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MCQOPTIONS
This section includes 1185 Mcqs, each offering curated multiple-choice questions to sharpen your 8th Class knowledge and support exam preparation. Choose a topic below to get started.
| 451. |
One of the factors of \[15{{p}^{4}}+3{{p}^{2}}-18\] is equated to 26. Find the integral value of p. |
| A. | \[~\pm \text{ }36\] |
| B. | \[\pm \,3\sqrt{3}\] |
| C. | \[~\pm \,2\] |
| D. | \[~\pm \,3\] |
| Answer» D. \[~\pm \,3\] | |
| 452. |
Which of the following is the correct factorization of \[9{{x}^{4}}-40{{x}^{2}}+16?\] |
| A. | \[(2x+1)(x-2)(x+3)(x-7)\] |
| B. | \[(3x+2)(3x-2)(x+2)(x-2)\] |
| C. | \[(x-4)(x+2)(x-3)(x+1)\] |
| D. | \[(2x-1)(2x+1)(x+1)\left( x-1 \right)\] |
| Answer» C. \[(x-4)(x+2)(x-3)(x+1)\] | |
| 453. |
Find the factors of\[~8{{x}^{6}}-65{{x}^{3}}+8.\] |
| A. | \[(8{{x}^{2}}-1)\] and \[({{x}^{2}}-8)\] |
| B. | \[(2{{x}^{3}}-1)\]and \[({{x}^{3}}-8)\] |
| C. | \[(8{{x}^{3}}-1)\]and\[({{x}^{3}}-8)\] |
| D. | \[~(2{{x}^{3}}-1)\] and \[(2{{x}^{3}}-2)\] |
| Answer» D. \[~(2{{x}^{3}}-1)\] and \[(2{{x}^{3}}-2)\] | |
| 454. |
The product of two binomials is \[25{{(m+n)}^{2}}-36{{(m-2n)}^{2}}.\]Find them. |
| A. | (5m - n) and (6m -n) |
| B. | (m + 5n) and (m - 6n) |
| C. | (5n - m) and (6n - m) |
| D. | (11m - 7n) and (17n - m) |
| Answer» E. | |
| 455. |
If \[x-y=3\]and \[{{x}^{2}}+{{y}^{2}}=29,\]find the value of \[xy:\] |
| A. | 11 |
| B. | 10 |
| C. | 12 |
| D. | 13 |
| Answer» C. 12 | |
| 456. |
The factors of \[{{a}^{2}}{{b}^{2}}+{{c}^{2}}{{d}^{2}}-{{a}^{2}}{{c}^{2}}-{{b}^{2}}{{d}^{2}}\]are binomials A and B. Identify them. |
| A. | \[A=({{b}^{2}}-{{c}^{2}})\] and \[B=({{a}^{2}}+{{d}^{2}})\] |
| B. | \[A=({{b}^{2}}-{{c}^{2}})\]and \[B=({{a}^{2}}-{{d}^{2}})\] |
| C. | \[A=({{a}^{2}}-{{b}^{2}})\]and \[B=({{c}^{2}}-{{d}^{2}})\] |
| D. | \[A=({{a}^{2}}-{{c}^{2}})\]and \[B=({{b}^{2}}-{{d}^{2}})\] |
| Answer» C. \[A=({{a}^{2}}-{{b}^{2}})\]and \[B=({{c}^{2}}-{{d}^{2}})\] | |
| 457. |
What are the possible expressions for the dimensions of the cuboid whose volume is \[2{{x}^{2}}+10x+12?\] |
| A. | Length = 2, breadth\[=x+3,\] height \[=x+2\] |
| B. | Length = 5, breadth \[=x+4,\]height\[=x+3\] |
| C. | Length = 3, breadth \[=x+6,\]height \[=x+2\] |
| D. | Length\[=4,\]breadth\[=x-12,\]height \[=x-1\] |
| Answer» B. Length = 5, breadth \[=x+4,\]height\[=x+3\] | |
| 458. |
Find the continued product \[(a+2)(a-2)({{a}^{2}}+4).\] |
| A. | \[{{a}^{2}}-16\] |
| B. | \[{{a}^{4}}+16\] |
| C. | \[{{a}^{2}}+16\] |
| D. | \[{{a}^{4}}-16\] |
| Answer» E. | |
| 459. |
Find the quotient obtained when \[15{{x}^{2}}-26x+8\]is divided by \[5x-2.\] |
| A. | \[6x-1\] |
| B. | \[~2x+3\] |
| C. | \[~4x+5\] |
| D. | \[3x-4\] |
| Answer» E. | |
| 460. |
What is the value of \[\frac{{{(2013+2012)}^{2}}+{{(2013-2012)}^{2}}}{2013\times 2013+2012\times 2012}?\] |
| A. | 6 |
| B. | 4 |
| C. | 2 |
| D. | 3 |
| Answer» D. 3 | |
| 461. |
If \[\frac{{{y}^{2}}-1}{y+1}=4,\]find the value of y. |
| A. | 1 |
| B. | 1 |
| C. | 5 |
| D. | 3 |
| Answer» D. 3 | |
| 462. |
Find the binomials obtained when\[{{(3x+2y)}^{2}}-2(3x+2y)(x+y)\]\[+\,{{(x+y)}^{2}}\]is resolved into factors. |
| A. | \[(3x+y)\]and \[(3x+y)\] |
| B. | \[(2x+y)\]and \[(2x+y)\] |
| C. | \[(5x+y)\]and \[(5x+y)\] |
| D. | \[(5x+4y)\]and \[(5x+4y)\] |
| Answer» C. \[(5x+y)\]and \[(5x+y)\] | |
| 463. |
Identify the factors of \[16-81{{a}^{4}}.\] |
| A. | \[(4+9{{a}^{2}}),(2+3a)\]and \[(2-3a)\] |
| B. | \[(4-9{{a}^{2}}),(2-3a)\]and \[(2-3a)\] |
| C. | \[(4-9{{a}^{2}}),(2a-3)\]and \[(2+3a)\] |
| D. | \[(4-9{{a}^{2}}),(2+3a)\]and \[(2-3a)\] |
| Answer» B. \[(4-9{{a}^{2}}),(2-3a)\]and \[(2-3a)\] | |
| 464. |
Which of the following trinomials has the binomial \[2x-3y\] as one of its factors? |
| A. | \[4{{x}^{2}}+12xy-9{{y}^{2}}\] |
| B. | \[4{{x}^{2}}-12xy-9{{y}^{2}}\] |
| C. | \[-4{{x}^{2}}-12xy+9{{y}^{2}}\] |
| D. | \[4{{x}^{2}}-12xy+9{{y}^{2}}\] |
| Answer» E. | |
| 465. |
Which of these expressions does not have x +\[x+3\] as one of its factors? |
| A. | \[{{x}^{2}}+7x+12\] |
| B. | \[{{x}^{2}}+x-12\] |
| C. | \[{{x}^{2}}-x-12\] |
| D. | \[{{x}^{2}}-2x-15\] |
| Answer» C. \[{{x}^{2}}-x-12\] | |
| 466. |
If\[a\,\text{+}b=11\]and \[ab=30,\]find the value of a - b. |
| A. | ± 1 |
| B. | ± 2 |
| C. | ± 4 |
| D. | ± 3 |
| Answer» B. ± 2 | |
| 467. |
\[{{(2x+3y)}^{2}}+2(2x+3y)(x+y)+{{(x+y)}^{2}}\]is resolved into two binomial factors. Find them. |
| A. | \[(2x+3y)\]and \[(2x+3y)\] |
| B. | \[(x+y)\]and \[(3x+2y)\] |
| C. | \[(3x+4y)\]and \[(3x+4y)\] |
| D. | \[(4x+y)\]and \[(x+2y)\] |
| Answer» D. \[(4x+y)\]and \[(x+2y)\] | |
| 468. |
The area of a square is \[4{{a}^{2}}-12ab+9{{b}^{2}}\]square units. Which of the given expressions represents a side of the square? |
| A. | (4a + 9b) units |
| B. | (4a - 9b) units |
| C. | (2a + 3b) units |
| D. | (2a - 3b) units |
| Answer» E. | |
| 469. |
Identify the factors of \[12ax+3ay+8bx+2by.\] |
| A. | \[~\left( 2a+3b \right)\] and \[(x+2y)\] |
| B. | \[(2a+b)\] and\[(4x+3y)\] |
| C. | \[(4a+b)\]and\[~\left( x+3y \right)\] |
| D. | \[(3a+2b)\]and \[(4x+y)\] |
| Answer» E. | |
| 470. |
Find the value \[x\]in the expression \[\sqrt{{{\left( \frac{3}{5} \right)}^{1-2x}}}=4\frac{17}{27}.\] |
| A. | \[\frac{3}{2}\] |
| B. | \[\frac{5}{2}\] |
| C. | \[\frac{7}{2}\] |
| D. | \[\frac{9}{2}\] |
| Answer» D. \[\frac{9}{2}\] | |
| 471. |
Simplify \[\frac{{{5}^{n+2}}-{{6.5}^{n+1}}}{{{13.5}^{n}}-{{2.5}^{n+1}}}.\] |
| A. | \[\frac{-2}{3}\] |
| B. | \[\frac{-5}{3}\] |
| C. | \[\frac{7}{3}\] |
| D. | \[\frac{8}{3}\] |
| Answer» C. \[\frac{7}{3}\] | |
| 472. |
If \[{{5}^{x-1}}+{{5}^{x+1}}=3250,\] find the value of x. |
| A. | 3 |
| B. | 4 |
| C. | 2 |
| D. | 1 |
| Answer» C. 2 | |
| 473. |
Find the value of 'x', if\[{{(18)}^{3.5}}\div {{(27)}^{3.5}}\times {{6}^{3.5}}={{2}^{x}}.\] |
| A. | 3.5 |
| B. | 4.5 |
| C. | 6 |
| D. | 7 |
| Answer» E. | |
| 474. |
Find the value of \[\frac{1}{{{(216)}^{-\frac{2}{3}}}}+\frac{1}{{{(256)}^{-\frac{3}{4}}}}+\frac{1}{{{(32)}^{-\frac{1}{5}}}}.\] |
| A. | 102 |
| B. | 105 |
| C. | 107 |
| D. | 109 |
| Answer» B. 105 | |
| 475. |
If \[{{4}^{44}}+{{4}^{44}}+{{4}^{44}}+{{4}^{44}}={{4}^{x}},\]what is the value of \['x'\,?\] |
| A. | 45 |
| B. | 44 |
| C. | 176 |
| D. | 11 |
| Answer» B. 44 | |
| 476. |
Find the value of \[\frac{{{(243)}^{0.13}}\times {{(243)}^{0.07}}}{{{(7)}^{0.25}}\times {{(49)}^{0.075}}\times {{(343)}^{0.2}}}.\] |
| A. | \[\frac{3}{7}\] |
| B. | \[\frac{7}{3}\] |
| C. | \[1\frac{3}{7}\] |
| D. | \[2\frac{2}{7}\] |
| Answer» C. \[1\frac{3}{7}\] | |
| 477. |
If \[\frac{{{4}^{5}}+{{4}^{5}}+{{4}^{5}}+{{4}^{5}}}{{{2}^{5}}+{{2}^{5}}}\times \frac{{{6}^{5}}+{{6}^{5}}+{{6}^{5}}+{{6}^{5}}+{{6}^{5}}+{{6}^{5}}}{{{3}^{5}}+{{3}^{5}}+{{3}^{5}}}={{8}^{n}},\]find the value of ?n?. |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» E. | |
| 478. |
If\[x={{a}^{m+n}}{{b}^{l}},y={{a}^{n+l}}{{b}^{m}},z={{a}^{l+m}}{{b}^{n}},\]find \[{{x}^{m-n}}\times {{y}^{n-l}}\times {{z}^{l-m}}.\] |
| A. | 0 |
| B. | -1 |
| C. | 1 |
| D. | 2 |
| Answer» D. 2 | |
| 479. |
If \[{{\left( \frac{1}{5} \right)}^{3\gamma }}=0.008,\]find the value of \[{{(0.25)}^{\gamma }}.\] |
| A. | 1.00 |
| B. | 0.25 |
| C. | 0.0625 |
| D. | 0.125 |
| Answer» B. 0.25 | |
| 480. |
What is the value of \[{{5}^{333}}+{{25}^{222}}-{{125}^{1111}}-{{625}^{111}}?\] |
| A. | 1 |
| B. | 25 |
| C. | 125 |
| D. | 0 |
| Answer» E. | |
| 481. |
Find the value of \[{{81}^{\frac{3}{4}}}\times {{64}^{\frac{-2}{3}}}\div {{({{3}^{6}}\times {{2}^{4}})}^{\frac{1}{2}}}.\] |
| A. | \[\frac{1}{8}\] |
| B. | \[\frac{1}{16}\] |
| C. | \[\frac{1}{12}\] |
| D. | \[\frac{1}{64}\] |
| Answer» E. | |
| 482. |
If \[{{a}^{m+n}}={{a}^{mn}}.\]find the value of \[m(n-2)+n(m-2).\] |
| A. | 1 |
| B. | -1 |
| C. | 0 |
| D. | ½ |
| Answer» D. ½ | |
| 483. |
Identify the value of \[1-{{(-0.3)}^{3}}.\] |
| A. | 0.73 |
| B. | 0.973 |
| C. | 1.027 |
| D. | 1.27 |
| Answer» D. 1.27 | |
| 484. |
Find the value of \[{{(256)}^{0.16}}\times {{(256)}^{0.09}}.\] |
| A. | 4 |
| B. | 16 |
| C. | 64 |
| D. | 256.25 |
| Answer» B. 16 | |
| 485. |
If \[{{2}^{a}}+{{3}^{b}}=43\]and \[{{2}^{a+3}}-{{3}^{b+1}}=47,\]find the respective values of 'a' and 'b'. |
| A. | 4, 3 |
| B. | 3, 4 |
| C. | 16, 27 |
| D. | 2, 6 |
| Answer» B. 3, 4 | |
| 486. |
What is the product of \[\left( \frac{{{x}^{a}}}{{{x}^{b}}} \right).\left( \frac{{{x}^{c}}}{{{x}^{a}}} \right).\left( \frac{{{x}^{b}}}{{{x}^{c}}} \right)?\] |
| A. | -1 |
| B. | 1 |
| C. | 0 |
| D. | \[{{x}^{a+b+c}}\] |
| Answer» C. 0 | |
| 487. |
If \[{{2}^{x-y}}=16\]and \[{{2}^{x+y}}=64,\]find the values of \[x\]and \[y.\] |
| A. | 3, 2 |
| B. | 4, 2 |
| C. | \[5,1\] |
| D. | \[6,3\] |
| Answer» D. \[6,3\] | |
| 488. |
Find the value of \[(0.0001){{(0.0001)}^{\frac{3}{4}}}.\] |
| A. | 0.1 |
| B. | 0.01 |
| C. | 0.001 |
| D. | 0.0001 |
| Answer» D. 0.0001 | |
| 489. |
If \[\sqrt{{{9}^{x}}}=81.\]find the value of \[x.\] |
| A. | 2 |
| B. | 4 |
| C. | 3 |
| D. | 9 |
| Answer» C. 3 | |
| 490. |
If \[{{3}^{x}}=27,\]what is the value of \[{{3}^{x-3}}?\] |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| Answer» E. | |
| 491. |
If \[{{x}^{{{m}^{2}}-6}}={{x}^{19}},\]find the value of ?m?. |
| A. | 6 |
| B. | 7 |
| C. | 5 |
| D. | 3 |
| Answer» D. 3 | |
| 492. |
Simplify \[({{6}^{1}}-{{8}^{-1}})+{{({{2}^{-1}}-{{3}^{-1}})}^{-1}}.\] |
| A. | 40 |
| B. | 30 |
| C. | 20 |
| D. | 50 |
| Answer» C. 20 | |
| 493. |
What is the value of \[\frac{1}{1+{{a}^{(n-m)}}}+\frac{1}{1+{{a}^{(m-n)}}}?\] |
| A. | \[{{a}^{m-n}}\] |
| B. | \[{{a}^{n-m}}\] |
| C. | \[-1\] |
| D. | 1 |
| Answer» E. | |
| 494. |
Which of the following is the exponential form of \[\frac{{{20}^{-2}}\times {{20}^{-2}}\times {{20}^{-2}}}{20}?\] |
| A. | \[{{20}^{-5}}\] |
| B. | \[{{20}^{-6}}\] |
| C. | \[~{{20}^{-7}}~\] |
| D. | \[~{{20}^{-1}}~\] |
| Answer» D. \[~{{20}^{-1}}~\] | |
| 495. |
Find the value of \[\frac{{{a}^{m+n}}\times {{a}^{n+l}}\times {{a}^{l+m}}}{{{({{a}^{m}}\times {{a}^{n}}\times {{a}^{l}})}^{2}}}.\] |
| A. | 0 |
| B. | -1 |
| C. | \[4+m\] |
| D. | 1 |
| Answer» E. | |
| 496. |
Find \['x'\]such that \[{{9}^{x+2}}={{3}^{3x-1}}.\] |
| A. | 7 |
| B. | 6 |
| C. | 5 |
| D. | 4 |
| Answer» D. 4 | |
| 497. |
If \[{{a}^{x}}=b,\,{{b}^{y}}=C,\,{{C}^{z}}=a,\]find the value of \[xyz.\] |
| A. | 0 |
| B. | 1 |
| C. | -1 |
| D. | 2 |
| Answer» C. -1 | |
| 498. |
Find the value of \[({{2013}^{o}}-{{2012}^{o}})\times (2013+2012).\] |
| A. | 4025 |
| B. | 1 |
| C. | 0 |
| D. | -1 |
| Answer» D. -1 | |
| 499. |
By what number should we multiply \[{{(-8)}^{-1}}\]to obtain a product equal to \[{{10}^{-1}}?\] |
| A. | \[\frac{-1}{5}\] |
| B. | \[\frac{-4}{5}\] |
| C. | \[\frac{-3}{5}\] |
| D. | \[\frac{-2}{5}\] |
| Answer» C. \[\frac{-3}{5}\] | |
| 500. |
Simplify \[\frac{{{\left( a+\frac{1}{b} \right)}^{x}}\times {{\left( a-\frac{1}{b} \right)}^{y}}}{{{\left( b+\frac{1}{a} \right)}^{x}}{{\left( b-\frac{1}{a} \right)}^{y}}}.\] |
| A. | \[\frac{a}{b}\] |
| B. | \[{{\left( \frac{a}{b} \right)}^{x}}\] |
| C. | \[{{\left( \frac{a}{b} \right)}^{y}}\] |
| D. | \[{{\left( \frac{a}{b} \right)}^{x+y}}\] |
| Answer» E. | |