31). If [p] means the greatest positive integer less than or equal to p, then \( \Large \left[ \frac{1}{4} \right]+\left[ 4-\frac{1}{4} \right]+\left[ 3 \right] \) is equal to
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32). The value of \( \Large \frac{\left(243\right)^{\frac{n}{5}}.3^{2n+1}}{9^{n}.3^{n-1}} \) is
A). 1 |
B). 9 |
C). 3 |
D). \( \Large 3^{n} \) |
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33). If x=0.5 and y=0.2, then the value of \( \Large \sqrt{0.6} \times \left(3y\right)^{x} \) is equal to
A). 1 |
B). 0.5 |
C). 0.6 |
D). 1.1 |
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34). If \( \Large x^{x\sqrt{x}}= \left(x\sqrt{x}\right)^{x} \) , the x equals
A). \( \Large \frac{4}{9} \) |
B). \( \Large \frac{2}{3} \) |
C). \( \Large \frac{9}{4} \) |
D). \( \Large \frac{3}{2} \) |
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35). If a=7, b=5 and =3, the value of \( \Large a^{2}+b^{2}+c^{2}-ab-bc-ca \) is
A). 12 |
B). -12 |
C). 0 |
D). 18 |
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36). If \( \Large 7^{x}=\frac{1}{343} \), then the value of x is
A). 3 |
B). -3 |
C). \( \Large \frac{1}{3} \) |
D). \( \Large \frac{1}{7} \) |
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37). \( \Large \frac{\frac{1}{3}.\frac{1}{3}.\frac{1}{3}+\frac{1}{4}.\frac{1}{4}.\frac{1}{4}-3\frac{1}{3}.\frac{1}{4}.\frac{1}{5}+\frac{1}{5}.\frac{1}{5}.\frac{1}{5}}{\frac{1}{3}.\frac{1}{3}+\frac{1}{4}.\frac{1}{4}+\frac{1}{5}.\frac{1}{5}-\left(\frac{1}{3}.\frac{1}{4}+\frac{1}{4}.\frac{1}{5}+\frac{1}{5}.\frac{1}{3}\right) } \) is
A). \( \Large \frac{2}{3} \) |
B). \( \Large \frac{3}{4} \) |
C). \( \Large \frac{47}{60} \) |
D). \( \Large \frac{49}{60} \) |
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38). If \( \Large 0.13 \times p^{3}=13 \), then p is equal to
A). 10 |
B). 0.01 |
C). 0.1 |
D). 100 |
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39). If \( \Large \frac{x}{y}=\frac{3}{4} \), the value of \( \Large \frac{6}{7}+\frac{y-x}{y+x} \) is:
A). 1 |
B). \( \Large \frac{2}{7} \) |
C). \( \Large \frac{3}{7} \) |
D). \( \Large 1\frac{3}{7} \) |
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40). If \( \Large x=7-4\sqrt{3} \), then \( \Large \sqrt{x}+\frac{1}{\sqrt{x}} \) is equal to:
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