Simplification Questions and answers

  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
21). \( \Large \sqrt{289} - \sqrt{625} \div \sqrt{25} \) is equal to
A). 17
B). 15
C). 12
D). \( \Large - \frac{8}{5} \)
22). If \( \Large a^{2} + 1 = a \), then what is the value of \( \Large a^{12} + a^{6} + 1 \) is
A). 2
B). 3
C). -3
D). 1
23). If a, b and c are non-zero, \( \Large a + \frac{1}{b} = 1 \) and \( \Large b + \frac{1}{c} = 1 \), then the value of abc is
A). -3
B). 1
C). -1
D). 3
24). If a + b + c = 0, then the value of \( \Large \left(\frac{a+b}{c} + \frac{b+c}{a} + \frac{c+a}{b}\right) \) \( \Large \left(\frac{a}{b+c} + \frac{b}{c+a} + \frac{c}{a+b}\right) \)
A). 9
B). 0
C). 8
D). -3
25). If \( \Large a * b = a + b + \frac{a}{b} \), then the value \( \Large 12 * 4 \) is
A). 48
B). 19
C). 20
D). 21


26). If \( \Large x = \frac{\sqrt{2}+1}{\sqrt{2}-1} \) and \( \Large x - y = 4\sqrt{2} \), then the value of \( \Large \left(x^{2} + y^{2}\right) \) is
A). 34
B). 38
C). 30
D). 32
27). If \( \Large x + \frac{a}{x} = 1 \), then the value of \( \Large \frac{x^{2}+x+a}{x^{3}-x^{2}} \) is
A). -2
B). \( \Large - \frac{a}{2} \)
C). \( \Large \frac{2}{a} \)
D). \( \Large - \frac{2}{a} \)
28). If \( \Large \sqrt{28 - 6\sqrt{3}} = \sqrt{3} a + b \), (where a, b are rationale), value of \( \Large \left(a + b\right) \) is
A). -2
B). 2
C). 1
D). -1
29). If \( \Large x + y = 1 \), then the value of \( \Large x^{3} + y^{3} + 3xy\) is
A). -2
B). 1
C). 2
D). 3
30). If \( \Large a = \left(\sqrt{2}-1\right)^{\frac{1}{3}} \), then the value of \( \Large \left(a - a^{-1}\right)^{3} + 3 \left(a - a^{-1}\right) \) is
A). -2
B). 2
C). \( \Large 2\sqrt{2} \)
D). \( \Large \sqrt{2} \)
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