Questions

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11 questions · self-marked practice — reveal the answer and mark yourself.

Question 11 Mark
The factorized form of $a^3+b^3+3 a b-1$ is _______________ .
Answer
$(a+b-1)\left(a^2+b^2+a+b+1-a b\right)$
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Question 21 Mark
The factorized form of $\frac{1}{x y z}\left(x^2+y^2+z^2\right)+2\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right)$ is _______________
Answer
$\frac{1}{x y z}(x+y+z)^2$
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Question 31 Mark
If $3 x-\frac{y}{5}=10$ and $x y=5$, then the value of $27 x^3-\frac{y^3}{125}$ is _______________
Answer
1090
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Question 41 Mark
The factorisation form of $a^4+b^4-a^2 b^2$ is _______________ .
Answer
$\left(a^2+b^2+\sqrt{3} a b\right)\left(a^2+b^2-\sqrt{3} a b\right)$
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Question 51 Mark
The polynomial, $x^6+64 y^6$ on factorisation gives _______________ .
Answer
$\left(x^2+4 y^2\right)\left(x^4-4 x^2 y^2+16 y^4\right)$
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Question 61 Mark
The factors of the expression $a+b+c+2 \sqrt{a b}-2 \sqrt{b c}-2 \sqrt{c a}$ are _______________ .
Answer
$(\sqrt{a}+\sqrt{b}-\sqrt{c}),(\sqrt{a}+\sqrt{b}-\sqrt{c})$
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Question 81 Mark
Factorization of the polynomial $11 x^2-10 \sqrt{3} x-3$ gives _______________ .
Answer
$(11 x+\sqrt{3})(x-\sqrt{3})$
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Question 91 Mark
If $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=1$ and $a b c=2$, then $a b^2 c^2+a^2 b c^2+a^2 b^2 c=$ _______________ .
Answer
4
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