By what number should we multiply \[\frac{-8}{13}\]so the product will be \[-24?\]
A)
\[-39\]
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B)
\[39\]
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C)
\[26\]
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D)
\[-26\]
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E)
None of these
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\[{{\left( \frac{-3}{5} \right)}^{2}}\div {{\left( \frac{-3}{5} \right)}^{5}}\] is equal to:
A)
\[\frac{9}{25}\]
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B)
\[\frac{-9}{25}\]
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C)
\[{{\left( \frac{-3}{5} \right)}^{12}}\]
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D)
\[{{\left( \frac{-5}{3} \right)}^{2}}\]
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E)
None of these
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If\[\sqrt{5184\,}=72,\]then\[\sqrt{5184\,}+\sqrt{51.84}+\sqrt{0.005184}\]is equal to:
A)
79.369
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B)
79.464
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C)
79.272
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D)
79.646
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E)
None of these
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If \[y=\sqrt[3]{2\frac{80}{216},}\]then find the value of y.
A)
\[\frac{4}{6}\]
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B)
\[\frac{2}{3}\]
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C)
\[\frac{3}{7}\]
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D)
\[\frac{4}{3}\]
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E)
None of these
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Multiply: \[(3{{x}^{2}}+{{y}^{2}})\]and \[({{x}^{2}}+2{{y}^{2}})\]
A)
\[3{{x}^{3}}+7{{x}^{4}}+2{{x}^{2}}\]
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B)
\[2{{x}^{4}}+4x{{y}^{3}}-2{{y}^{4}}\]
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C)
\[3{{x}^{4}}+7{{x}^{2}}{{y}^{2}}+2{{y}^{4}}\]
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D)
\[4{{x}^{4}}+7xy+3{{y}^{2}}\]
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E)
None of these
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Factorise: \[36{{u}^{2}}+\frac{1}{25}{{v}^{2}}+25{{w}^{2}}-\frac{12}{5}uv-2vw+60wu\]
A)
\[{{\left( 6u-\frac{v}{5}-5w \right)}^{2}}\]
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B)
\[{{\left( 6u+\frac{v}{5}-5w \right)}^{2}}\]
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C)
\[{{\left( 6u-\frac{v}{5}+5w \right)}^{2}}\]
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D)
\[{{\left( 6u-\frac{v}{5}+5w \right)}^{2}}\]
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E)
None of these
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If the age of X and Y are added to thrice the age of Z, the total becomes 70. If the age of Y and Z are added to twice the age of X, the total becomes 84 and if the age of X is added to twice the age of Z and twice the age of Y the total becomes 111. The age of X is:
A)
19 years
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B)
15 years
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C)
8 years
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D)
18 years
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E)
None of these
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Three friends Thomas, Harry and James went for the marathon and start their run at 6 a.m. and run through planes and hills on their way and return at 12 p.m. If their speed on the plane ground is 4 km/h, up the hill it is 3km/h and down the hill it is 6km/h. find the total distance they cover during the whole journey.
A)
15km
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B)
10km
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C)
12km
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D)
18km
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E)
None of these
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If 34 men can complete a work in 8 days working 9 hours a day, then find number of men required to finish the work in 2 days if they work 9 hours in a day.
A)
100 men
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B)
200 men
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C)
300 men
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D)
136 men
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E)
None of these
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Thomas asked Harry to think of two different numbers such that 30 % greater number is equal to the 50% of the smaller number. If Harry said that the sum of two numbers is 120, then the greater number he thinks of is:
A)
25
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B)
15
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C)
45
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D)
75
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E)
None of these
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By selling a stool for Rs. 67.50 a carpenter loses 10%. How much would he gain or loss by selling it for Rs. 82.50?
A)
12% loss
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B)
10% gain
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C)
11% gain
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D)
18% loss
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E)
None of these
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A beam 5 m long and 40 cm wide contains 0.6 cubic metre of wood. How thick is the beam?
A)
20cm
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B)
30cm
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C)
50cm
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D)
70cm
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E)
None of these
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If we subtract\[-3{{x}^{2}}{{y}^{2}}\] from \[{{x}^{2}}{{y}^{2}},\]then we get
A)
\[-4{{x}^{2}}{{y}^{2}}\]
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B)
\[-2{{x}^{2}}{{y}^{2}}\]
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C)
\[2{{x}^{2}}{{y}^{2}}\]
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D)
\[4{{x}^{2}}{{y}^{2}}\]
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E)
None of these
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The value of \[{{\left( a+b \right)}^{2}}-{{\left( a-b \right)}^{2}}\]is
A)
\[4ab\]
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B)
\[-4ab\]
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C)
\[2{{a}^{2}}+2{{b}^{2}}\]
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D)
\[2{{a}^{2}}-2{{b}^{2}}\]
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E)
None of these
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A farmer has enough food to feed 20 animals for 6 days. How long would the food last if there were10 more animals joins with them?
A)
8 days
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B)
6 days
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C)
4 days
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D)
2 days
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E)
None of these
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In a village, 120 men had provision for food for 210 days. After 10 days 40 men left the village. How long the remaining food last?
A)
240 days
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B)
300 days
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C)
270 days
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D)
280 days
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E)
None of these
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If \[\sqrt{3018+\sqrt{36+\sqrt{169}}}=x,\]then find the value of x.
A)
44
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B)
33
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C)
42
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D)
55
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E)
None of these
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Factorise the expression \[6xy-4y+6-9x\]
A)
\[(2y+3)(3x-2)\]
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B)
\[(2y-3)(3x-2)\]
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C)
\[(2y-3)(3x+2)\]
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D)
\[(3x+2)(3x-2)\]
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E)
None of these
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The diameter of a semicircular field is 14 meters. What is the cost of fencing the plot at Rs. 10 per meter.
A)
Rs. 220
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B)
Rs. 360
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C)
Rs. 140
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D)
Rs. 351
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E)
None of these
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Simplify: \[{{\left( \frac{{{x}^{-3}}}{{{y}^{2}}} \right)}^{-3}}{{\left( \frac{{{x}^{-3}}}{{{y}^{5}}} \right)}^{2}}\]
A)
\[\frac{1}{{{y}^{2}}}\]
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B)
\[\frac{1}{{{y}^{4}}}\]
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C)
\[\frac{{{x}^{2}}}{{{y}^{3}}}\]
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D)
\[\frac{{{x}^{3}}}{{{y}^{4}}}\]
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E)
None of these
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If \[a=\sqrt{2}+1\]and \[b=\sqrt{2}-1,\]then find the value of \[\frac{{{a}^{2}}+ab+{{b}^{2}}}{{{a}^{2}}-ab+{{b}^{2}}}\]
A)
\[\frac{2}{3}\]
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B)
\[\frac{7}{5}\]
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C)
\[2-3\sqrt{2}\]
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D)
\[3-2\sqrt{2}\]
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E)
None of these
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If \[a+\frac{1}{a}=14,\]then find the value of \[{{a}^{3}}+\frac{1}{{{a}^{3}}}\]
A)
2072
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B)
2744
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C)
2786
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D)
2702
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E)
None of these
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If \[\frac{a}{b-a}=\frac{7}{8,}\]find the value of \[\frac{a}{b}\].
A)
\[\frac{-7}{15}\]
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B)
\[\frac{7}{15}\]
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C)
\[\frac{-15}{7}\]
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D)
\[\frac{15}{7}\]
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E)
None of these
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