x\left( x+2y \right)\left( x-3y \right)\] |
| Answer» C. \[~x\left( x-4y \right)\left( 2x-3y \right)\] | |
| 19. |
Factorization: \[\mathbf{1}-\mathbf{18z}-\mathbf{63}{{\mathbf{z}}^{\mathbf{2}}}\] |
| A. | \[\left( 3-21z \right)\left( 1+3z \right)\] |
| B. | \[\left( 1-21z \right)\left( 1+3z \right)\] |
| C. | \[\left( 2+21z \right)\left( 1+3z \right)\] |
| D. | \[\left( 1-7z \right)\left( 1+2z \right)\] |
| Answer» C. \[\left( 2+21z \right)\left( 1+3z \right)\] | |
| 20. |
Factorization: \[\mathbf{7}-\mathbf{12x}-\mathbf{4}{{\mathbf{x}}^{\mathbf{2}}}\] |
| A. | \[\left( 1-2x \right)\left( 7+2x \right)\] |
| B. | \[\left( 1-2x \right)\left( 7-2x \right)\] |
| C. | \[\left( 1-x \right)\left( 7+x \right)\] |
| D. | \[\left( 1+2x \right)\left( 4+x \right)\] |
| Answer» B. \[\left( 1-2x \right)\left( 7-2x \right)\] | |
| 21. |
Factorization: \[2{{x}^{2}}+5x-3\] |
| A. | \[\left( x+3 \right)\left( 2x+1 \right)\] |
| B. | \[\left( x-3 \right)\left( 2x-1 \right)\] |
| C. | \[\left( x+2 \right)(x-1)\] |
| D. | \[\left( x+3 \right)(2x-1)\] |
| Answer» E. | |
| 22. |
Factorize \[{{\mathbf{a}}^{\mathbf{3}}}-\mathbf{2}\sqrt{\mathbf{2}}{{\mathbf{b}}^{\mathbf{3}}}\]is |
| A. | \[(a+\sqrt{2}b)({{a}^{2}}-\sqrt{2}ab+2{{b}^{2}})\] |
| B. | \[(a-\sqrt{2}b)({{a}^{2}}+\sqrt{2}ab+2{{b}^{2}})\] |
| C. | \[(a-\sqrt{2}b)({{a}^{2}}-\sqrt{2}ab+2{{b}^{2}})\] |
| D. | \[(a-\sqrt{2}b)({{a}^{2}}+\sqrt{2}ab+{{b}^{2}})\] |
| Answer» C. \[(a-\sqrt{2}b)({{a}^{2}}-\sqrt{2}ab+2{{b}^{2}})\] | |
| 23. |
The factors of \[(\mathbf{1}-\mathbf{6z}-\mathbf{9}{{\mathbf{z}}^{2}})\] are |
| A. | \[\left( 1+3z \right)\left( 1-3z \right)\] |
| B. | \[{{\left( z+3 \right)}^{2}}\] |
| C. | \[{{\left( 3z-1 \right)}^{2}}\] |
| D. | \[{{\left( z-3 \right)}^{2}}\] |
| Answer» D. \[{{\left( z-3 \right)}^{2}}\] | |
| 24. |
Find the quotient when \[5{{a}^{2}}{{b}^{2}}{{c}^{2}}\] is divided by15abc. |
| A. | \[\frac{abc}{3}\] |
| B. | \[3\,abc\] |
| C. | \[3\,{{a}^{2}}{{b}^{2}}{{c}^{2}}\] |
| D. | \[5\,{{a}^{2}}{{b}^{2}}{{c}^{2}}\] |
| Answer» B. \[3\,abc\] | |
| 25. |
The factors of \[\sqrt{3}{{x}^{2}}+11x+6\sqrt{3}\] are __. |
| A. | \[\left( x-3\sqrt{3} \right)\left( \sqrt{3}x+2 \right)\] |
| B. | \[\left( x-3\sqrt{3} \right)\left( \sqrt{3}x-2 \right)\] |
| C. | \[\left( x+3\sqrt{3} \right)\left( \sqrt{3}x-2 \right)\] |
| D. | \[\left( x+3\sqrt{3} \right)\left( \sqrt{3}x+2 \right)\] |
| Answer» E. | |
| 26. |
Which of the following factorizations is correct? |
| A. | \[2-32{{x}^{2}}=2{{(1-4x)}^{2}}\] |
| B. | \[4{{x}^{2}}-49=(7-2x)\,(7+2x)\] |
| C. | \[-18{{x}^{2}}+27x=9x(2x-3)\] |
| D. | \[-25-150{{p}^{2}}=(-25)\,(1+6{{p}^{2}})\] |
| Answer» E. | |
| 27. |
What is the factor form of \[9{{x}^{4}}-40{{x}^{2}}+16\]? |
| A. | \[(x+1)\,(x-1)\,(2x+1)\,(2x-1)\] |
| B. | \[(2x-1)\,(4{{x}^{2}}+2x+1)\] |
| C. | \[(x+2)\,(2x-3)(x-1)\,(2x+3)\] |
| D. | \[(x+2)\,(x-2)\,(3x+2)\,(3x-2)\] |
| Answer» E. | |
| 28. |
Give the factor form of \[6{{m}^{2}}n+9m{{n}^{2}}l+12mnl\]. |
| A. | \[3mn(2m+3nl+4l)\] |
| B. | \[4mn(4m+4nl+2l)\] |
| C. | \[5mn(2m+2nl+l)\] |
| D. | \[3mn(m+2nl+2l)\] |
| Answer» B. \[4mn(4m+4nl+2l)\] | |
| 29. |
What are the factors of \[{{(2x+3y)}^{2}}+2(2x+3y)\,(x+y)+{{(x+y)}^{2}}\]? |
| A. | \[(3x+4y)\] and \[(3x-4y)\] |
| B. | \[(3x+4y)\]and \[(3x+4y)\] |
| C. | \[(3x+2y)\] and \[(2x-3y)\] |
| D. | \[(3x-4y)\] and \[(3x+2y)\] |
| Answer» C. \[(3x+2y)\] and \[(2x-3y)\] | |
| 30. |
Which of the following is one of the factors of \[{{x}^{4}}+4\]? |
| A. | \[{{x}^{2}}+2\] |
| B. | \[{{x}^{2}}-2x+2\] |
| C. | \[{{x}^{2}}-2\] |
| D. | \[{{x}^{2}}+2x-2\] |
| Answer» C. \[{{x}^{2}}-2\] | |
| 31. |
Match the expression given in Column-I to one of their factors given in Column-II. Column - I Column - II P. \[9{{x}^{2}}+24x+16\] (i) \[(2x-4)\] Q. \[25{{x}^{2}}+30x+9\] (ii) \[(4x+1)\] R. \[40{{x}^{2}}+14x+1\] (iii) \[(5x+3)\] S. \[4{{x}^{2}}-16x+16\] (iv) \[(3x+4)\] |
| A. | P\[\to \](iv); Q\[\to \](iii); R\[\to \](ii); S\[\to \](i) |
| B. | P\[\to \](iii): Q\[\to \](i); R\[\to \](iv); S\[\to \](ii) |
| C. | P\[\to \](ii); Q\[\to \](i); R\[\to \](iv): S\[\to \](iii) |
| D. | P\[\to \](iv); Q\[\to \](iii); R\[\to \](i); S\[\to \](ii) |
| Answer» B. P\[\to \](iii): Q\[\to \](i); R\[\to \](iv); S\[\to \](ii) | |
| 32. |
The expression \[({{p}^{2}}+7p+10)\] is factorized and then divided by \[(p+5)\]. What is the quotient? |
| A. | \[p-5\] |
| B. | \[p-2\] |
| C. | \[p+2\] |
| D. | \[p+5\] |
| Answer» D. \[p+5\] | |
| 33. |
One of the factors of \[4(x+y)\,(3a-b)+6(x+y)\,(2b-3a)\] is |
| A. | \[(2b-3a)\] |
| B. | \[(3a-b)\] |
| C. | \[(4a-3b)\] |
| D. | \[(-3a+4b)\] |
| Answer» E. | |