Elementary Mathematics 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
51). \( \Large \left(x+\frac{1}{x}\right) \left(x-\frac{1}{x}\right) \left(x^{2}+\frac{1}{x^{2}}-1\right) \left(x^{2}+\frac{1}{x^{2}+1}\right) \) is equal to:
A). \( \Large x^{6}+\frac{1}{x^{6}} \)
B). \( \Large x^{8}+\frac{1}{x^{8}} \)
C). \( \Large x^{8}-\frac{1}{x^{8}} \)
D). \( \Large x^{6}-\frac{1}{x^{6}} \)
52). If \( \Large a^{2x+2}=1 \), where a is a positive real number other than 1, then x is equal to:
A). -2
B). -1
C). 0
D). 1
53). If x is real then the minimum value of \( \Large \left(x^{2}-x-1\right) \) is
A). \( \Large \frac{3}{4} \)
B). 0
C). 1
D). \( \Large -\frac{5}{4} \)
54). If \( \Large \frac{\sqrt{7}-2}{\sqrt{7}+2}=a\sqrt{7}+b \), then the value of a is:
A). \( \Large \frac{11}{3} \)
B). \( \Large -\frac{4}{3} \)
C). \( \Large \frac{4}{3} \)
D). \( \Large \frac{-4\sqrt{7}}{3} \)
55). If \( \Large a+\frac{1}{b}=1\ and\ b+\frac{1}{c}=1\ then\ c+\frac{1}{a} \) is equal to
A). 0
B). \( \Large \frac{1}{2} \)
C). 1
D). 2


56). If \( \Large x=\sqrt{3}+\sqrt{2} \), then the value of \( \Large \left(x^{3}+\frac{1}{x^{3}}\right) \) is
A). \( \Large 6\sqrt{3} \)
B). \( \Large 12\sqrt{3} \)
C). \( \Large 18\sqrt{3} \)
D). \( \Large 24\sqrt{3} \)
57). If \( \Large x+y=7 \), then the value of \( \Large x^{3}+y^{3}+21xy \) is
A). 243
B). 143
C). 343
D). 443
58). If \( \Large \otimes \) is an operation such that \( \Large a \otimes b=2a \) when a>b, a+b when a
A). \( \Large \frac{1}{3} \)
B). \( \Large \frac{14}{23} \)
C). \( \Large \frac{2}{3} \)
D). \( \Large \frac{14}{13} \)
59). If \( \Large \left(125\right)^{x}=3125 \), then the value of x is
A). \( \Large \frac{1}{5} \)
B). \( \Large \frac{3}{5} \)
C). \( \Large \frac{5}{3} \)
D). \( \Large \frac{5}{7} \)
60). If \( \Large 5^{\sqrt{x}}+12^{\sqrt{x}}=13^{\sqrt{x}} \), then x is equal to
A). \( \Large \frac{25}{4} \)
B). 4
C). 9
D). 16
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