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question_answer1)
Write the degree of the polynomial 0.
A)
\[1\] done
clear
B)
\[0\] done
clear
C)
\[N\] done
clear
D)
Not defined done
clear
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question_answer2)
If the quotient is\[3{{x}^{2}}-2x+1\], remainder is\[2x-5\]and divisor is\[x+2\], what is the dividend?
A)
\[3{{x}^{3}}-4{{x}^{2}}+x-3\] done
clear
B)
\[3{{x}^{3}}-4{{x}^{2}}-x+3\] done
clear
C)
\[3{{x}^{3}}+4{{x}^{2}}-x+3\] done
clear
D)
\[3{{x}^{3}}+4{{x}^{2}}-x-3\] done
clear
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question_answer3)
If \[(x-2)\] is one factor of\[{{x}^{2}}+ax-6=0\]and\[{{x}^{2}}-9x+b=0\], find\[a+b\].
A)
\[15\] done
clear
B)
\[13\] done
clear
C)
\[11\] done
clear
D)
\[10\] done
clear
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question_answer4)
Given \[P=\]Product of \[{{x}^{2}}y\] and \[\frac{x}{y}\] and \[Q=\] Quotient obtained when \[{{x}^{2}}\] is divided by\[D\]. If\[P=Q\], what is the value of\[D\]?
A)
\[0\] done
clear
B)
\[1\] done
clear
C)
\[x\] done
clear
D)
\[\frac{1}{x}\] done
clear
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question_answer5)
Which of the following is one of the factors of\[{{a}^{3}}+8{{b}^{3}}-64{{c}^{3}}+24abc\]?
A)
\[a+2b-4c\] done
clear
B)
\[a-2b+4c\] done
clear
C)
\[a+2b+4c\] done
clear
D)
\[a-2b-4c\] done
clear
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question_answer6)
Which of the following is a trinomial in\[p\]?
A)
\[{{x}^{2}}+5\] done
clear
B)
\[{{p}^{3}}+{{p}^{2}}+\sqrt{2}\] done
clear
C)
\[\sqrt{p}\left( 1+\sqrt{2p} \right)\] done
clear
D)
\[y+\frac{1}{y}+\frac{1}{2}\] done
clear
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question_answer7)
Identify one of the factors of\[{{x}^{2}}+\frac{1}{{{x}^{2}}}+2-2x-\frac{2}{x}\]from the following.
A)
\[x-\frac{1}{x}\] done
clear
B)
\[x+\frac{1}{x}-1\] done
clear
C)
\[x+\frac{1}{x}\] done
clear
D)
\[{{x}^{2}}+\frac{1}{{{x}^{2}}}\] done
clear
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question_answer8)
If the factors of\[{{a}^{2}}+{{b}^{2}}+2(ab+bc+ca)\]are\[(a+b+m)\]and\[(a+b+nc)\], find the value of\[m+n\].
A)
\[0\] done
clear
B)
\[2\] done
clear
C)
\[4\] done
clear
D)
\[6\] done
clear
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question_answer9)
If\[({{x}^{2}}+3x+5)({{x}^{2}}-3x+5)={{m}^{2}}-{{n}^{2}}\], find\[m\].
A)
\[{{x}^{2}}-3x\] done
clear
B)
\[3x+5\] done
clear
C)
\[{{x}^{2}}+5\] done
clear
D)
\[{{x}^{2}}-5\] done
clear
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question_answer10)
If\[\frac{x}{y}+\frac{y}{x}=-1(x,\,\,y\ne 0)\], what is the value of\[{{x}^{3}}-{{y}^{3}}\]?
A)
\[1\] done
clear
B)
\[-1\] done
clear
C)
\[\frac{1}{2}\] done
clear
D)
\[0\] done
clear
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question_answer11)
What are the factors of \[{{x}^{2}}+(a+b+c)x+ab+bc\]?
A)
\[(x+a)(x+b+c)\] done
clear
B)
\[(x+a)(x+a+c)\] done
clear
C)
\[(x+b)(x+a+c)\] done
clear
D)
\[(x+b)(x+b+c)\] done
clear
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question_answer12)
Factorise:\[{{a}^{4}}+4\]
A)
\[({{a}^{2}}+2a-2)({{a}^{2}}+2a+2)\] done
clear
B)
\[({{a}^{2}}-2a-2)({{a}^{2}}+2a-2)\] done
clear
C)
\[({{a}^{2}}+2a-2)({{a}^{2}}-2a+2)\] done
clear
D)
\[({{a}^{2}}+2a+2)({{a}^{2}}-2a+2)\] done
clear
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question_answer13)
Identify one of the factors of\[{{x}^{12}}-{{y}^{12}}\].
A)
\[({{x}^{2}}-xy+{{y}^{2}})\] done
clear
B)
\[({{x}^{4}}+{{x}^{2}}{{y}^{2}}+{{y}^{4}})\] done
clear
C)
\[({{x}^{2}}+xy-{{y}^{2}})\] done
clear
D)
\[({{x}^{4}}-xy+{{y}^{4}})\] done
clear
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question_answer14)
If\[x+y+z=0\], what is the value of\[{{x}^{3}}+{{y}^{3}}+{{z}^{3}}\]?
A)
\[xyz\] done
clear
B)
\[2xyz\] done
clear
C)
\[3xyz\] done
clear
D)
\[0\] done
clear
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question_answer15)
If\[a+b+c=0\], evaluate\[\frac{{{a}^{2}}}{bc}+\frac{{{b}^{2}}}{ca}+\frac{{{c}^{2}}}{ab}\].
A)
\[1\] done
clear
B)
\[2\] done
clear
C)
\[3\] done
clear
D)
\[4\] done
clear
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question_answer16)
Resolve into factors: \[6{{x}^{3}}-24x{{y}^{2}}-4{{x}^{2}}y+12{{y}^{3}}\]
A)
\[3(2x-y)(x-2y)(x+y)\] done
clear
B)
\[3(2x-y)(x+y)(x+2y)\] done
clear
C)
\[3(2x-y)(x+2y)(x-2y)\] done
clear
D)
\[3(2x+y)(x-y)(x+2y)\] done
clear
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question_answer17)
Identify the degree of the polynomial\[4-{{x}^{2}}-{{x}^{3}}+\frac{5{{x}^{7}}}{3}\].
A)
\[2\] done
clear
B)
\[7\] done
clear
C)
\[0\] done
clear
D)
\[3\] done
clear
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question_answer18)
If \[x+\frac{1}{x}=a+b\] and \[x-\frac{1}{x}=a-b\], which of the following is true?
A)
\[ab=1\] done
clear
B)
\[a=b\] done
clear
C)
\[ab=2\] done
clear
D)
\[a+b=0\] done
clear
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question_answer19)
Find the value of \[{{2}^{\frac{1}{4}}}{{.4}^{\frac{1}{8}}}{{.16}^{\frac{1}{16}}}{{.256}^{\frac{1}{32}}}\].
A)
\[1\] done
clear
B)
\[2\] done
clear
C)
\[4\] done
clear
D)
\[8\] done
clear
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question_answer20)
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)
\[0\] done
clear
B)
\[2\] done
clear
C)
\[1\] done
clear
D)
Not defined done
clear
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question_answer21)
Express \[x-8x{{y}^{3}}\] as product of factors.
A)
\[x(1-2y)(1+2y+4{{y}^{2}})\] done
clear
B)
\[x(1+2y)(1+2y+4{{y}^{2}})\] done
clear
C)
\[x(1-2y)(1-2y+4{{y}^{2}})\] done
clear
D)
\[x(1+2y)(1-2y+4{{y}^{2}})\] done
clear
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question_answer22)
Factorise\[{{a}^{2x}}-{{b}^{2x}}\].
A)
\[({{a}^{x}}+{{b}^{x}})({{a}^{x}}-{{b}^{x}})\] done
clear
B)
\[{{({{a}^{x}}-{{b}^{x}})}^{2}}\] done
clear
C)
\[({{a}^{x}}+{{b}^{x}})({{a}^{2}}-{{b}^{2}})\] done
clear
D)
\[({{a}^{x}}-{{b}^{x}})({{a}^{2}}+{{b}^{2}})\] done
clear
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question_answer23)
If\[p=(2-a)\], what is\[{{a}^{3}}+6ap+{{p}^{3}}-8\]?
A)
\[1\] done
clear
B)
\[0\] done
clear
C)
\[2\] done
clear
D)
\[3\] done
clear
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question_answer24)
Find the value of\[{{(x-a)}^{3}}+{{(x-b)}^{3}}+{{(x-c)}^{3}}\]\[-3(x-a)(x-b)(x-c)\]when\[a+b+c=3x\].
A)
\[3\] done
clear
B)
\[2\] done
clear
C)
\[1\] done
clear
D)
\[0\] done
clear
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question_answer25)
Find the zero of the polynomial\[f(x)=qx,\,\,q\ne 0\].
A)
\[1\] done
clear
B)
\[b\] done
clear
C)
\[0\] done
clear
D)
\[-1\] done
clear
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question_answer26)
If\[{{x}^{\frac{1}{3}}}+{{y}^{\frac{1}{3}}}+{{z}^{\frac{1}{3}}}=0\], which of the following is true?
A)
\[{{x}^{3}}+{{y}^{3}}+{{z}^{3}}=0\] done
clear
B)
\[x+y+z=27xyz\] done
clear
C)
\[{{(x+y+z)}^{3}}=27xyz\] done
clear
D)
\[{{x}^{3}}+{{y}^{3}}+{{z}^{3}}=27xyz\] done
clear
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question_answer27)
Find the value of 'a' if the polynomials\[2{{x}^{3}}+a{{x}^{2}}+3x-5\]and\[{{x}^{3}}+{{x}^{2}}-4x-a\] leave the same remainder when divided by\[x-1\].
A)
\[a=1\] done
clear
B)
\[a=-1\] done
clear
C)
\[a=2\] done
clear
D)
\[a=-2\] done
clear
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question_answer28)
Factorise:\[ab{{(a+b)}^{2}}-3ab(a+b)\]
A)
\[(a+b)(a-b)ab\] done
clear
B)
\[(a+b-5)(2a+b)(a-b)\] done
clear
C)
\[ab(a+b)(a+b-3)\] done
clear
D)
\[ab(2a-b)(2a+b-6)\] done
clear
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question_answer29)
If\[x-1\]is a factor of\[f(x)={{x}^{3}}-6{{x}^{2}}+11x-6\], which of the following is true?
A)
\[f(-x)=0\] done
clear
B)
\[f(-1)=0\] done
clear
C)
\[f(x)=0\] done
clear
D)
\[f(1)=0\] done
clear
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question_answer30)
If\[y-2\]and\[y-\frac{1}{2}\]are the factors of \[p{{y}^{2}}+5y+r\], which of the following holds good?
A)
\[p>r\] done
clear
B)
\[p=r\] done
clear
C)
\[p<r\] done
clear
D)
Both (a) and (c) done
clear
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question_answer31)
Which of the following polynomials has \[-5\] as a zero?
A)
\[(p-5)\] done
clear
B)
\[{{x}^{2}}-25\] done
clear
C)
\[{{p}^{2}}-5p\] done
clear
D)
\[{{x}^{2}}+5\] done
clear
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question_answer32)
Factorise:\[{{x}^{2}}-{{z}^{2}}+{{y}^{2}}-{{p}^{2}}+2pz-2xy\]
A)
\[(x-y-p-z)(x-y-p+z)\] done
clear
B)
\[(x-y+p-z)(x-y-p+z)\] done
clear
C)
\[(x+y+p-z)(x+y+p+z)\] done
clear
D)
\[(x+y-p+z)(x-y-p+z)\] done
clear
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question_answer33)
Find the zeroes of the polynomial\[p(z)=(4z+\pi )(z-4\pi )\]
A)
\[4\pi ,\,\,-\frac{\pi }{4}\] done
clear
B)
\[-4\pi ,\,\,\frac{\pi }{4}\] done
clear
C)
\[4\pi ,\,\,\frac{\pi }{4}\] done
clear
D)
\[-4\pi ,\,\,-\frac{\pi }{4}\] done
clear
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question_answer34)
If\[(x+1)\]is factor of\[{{x}^{n}}+1\], which of the following statements is true?
A)
\[n\] is an odd integer done
clear
B)
\[n\] is an even integer done
clear
C)
\[n\] is a negative integer done
clear
D)
\[n\] is a positive integer done
clear
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question_answer35)
When \[{{x}^{3}}-2{{x}^{2}}+ax-b\] is divided by \[{{x}^{2}}-2x-3\]the remainder is\[x-6\]. Find the values of \[a\] and\[b\].
A)
\[-2\] and \[-6\] done
clear
B)
\[2\] and\[-6\] done
clear
C)
\[-2\] and \[6\] done
clear
D)
\[2\] and \[6\] done
clear
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question_answer36)
Find the coefficient of \[{{x}^{2}}\] in the product of\[(x-1)(1-2x)\].
A)
\[-3\] done
clear
B)
\[3\] done
clear
C)
\[-2\] done
clear
D)
\[1\] done
clear
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question_answer37)
If \[{{x}^{2}}+x+1\] is a factor of the polynomial \[3{{x}^{3}}+8{{x}^{2}}+8x+3+5k\], what is the value of\[k\]?
A)
\[0\] done
clear
B)
\[2/5\] done
clear
C)
\[5/2\] done
clear
D)
\[-1\] done
clear
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question_answer38)
If \[(x-1)\] is a factor of polynomial \[f(x)\] but not of\[g(x)\], it must be a factor of which of the following polynomials?
A)
\[f(x)\,\,g(x)\] done
clear
B)
\[-f(x)+g(x)\] done
clear
C)
\[f(x)-g(x)\] done
clear
D)
\[\{f(x)-g(x)\}g(x)\] done
clear
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question_answer39)
If \[(x-a)(x-b)\] are factors of polynomial\[g(x)\], which of the following statements is correct?
A)
\[g(a)=0,\,\,g(b)\ne 0\] done
clear
B)
\[g(a)=0,\,\,g(b)=0\] done
clear
C)
\[g(a)\ne 0,\,\,g(b)\ne 0\] done
clear
D)
\[g(a)\ne 0,\,\,g(b)=0\] done
clear
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question_answer40)
If \[{{x}^{2014}}+2014\] is divided by\[(x+1)\], what is the remainder?
A)
\[2014\] done
clear
B)
\[1\] done
clear
C)
\[2013\] done
clear
D)
\[2015\] done
clear
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question_answer41)
If\[{{x}^{2}}+kx+6=(x+2)(x+3)\]for all\[x\], what is the value of\[k\]?
A)
\[1\] done
clear
B)
\[6\] done
clear
C)
\[5\] done
clear
D)
\[3\] done
clear
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question_answer42)
If\[x+\frac{1}{x}=3\], find the value of\[{{x}^{2}}+\frac{1}{{{x}^{2}}}\]?
A)
\[9\] done
clear
B)
\[11\] done
clear
C)
\[7\] done
clear
D)
\[8\] done
clear
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question_answer43)
Find one of the factors of\[(x-1)-({{x}^{2}}-1)\].
A)
\[{{x}^{2}}-1\] done
clear
B)
\[x+1\] done
clear
C)
\[x-1\] done
clear
D)
\[x+4\] done
clear
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question_answer44)
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)
\[{{y}^{4}}+\frac{1}{{{y}^{4}}}\] done
clear
B)
\[{{y}^{2}}+\frac{1}{{{y}^{2}}}+2\] done
clear
C)
\[{{y}^{4}}-\frac{1}{{{y}^{4}}}\] done
clear
D)
\[{{y}^{3}}+\frac{1}{{{y}^{3}}}-2\] done
clear
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question_answer45)
If\[{{(x+y)}^{3}}-{{(x-y)}^{3}}-6y({{x}^{2}}-{{y}^{2}})=k{{y}^{3}}\], find\[k\].
A)
\[1\] done
clear
B)
\[2\] done
clear
C)
\[4\] done
clear
D)
\[8\] done
clear
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question_answer46)
Factorise\[:\]\[\frac{{{a}^{2}}}{{{b}^{2}}}+2+\frac{{{b}^{2}}}{{{a}^{2}}}\].
A)
\[{{\left( \frac{a}{b}+\frac{b}{a} \right)}^{2}}\] done
clear
B)
\[{{\left( 1+\frac{a}{b} \right)}^{2}}\] done
clear
C)
\[{{\left( 1-\frac{b}{a} \right)}^{2}}\] done
clear
D)
\[{{\left( \frac{b}{a}-\frac{a}{b} \right)}^{2}}\] done
clear
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question_answer47)
Factorise\[:\]\[4{{a}^{2}}+9{{b}^{2}}+{{c}^{2}}+12ab+4ac+6bc\].
A)
\[{{(2a+3b+c)}^{2}}\] done
clear
B)
\[{{(a+3b+2c)}^{2}}\] done
clear
C)
\[{{(a-3b+2c)}^{2}}\] done
clear
D)
\[{{(2a+3b-c)}^{2}}\] done
clear
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question_answer48)
What is the remainder obtained when the polynomial \[p(x)\] is divided by\[(b-ax)\]?
A)
\[p\left( \frac{-b}{a} \right)\] done
clear
B)
\[p\left( \frac{a}{b} \right)\] done
clear
C)
\[p\left( \frac{b}{a} \right)\] done
clear
D)
\[p\left( \frac{-a}{b} \right)\] done
clear
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question_answer49)
If\[a+b+c=10\], \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}=38\] and\[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}=160\], find the value of\[abc\].
A)
\[45\] done
clear
B)
\[15\] done
clear
C)
\[10\] done
clear
D)
\[30\] done
clear
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question_answer50)
What are the factors of\[{{x}^{3}}+{{x}^{2}}-\frac{1}{{{x}^{2}}}+\frac{1}{{{x}^{3}}}\]?
A)
\[\left( {{x}^{2}}+1 \right)\left( x+\frac{1}{x}-1+\frac{1}{{{x}^{2}}} \right)\] done
clear
B)
\[\left( x+1 \right)\left( {{x}^{2}}+\frac{1}{{{x}^{2}}}-1+\frac{1}{x}-x \right)\] done
clear
C)
\[\left( x+\frac{1}{x} \right)\left( {{x}^{2}}+x-1-\frac{1}{x}+\frac{1}{{{x}^{2}}} \right)\] done
clear
D)
\[\left( {{x}^{2}}+\frac{1}{{{x}^{2}}} \right)\left( x+\frac{1}{x}-1 \right)\] done
clear
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question_answer51)
Evaluate\[\frac{{{(3.78)}^{2}}-{{(2.22)}^{2}}}{1.56}\]
A)
\[6\] done
clear
B)
\[3\] done
clear
C)
\[9\] done
clear
D)
\[15\] done
clear
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question_answer52)
Let \[{{R}_{1}}\] and \[{{R}_{2}}\] be the remainders when the polynomials \[f(x)=4{{x}^{3}}+3{{x}^{2}}-12ax-15\] and \[g(x)=2{{x}^{3}}+a{{x}^{2}}-6x+12\] are divided by \[(x-1)\] and \[(x-2)\] respectively. If \[3{{R}_{1}}+{{R}_{2}}+28=0\] find the value of\['a'\].
A)
\[0\] done
clear
B)
\[-1\] done
clear
C)
\[1\] done
clear
D)
\[32\] done
clear
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question_answer53)
What is the value of\[\frac{{{(2.3)}^{3}}-0.027}{{{(2.3)}^{2}}+0.69+0.09}\]?
A)
\[2\] done
clear
B)
\[3\] done
clear
C)
\[2.327\] done
clear
D)
\[2.273\] done
clear
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question_answer54)
If\[{{(x-1)}^{7}}={{a}_{7}}{{x}^{7}}+{{a}_{6}}{{x}^{6}}+{{a}_{5}}{{x}^{5}}+....+{{a}_{1}}x+{{a}_{0}}\], what is the value of \[{{a}_{7}}+{{a}_{6}}+{{a}_{5}}+....+{{a}_{1}}+{{a}_{0}}\]?
A)
\[0\] done
clear
B)
\[1\] done
clear
C)
\[128\] done
clear
D)
\[64\] done
clear
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question_answer55)
Resolve into factors: \[1+a+b+c+ab+bc+\]\[ca+abc\]
A)
\[(1+a)(1+b)(1+c)\] done
clear
B)
\[(a+b+c+1)(a-b-c)\] done
clear
C)
\[(a+b)(b+c)(c+a)\] done
clear
D)
\[({{a}^{2}}+{{b}^{2}}+{{c}^{2}})(1-a-b-c)\] done
clear
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question_answer56)
Which of the following are the factors of\[4{{x}^{2}}-{{y}^{2}}+2x-2y-3xy\]?
A)
\[(x+y)\]and\[(4x+y-2)\] done
clear
B)
\[(x-y)\]and\[(4x-y+2)\] done
clear
C)
\[(x+y)\]and\[(4x-y-2)\] done
clear
D)
\[(x-y)\]and\[(4x+y+2)\] done
clear
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question_answer57)
Find the value of the polynomial\[{{x}^{2}}-x-1\]at\[x=-1\].
A)
\[-3\] done
clear
B)
\[1\] done
clear
C)
\[-1\] done
clear
D)
\[0\] done
clear
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question_answer58)
Given that\[(1-x)(1+x+{{x}^{2}}+{{x}^{3}}+{{x}^{4}})\]is \[\frac{31}{32}\] and \[x\] is a rational number, what is\[1+x+{{x}^{2}}+{{x}^{3}}+{{x}^{4}}+{{x}^{5}}\]?
A)
\[\frac{31}{64}\] done
clear
B)
\[\frac{63}{32}\] done
clear
C)
\[\frac{63}{64}\] done
clear
D)
\[\frac{31}{32}\] done
clear
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question_answer59)
If\[p(x)=4{{x}^{3}}-3{{x}^{2}}+2x+1\],\[q(x)={{x}^{3}}-{{x}^{2}}+x+1\]and\[r(x)={{x}^{2}}-2x+1\]find the value of\[3p(x)+7q(x)+r(x)\]
A)
\[19{{x}^{3}}-15{{x}^{2}}+11x+11\] done
clear
B)
\[-19{{x}^{3}}-15{{x}^{2}}+11x-11\] done
clear
C)
\[19{{x}^{3}}-15{{x}^{2}}-11x+11\] done
clear
D)
\[19{{x}^{3}}-15{{x}^{2}}-11x-11\] done
clear
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question_answer60)
If\[{{x}^{3}}+{{y}^{3}}+{{z}^{3}}-3xyz=k(x+y+z)\] \[\{{{(x-y)}^{2}}+{{(y-z)}^{2}}+{{(z-x)}^{2}}\}\], find\[k\].
A)
\[1\] done
clear
B)
\[\frac{1}{4}\] done
clear
C)
\[\frac{1}{2}\] done
clear
D)
\[\frac{1}{3}\] done
clear
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