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>> Elementary Mathematics >> Rational expression
1). If \( \Large a+b+c=0 \), then \( \Large a^{3}+b^{3}+c^{3} \) is equal to
A). \( \Large a^{2} \left(b+c\right)+b^{2} \left(c+a\right)+c^{2} \left(a+b\right) \)
B). \( \Large 3 \left(b+c\right) \left(c+a\right) \left(a+b\right) \)
C). \( \Large 3abc \)
D). \( \Large 6a^{2}b^{2}c^{2} \)
2). Largest number among \( \Large 2^{2^{2}},\ 2^{22},\ 222,\ \left(22\right)^{2} \) is
A). \( \Large 2^{22} \)
B). \( \Large 2^{2^{2}} \)
C). 222
D). \( \Large \left(22\right)^{2} \)
3). Both addition and multiplication of numbers are operations which are
A). commutative but not associative
B). commutative and associative
C). associative but not commutative
D). neither commutative nor associative
4). The positive square root of \( \Large \left(x^{2}+2x-1\right)+\frac{1}{x^{2}+2x+1} \) is
A). \( \Large \left(x+1\right)+\frac{1}{ \left(x+1\right) } \)
B). \( \Large \left(x+1\right)-\frac{1}{ \left(x+1\right) } \)
C). \( \Large \left(x+2\right)-\frac{1}{ \left(x+1\right) } \)
D). \( \Large \left(x+2\right)+\frac{1}{ \left(x+1\right) } \)
5). The simplified value of the decimal fraction \( \Large \frac{1.59 \times 1.59-.41 \times .41}{1.59-.41} \)
A). 1
B). 1.4
C). 2
D). 2.6


6). The fraction \( \Large 101\frac{27}{100000} \) in decimal form is
A). 101.000027
B). 101.00027
C). 0.10127
D). 0.010127
7). If \( \Large X^{y}=Y^{z},\ then\ \left(\frac{X}{Y}\right)^{x/y} \) equals
A). \( \Large X^{x/y} \)
B). \( \Large X^{ \left(x/y\right)-1 } \)
C). \( \Large X^{y/x} \)
D).
8). Which of the following statement is correct?
A). \( \Large 9^{60}<27^{35} \)
B). \( \Large 9^{60} \le 27^{35} \)
C). \( \Large 9^{60}>27^{35} \)
D). \( \Large 9^{60}\ge 27^{35} \)
9). Solve \( \Large \left[ 5^{3} \times 8^{2} \times \left(x^{-9}\right)^{1/3} \right]^{-1/3} \) is
A). 20x
B). \( \Large \frac{x}{20} \)
C). \( \Large \frac{20}{x} \)
D). 40x
10). If \( \Large \left( a^{n^{2}} \right) = \left( a^{2^{n}} \right)^{2} \), then
A). \( \Large n^{2} = 2n \)
B). \( \Large n^{n} = 2^{n-1} \)
C). \( \Large n^{2n} = 2^{n + 1} \)
D). \( \Large n^{2} = 2^{n + 1} \)
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