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Surds and indices Practice Questions & Answers

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If m and n (n>l) are whole numbers such that $m^{n}$ =121.the value of $(m-1)^{n+1}$ is

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If m and n (n>l) are whole numbers such that $m^{n}$ =121.the value of $(m-1)^{n+1}$ is
1). 1
2). 10
3). 121
4). 1000

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If $x+\frac{1}{x}$ = -2 , then the value of $x^{2n+1}+\frac{1}{x^{2n+1}}$ , where n la a positive integer, is

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If $x+\frac{1}{x}$ = -2 , then the value of $x^{2n+1}+\frac{1}{x^{2n+1}}$ , where n la a positive integer, is
1). 0
2). 2
3). -2
4). -5

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If x= $1+\sqrt{2}+\sqrt{3}$ then the value of $\left(x+\frac{1}{x-1}\right)$ is

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If x= $1+\sqrt{2}+\sqrt{3}$ then the value of $\left(x+\frac{1}{x-1}\right)$ is
1). $1+2\sqrt{3}$
2). $2+\sqrt{3}$
3). $3+\sqrt{2}$
4). $2\sqrt{3}-1$

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If a= $\frac{\sqrt{5}+1}{\sqrt{5}-1}$ and b = $\frac{\sqrt{5}-1}{\sqrt{5}+1}$ , the value of $\left(\frac{a^{2}+ab+b^{2}}{a^{2}-ab+b^{2}}\right)$ is

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If a= $\frac{\sqrt{5}+1}{\sqrt{5}-1}$ and b = $\frac{\sqrt{5}-1}{\sqrt{5}+1}$ , the value of $\left(\frac{a^{2}+ab+b^{2}}{a^{2}-ab+b^{2}}\right)$ is
1). $\frac{3}{4}$
2). $\frac{4}{3}$
3). $\frac{3}{5}$
4). $\frac{5}{3}$

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If a= $\frac{\sqrt{3}}{2}$ , then the value of $\sqrt{1+a}+\sqrt{1-a}$

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If a= $\frac{\sqrt{3}}{2}$ , then the value of $\sqrt{1+a}+\sqrt{1-a}$
1). $\sqrt{3}$
2). $\frac{\sqrt{3}}{2}$
3). $2+\sqrt{3}$
4). $2-\sqrt{3}$