The value of the expression\[\frac{1024\times 243\times 625}{2048\times 729\times 3125}\] is given by:
A)
\[\frac{1}{30}\]
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B)
\[\frac{1}{15}\]
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C)
\[\frac{1}{6}\]
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D)
\[\frac{1}{10}\]
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E)
None of these
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Find the value of: \[{{\left( \frac{25}{15} \right)}^{2}}\times {{\left( \frac{45}{25} \right)}^{2}}\times {{\left( \frac{63}{95} \right)}^{0}}\]
A)
\[10\]
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B)
\[9\]
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C)
\[20\]
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D)
\[30\]
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E)
None of these
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Simplify: \[{{\left( \sqrt{5}-\frac{1}{\sqrt{5}} \right)}^{2}}\]
A)
\[\frac{5}{16}\]
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B)
\[\frac{16}{5}\]
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C)
\[\frac{2}{5}\]
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D)
\[\frac{3}{5}\]
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E)
None of these
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By what number must we multiply with the sum of the cubes of first ten natural numbers so that the resultant product will be a perfect cube?
A)
11
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B)
55
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C)
110
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D)
125
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E)
None of these
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The value of \[\left( {{x}^{\frac{1}{8}}}+{{x}^{\frac{-1}{8}}} \right)\left( {{x}^{\frac{1}{8}}}-{{x}^{\frac{-1}{8}}} \right)\]\[\left( {{x}^{\frac{1}{4}}}+{{x}^{\frac{-1}{4}}} \right)\left( {{x}^{\frac{1}{2}}}-{{x}^{\frac{-1}{2}}} \right)\] is:
A)
\[\left( x+\frac{1}{x} \right)\]
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B)
\[\left( x-\frac{1}{x} \right)\]
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C)
\[\left( {{x}^{2}}+\frac{1}{{{x}^{2}}} \right)\]
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D)
\[\left( {{x}^{3}}+\frac{1}{{{x}^{3}}} \right)\]
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E)
None of these
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Factorize: \[{{a}^{4}}-14{{a}^{2}}{{b}^{2}}-51{{b}^{2}}\]
A)
\[({{a}^{2}}+17{{b}^{2}})({{a}^{2}}-7{{b}^{2}})({{a}^{2}}-7{{b}^{2}})\]
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B)
\[({{a}^{2}}-17{{b}^{2}})({{a}^{2}}-3{{b}^{2}})\]
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C)
\[(a+b\sqrt{17})(a-b\sqrt{17})({{a}^{2}}+3{{b}^{2}})\]
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D)
\[(a+b\sqrt{17})(a-b\sqrt{17})({{a}^{2}}-3{{b}^{2}})\]
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E)
None of these
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Ram has a total of Rs. 34 in the denominations of fifty-paise and twenty-five paise coins. If the number of 25 paise coins is twice the number of 50 paise coins, then how many coins of 25paise does he have?
A)
30
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B)
68
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C)
70
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D)
72
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E)
None of these
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A work force of 50 men with a contractor can finish a piece of work in 5 months. In how many months the same work can be completed by 125 men?
A)
2
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B)
\[1\frac{1}{2}\]
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C)
\[2\frac{1}{2}\]
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D)
3
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E)
None of these
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If 15 boys earn Rs. 900 in 5 days, how much will 20 boys earn in 7 days?
A)
Rs. 1600
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B)
Rs. 1680
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C)
Rs. 1650
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D)
Rs. 1700
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E)
None of these
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Rachna gets 98 marks in her exams. This amounts to 56% of the total marks. What are the maximum marks?
A)
180
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B)
175
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C)
150
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D)
160
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E)
None of these
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Rs.800 amounts to Rs. 920 in three years at simple interest. If the interest rate is increased by 3%, then in three years it would amount to:
A)
Rs. 992
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B)
Rs. 987
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C)
Rs. 989
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D)
Rs. 1008
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E)
None of these
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The mean of 30 observations is 40. If 16 is subtracted from each observation, then the new mean will be:
A)
24
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B)
28
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C)
32
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D)
36
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E)
None of these
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If \[\frac{x}{2y}=\frac{3}{2},\]then the value of \[\frac{2x+y}{x-2y}\] is equal to:
A)
\[7.1\]
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B)
\[\frac{1}{7}\]
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C)
7
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D)
3.2
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E)
None of these
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How many\[\frac{1}{8}\],s are there in \[17\frac{1}{2}\]?
A)
410
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B)
104
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C)
401
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D)
140
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E)
None of these
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\[{{a}^{x-y}}\times {{b}^{y-z}}\times {{a}^{y-x}}\times {{b}^{z-y}}\times {{2}^{5}}\]is equal to:
A)
\[{{a}^{2}}{{b}^{3}}\]
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B)
\[{{2}^{5}}{{a}^{3}}{{b}^{2}}\]
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C)
32
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D)
\[{{2}^{5}}a{{b}^{2}}\]
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E)
None of these
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By what number should be divide \[{{\left( -24 \right)}^{-1}}\]so that the quotient may be\[{{3}^{-1}}\]?
A)
\[-1\]
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B)
\[-8\]
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C)
\[-\frac{1}{8}\]
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D)
\[\frac{1}{8}\]
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E)
None of these
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If \[a+\frac{1}{a}=x+y\]and \[a-\frac{1}{a}=x-y,\]then which of the following options is correct?
A)
\[x=y\]
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B)
\[xy=1\]
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C)
\[x+y=0\]
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D)
\[xy=2\]
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E)
None of these
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\[\frac{2}{3}\]rd of a number when multiplied by \[\frac{3}{4}\]th of the same number makes 338. The number is:
A)
18
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B)
26
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C)
24
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D)
36
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E)
None of these
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If \[3\frac{1}{x}\times 3\frac{3}{4}=12\frac{1}{2},\]then the value of x is:
A)
1
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B)
2
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C)
\[\frac{1}{3}\]
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D)
3
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E)
None of these
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The area of a circular field is\[3850\text{ }{{m}^{2}}\]. What is its diametre?
A)
35 m
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B)
70 m
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C)
15 m
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D)
51 m
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E)
None of these
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The ratio of ages of a father and his son at present is\[6:1\]. After 5 years the ratio will become\[7:2\]. Find the present age of the son.
A)
5 years
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B)
8 years
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C)
15 years
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D)
7 years
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E)
None of these
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\[\frac{2}{5}\]People in a joint family are students, \[\frac{1}{4}\]people are house wives and rest are working people. If there are 20 members in the family, then the number of working persons in the family are:
A)
9
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B)
3
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C)
7
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D)
11
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E)
None of these
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Simplify: \[\sqrt{3\frac{33}{289}}\]
A)
\[\sqrt{\frac{3}{17}}\]
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B)
\[\frac{30}{17}\]
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C)
\[\sqrt{\frac{17}{30}}\]
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D)
\[\frac{17}{3}\]
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E)
None of these
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