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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.
| 501. |
If \[\mathbf{3x}+\frac{1}{\mathbf{3x}}=\mathbf{3}\], then the value of \[27{{x}^{3}}+\frac{1}{27{{x}^{3}}}\] is |
| A. | -52 |
| B. | 52 |
| C. | 18 |
| D. | -18 |
| Answer» D. -18 | |
| 502. |
Vikas has Rs. \[({{x}^{3}}+2ax+b),\] with this money he can buy exactly \[(x-1)\] jeans or\[(x+1)\] shirts with no money left. How much money Vikas has, if\[x=4?\] |
| A. | Rs. 80 |
| B. | Rs. 120 |
| C. | Rs. 30 |
| D. | Rs. 60 |
| Answer» E. | |
| 503. |
If \[{{\left( \mathbf{3a+1} \right)}^{\mathbf{2}}}\mathbf{+}{{\left( \mathbf{b-1} \right)}^{\mathbf{2}}}\mathbf{+}{{\left( \mathbf{2c-3} \right)}^{\mathbf{2}}}\mathbf{=0,}\] than value of \[\left( \mathbf{3a+b+2c} \right)\]is equal to: |
| A. | 3 |
| B. | -1 |
| C. | 2 |
| D. | 5 |
| Answer» B. -1 | |
| 504. |
If the quotient is\[3{{x}^{2}}-2x+1\], remainder is\[2x-5\]and divisor is\[x+2\], what is the dividend? |
| A. | \[3{{x}^{3}}-4{{x}^{2}}+x-3\] |
| B. | \[3{{x}^{3}}-4{{x}^{2}}-x+3\] |
| C. | \[3{{x}^{3}}+4{{x}^{2}}-x+3\] |
| D. | \[3{{x}^{3}}+4{{x}^{2}}-x-3\] |
| Answer» E. | |
| 505. |
If \[\mathbf{x}=\mathbf{2},\] \[\mathbf{y}=\mathbf{3}\] and \[\mathbf{z}=-\mathbf{5},\] then \[{{\mathbf{x}}^{\mathbf{3}}}\mathbf{+}{{\mathbf{y}}^{\mathbf{3}}}\mathbf{+}{{\mathbf{z}}^{\mathbf{3}}}\mathbf{=}\] |
| A. | 90 |
| B. | -90 |
| C. | 0 |
| D. | 368 |
| Answer» C. 0 | |
| 506. |
Area of a rectangular field is \[(2{{x}^{3}}-11{{x}^{2}}-4x+5)\,sq.\]units and side of a square field is (\[(2{{x}^{2}}+4)\]units. Find the difference between their areas (in sq. units). |
| A. | \[4{{x}^{4}}-2{{x}^{3}}-4x+11\] |
| B. | \[4{{x}^{4}}-2{{x}^{3}}+27{{x}^{2}}+4x+11\] |
| C. | \[4{{x}^{4}}+27{{x}^{2}}+4x-11\] |
| D. | \[4{{x}^{4}}+2{{x}^{3}}+27{{x}^{2}}+4x+11\] |
| Answer» C. \[4{{x}^{4}}+27{{x}^{2}}+4x-11\] | |
| 507. |
Find the value of \[{{2}^{\frac{1}{4}}}{{.4}^{\frac{1}{8}}}{{.16}^{\frac{1}{16}}}{{.256}^{\frac{1}{32}}}\]. |
| A. | \[1\] |
| B. | \[2\] |
| C. | \[4\] |
| D. | \[8\] |
| Answer» C. \[4\] | |
| 508. |
If \[x+\frac{1}{x}=a+b\] and \[x-\frac{1}{x}=a-b\], which of the following is true? |
| A. | \[ab=1\] |
| B. | \[a=b\] |
| C. | \[ab=2\] |
| D. | \[a+b=0\] |
| Answer» B. \[a=b\] | |
| 509. |
A rectangular field has an area \[(35{{x}^{2}}+13x-12){{m}^{2}}.\]What could be the possible expression for length and breadth of the field? |
| A. | \[(5x+4)\]and\[(7x-3)m\] |
| B. | \[(3x+9)m\]and\[(7x-12)m\] |
| C. | Both (a) and (b) |
| D. | None of these |
| Answer» B. \[(3x+9)m\]and\[(7x-12)m\] | |
| 510. |
2 is a root of \[\mathbf{k}{{\mathbf{x}}^{\mathbf{4}}}-\mathbf{13}{{\mathbf{x}}^{\mathbf{3}}}+\mathbf{k}{{\mathbf{x}}^{\mathbf{2}}}+\mathbf{12x}.\]What is the value of k? |
| A. | \[k=1\] |
| B. | \[k=2\] |
| C. | \[k=3\] |
| D. | \[k=4\] |
| Answer» E. | |
| 511. |
Length, breadth and height of a cuboidal tank are \[(x-3y)m,\,(x+3y)m\]and\[({{x}^{2}}+9{{y}^{2}})m\] respectively. Find the volume of the tank. |
| A. | \[({{x}^{3}}+3xy+27{{y}^{3}}){{m}^{3}}\] |
| B. | \[({{x}^{4}}+2{{x}^{2}}{{y}^{2}}+81{{y}^{4}}){{m}^{3}}\] |
| C. | \[({{x}^{2}}-81{{y}^{4}}){{m}^{3}}\] |
| D. | \[({{x}^{4}}+81{{y}^{4}}){{m}^{3}}\] |
| Answer» D. \[({{x}^{4}}+81{{y}^{4}}){{m}^{3}}\] | |
| 512. |
Resolve into factors: \[6{{x}^{3}}-24x{{y}^{2}}-4{{x}^{2}}y+12{{y}^{3}}\] |
| A. | \[3(2x-y)(x-2y)(x+y)\] |
| B. | \[3(2x-y)(x+y)(x+2y)\] |
| C. | \[3(2x-y)(x+2y)(x-2y)\] |
| D. | \[3(2x+y)(x-y)(x+2y)\] |
| Answer» B. \[3(2x-y)(x+y)(x+2y)\] | |
| 513. |
If a, b, c are all non-zeroes and \[a+b+c=0,\]then \[\frac{{{a}^{2}}}{bc}+\frac{{{b}^{2}}}{ca}+\frac{{{c}^{2}}}{ab}=\_\_\_\_\_.\] |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| Answer» E. | |
| 514. |
If\[a+b+c=0\], evaluate\[\frac{{{a}^{2}}}{bc}+\frac{{{b}^{2}}}{ca}+\frac{{{c}^{2}}}{ab}\]. |
| A. | \[1\] |
| B. | \[2\] |
| C. | \[3\] |
| D. | \[4\] |
| Answer» D. \[4\] | |
| 515. |
What is the remainder when \[\mathbf{2}{{\mathbf{x}}^{\mathbf{2}}}-\mathbf{3x}+\mathbf{5}\] is divided by\[\mathbf{2x}-1\]? |
| A. | 2 |
| B. | 3 |
| C. | 4 |
| D. | 5 |
| Answer» D. 5 | |
| 516. |
If \[{{x}^{2}}-1\]is a factor of \[a{{x}^{4}}+b{{x}^{3}}+e{{x}^{2}}+dx+e,\] then |
| A. | \[a+b+e=c+d\] |
| B. | \[a+b+c=d+e\] |
| C. | \[b+c+d=a+e\] |
| D. | None of these |
| Answer» E. | |
| 517. |
If\[x+y+z=0\], what is the value of\[{{x}^{3}}+{{y}^{3}}+{{z}^{3}}\]? |
| A. | \[xyz\] |
| B. | \[2xyz\] |
| C. | \[3xyz\] |
| D. | \[0\] |
| Answer» D. \[0\] | |
| 518. |
The degree of the polynomial \[\frac{{{\mathbf{x}}^{\mathbf{4}}}\mathbf{+}{{\mathbf{x}}^{\mathbf{5}}}\mathbf{-}{{\mathbf{x}}^{\mathbf{8}}}}{{{\mathbf{x}}^{\mathbf{3}}}}\] is |
| A. | 2 |
| B. | 3 |
| C. | 4 |
| D. | 5 |
| Answer» E. | |
| 519. |
Identify one of the factors of\[{{x}^{12}}-{{y}^{12}}\]. |
| A. | \[({{x}^{2}}-xy+{{y}^{2}})\] |
| B. | \[({{x}^{4}}+{{x}^{2}}{{y}^{2}}+{{y}^{4}})\] |
| C. | \[({{x}^{2}}+xy-{{y}^{2}})\] |
| D. | \[({{x}^{4}}-xy+{{y}^{4}})\] |
| Answer» B. \[({{x}^{4}}+{{x}^{2}}{{y}^{2}}+{{y}^{4}})\] | |
| 520. |
If \[\mathbf{x}=\mathbf{999}\], then the value of \[\sqrt[\mathbf{3}]{\mathbf{x}\left( {{\mathbf{x}}^{\mathbf{2}}}\mathbf{+3x+3} \right)\mathbf{+1}}\]is |
| A. | 1000 |
| B. | 999 |
| C. | 998 |
| D. | 1002 |
| Answer» B. 999 | |
| 521. |
When \[({{x}^{3}}-2{{x}^{2}}+px-q)\] is divided by \[({{x}^{2}}-2x-3),\]the remainder is\[(x-6).\]The values of p and q respectively are |
| A. | -2,-6 |
| B. | 2,-6 |
| C. | -2, 6 |
| D. | 2, 6 |
| Answer» D. 2, 6 | |
| 522. |
If \[\mathbf{x+y+z=6}\], then the value of \[{{\left( \mathbf{x-1} \right)}^{\mathbf{3}}}\mathbf{+}{{\left( \mathbf{y-2} \right)}^{\mathbf{3}}}\mathbf{+}{{\left( \mathbf{z-3} \right)}^{\mathbf{3}}}\] is |
| A. | \[3\left( x-1 \right)\left( y+2 \right)\left( z-3 \right)\] |
| B. | \[3\left( x+1 \right)\left( y-2 \right)\left( z-3 \right)\] |
| C. | \[3\left( x-1 \right)\left( y-2 \right)\left( z+3 \right)\] |
| D. | \[3\left( x-1 \right)\left( y-2 \right)\left( z-3 \right)\] |
| Answer» E. | |
| 523. |
Value of R, if \[\frac{{{a}^{2}}-19a-25}{a-7}=a-12+\frac{R}{a-7}\]is _____. |
| A. | -109 |
| B. | -88 |
| C. | -84 |
| D. | -64 |
| Answer» B. -88 | |
| 524. |
What are the factors of \[{{x}^{2}}+(a+b+c)x+ab+bc\]? |
| A. | \[(x+a)(x+b+c)\] |
| B. | \[(x+a)(x+a+c)\] |
| C. | \[(x+b)(x+a+c)\] |
| D. | \[(x+b)(x+b+c)\] |
| Answer» D. \[(x+b)(x+b+c)\] | |
| 525. |
The value of \[{{(x-a)}^{3}}+{{(x-b)}^{3}}+{{(x-c)}^{3}}\]\[-3(x-a)(x-b)(x-c),\]when \[a+b+c=3x\]is ______. |
| A. | 3 |
| B. | 2 |
| C. | 1 |
| D. | 0 |
| Answer» E. | |
| 526. |
If\[\frac{x}{y}+\frac{y}{x}=-1(x,\,\,y\ne 0)\], what is the value of\[{{x}^{3}}-{{y}^{3}}\]? |
| A. | \[1\] |
| B. | \[-1\] |
| C. | \[\frac{1}{2}\] |
| D. | \[0\] |
| Answer» E. | |
| 527. |
If \[\mathbf{x=(}\sqrt{\mathbf{2}}\mathbf{+1}{{\mathbf{)}}^{\mathbf{-}\frac{\mathbf{1}}{\mathbf{3}}}}\]the value of \[\left( {{\mathbf{x}}^{\mathbf{3}}}\frac{\mathbf{1}}{{{\mathbf{x}}^{\mathbf{3}}}} \right)\] is |
| A. | 0 |
| B. | \[-\sqrt{2}\] |
| C. | \[2\sqrt{2}\] |
| D. | \[3\sqrt{2}\] |
| Answer» D. \[3\sqrt{2}\] | |
| 528. |
The value of k for which \[(x+2)\] is a factor of (x \[{{(x+1)}^{7}}+{{(3x+k)}^{3}}\] is ____. |
| A. | -7 |
| B. | 7 |
| C. | -1 |
| D. | \[-6-{{3}^{(7/3)}}\] |
| Answer» C. -1 | |
| 529. |
Write the degree of the polynomial 0. |
| A. | \[1\] |
| B. | \[0\] |
| C. | \[N\] |
| D. | Not defined |
| Answer» E. | |
| 530. |
In a test paper there are total 10 questions. In how many different ways can you choose 6 questions to answer? |
| A. | 210 |
| B. | 540 |
| C. | 336 |
| D. | 340 |
| E. | None of these |
| Answer» B. 540 | |
| 531. |
Find the number of ways of selecting 4 letters from the word EXAMINATION. |
| A. | 136 |
| B. | 126 |
| C. | 252 |
| D. | 525 |
| E. | None of these |
| Answer» B. 126 | |
| 532. |
A committee of 5 persons is to be formed out of 6 gents and 4 ladies. In how many ways this can be done, when at most two ladies are included? |
| A. | 186 |
| B. | 168 |
| C. | 136 |
| D. | 169 |
| E. | None of these |
| Answer» B. 168 | |
| 533. |
In how many ways three different rings can be in four fingers with at most in each finger? |
| A. | 24 |
| B. | 12 |
| C. | 36 |
| D. | 120 |
| E. | None of these |
| Answer» B. 12 | |
| 534. |
The denominator of \[\frac{a+\sqrt{{{a}^{2}}-{{b}^{2}}}}{a-\sqrt{{{a}^{2}}-{{b}^{2}}}}+\frac{a-\sqrt{{{a}^{2}}-{{b}^{2}}}}{a+\sqrt{{{a}^{2}}-{{b}^{2}}}}\]is ______. |
| A. | \[{{a}^{2}}\] |
| B. | \[{{b}^{2}}\] |
| C. | \[{{a}^{2}}-{{b}^{2}}\] |
| D. | \[\frac{4{{a}^{2}}-2{{b}^{2}}}{{{b}^{2}}}\] |
| Answer» C. \[{{a}^{2}}-{{b}^{2}}\] | |
| 535. |
What is the rational denominator of\[\frac{2\sqrt[3]{5}}{\sqrt[3]{9}}\]? |
| A. | \[1\] |
| B. | \[2\] |
| C. | \[3\] |
| D. | \[4\] |
| Answer» D. \[4\] | |
| 536. |
An irrational number between \[\frac{1}{7}\]and \[\frac{2}{7}\] is _____. |
| A. | \[\frac{1}{2}\left( \frac{1}{7}+\frac{2}{7} \right)\] |
| B. | \[\left( \frac{1}{7}\times \frac{2}{7} \right)\] |
| C. | \[\sqrt{\frac{1}{7}\times \frac{2}{7}}\] |
| D. | None of these |
| Answer» D. None of these | |
| 537. |
What is the rationalizing factor of\[\sqrt[5]{{{a}^{2}}{{b}^{3}}{{c}^{4}}}\]? |
| A. | \[\sqrt[5]{{{a}^{3}}{{b}^{2}}c}\] |
| B. | \[\sqrt[4]{{{a}^{3}}{{b}^{2}}c}\] |
| C. | \[\sqrt[3]{{{a}^{3}}{{b}^{2}}c}\] |
| D. | \[\sqrt{{{a}^{3}}{{b}^{2}}c}\] |
| Answer» B. \[\sqrt[4]{{{a}^{3}}{{b}^{2}}c}\] | |
| 538. |
Rational number \[\frac{-18}{5}\] lies between consecutive integers ____. |
| A. | -2 and-3 |
| B. | -3 and-4 |
| C. | -4 and -5 |
| D. | -5 and -6 |
| Answer» C. -4 and -5 | |
| 539. |
What is the rationalizing factor of\[\left( 2\sqrt[3]{5} \right)\]? |
| A. | \[\sqrt[3]{5}\] |
| B. | \[\sqrt[3]{{{5}^{2}}}\] |
| C. | \[{{5}^{2}}\] |
| D. | \[{{5}^{3}}\] |
| Answer» C. \[{{5}^{2}}\] | |
| 540. |
The rationalizing factor of\[\sqrt[5]{{{a}^{2}}{{b}^{3}}{{c}^{4}}}\]is ______. |
| A. | \[\sqrt[5]{{{a}^{3}}{{b}^{2}}c}\] |
| B. | \[\sqrt[4]{{{a}^{3}}{{b}^{2}}c}\] |
| C. | \[\sqrt[3]{{{a}^{3}}{{b}^{2}}c}\] |
| D. | \[\sqrt{{{a}^{3}}{{b}^{2}}c}\] |
| Answer» B. \[\sqrt[4]{{{a}^{3}}{{b}^{2}}c}\] | |
| 541. |
\[\frac{7\sqrt{3}}{(\sqrt{10}+\sqrt{3})}-\frac{2\sqrt{5}}{(\sqrt{6}+\sqrt{5})}-\frac{3\sqrt{2}}{(\sqrt{15}+3\sqrt{2})}=\_\_\_\_\_.\] |
| A. | 1 |
| B. | 2 |
| C. | \[\frac{1}{2}\] |
| D. | 3 |
| Answer» B. 2 | |
| 542. |
What type of a number is\[{{\left( \sqrt{2}+\sqrt{3} \right)}^{2}}\]? |
| A. | A rational number |
| B. | An irrational number |
| C. | A fraction |
| D. | A decimal number |
| Answer» C. A fraction | |
| 543. |
Find the simplest rationalising factor of\[{{5}^{1/3}}+{{5}^{-1/3}}\] |
| A. | \[{{5}^{2/3}}+1+{{5}^{-2/3}}\] |
| B. | \[{{5}^{1/3}}-{{5}^{-1/3}}\] |
| C. | \[{{5}^{2/3}}-1+{{5}^{-2/3}}\] |
| D. | \[{{5}^{2/3}}+1-{{5}^{-2/3}}\] |
| Answer» D. \[{{5}^{2/3}}+1-{{5}^{-2/3}}\] | |
| 544. |
If\[x=\sqrt[3]{2+\sqrt{3}}\], find the value of\[{{x}^{3}}+\frac{1}{{{x}^{3}}}\]. |
| A. | \[2\] |
| B. | \[4\] |
| C. | \[8\] |
| D. | \[9\] |
| Answer» C. \[8\] | |
| 545. |
Find the value of \[0.9999.......\] in the form of\[\frac{p}{q}\](\[p,\,\,q\in Z\]and\[q\ne 0\]) |
| A. | \[\frac{1}{9}\] |
| B. | \[\frac{2}{9}\] |
| C. | \[\frac{9}{10}\] |
| D. | \[1\] |
| Answer» E. | |
| 546. |
Simplify\[\frac{{{a}^{\frac{1}{2}}}+{{a}^{-\frac{1}{2}}}}{1-a}+\frac{1-{{a}^{-\frac{1}{2}}}}{1+\sqrt{a}}\]. |
| A. | \[1\] |
| B. | \[0\] |
| C. | \[\frac{2}{1-a}\] |
| D. | \[1+a\] |
| Answer» D. \[1+a\] | |
| 547. |
Which symbol is used to denote a collection of all positive integers? |
| A. | \[N\] |
| B. | \[W\] |
| C. | \[Z\] |
| D. | \[Q\] |
| Answer» B. \[W\] | |
| 548. |
If\[{{x}^{x\sqrt{x}}}={{\left( x\sqrt{x} \right)}^{x}}\], find the value of\[x\]. |
| A. | \[\frac{3}{2}\] |
| B. | \[\frac{2}{9}\] |
| C. | \[\frac{9}{4}\] |
| D. | \[\frac{4}{9}\] |
| Answer» D. \[\frac{4}{9}\] | |
| 549. |
If \[x=(7+4\sqrt{3}),\]then \[\left( x+\frac{1}{x} \right)=\_\_\_\_\_.\] |
| A. | \[8\sqrt{3}\] |
| B. | 14 |
| C. | 49 |
| D. | 48 |
| Answer» C. 49 | |
| 550. |
What type of a number is\[\left( 6+\sqrt{2} \right)\left( 6-\sqrt{2} \right)\]? |
| A. | Rational number |
| B. | Irrational number |
| C. | Prime number |
| D. | Negative Integer |
| Answer» B. Irrational number | |