Rational expression Questions and answers

Topics

  1. Elementary Mathematics
    1. Quadratic Equations
    2. Simplification
    3. Area and perimeter
    4. Volume and surface area
    5. Geometry
    6. Trigonometry
    7. Polynomials
    8. Height and Distance
    9. Simple and Decimal fraction
    10. Indices and Surd
    11. Logarithms
    12. Trigonometric ratio
    13. Straight lines
    14. Triangle
    15. Circles
    16. Quadrilateral and parallelogram
    17. Loci and concurrency
    18. Statistics
    19. Rectangular and Cartesian products
    20. Rational expression
    21. Set theory
    22. Factorisation
    23. LCM and HCF
    24. Clocks
    25. Real Analysis
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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