\[\frac{5}{3}-\frac{1}{6}\]in its simplest form is equal to:
A)
\[\frac{-1}{6}\]
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B)
\[\frac{-2}{3}\]
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C)
\[\frac{2}{3}\]
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D)
\[\frac{3}{2}\]
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E)
None of these
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Find the value of a such that \[{{\left( \frac{5}{3} \right)}^{-5}}\times {{\left( \frac{5}{3} \right)}^{-11}}={{\left( \frac{5}{3} \right)}^{8a}}\]
A)
1
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B)
2
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C)
\[-2\]
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D)
4
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E)
None of these
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Find the square root of \[21\frac{2797}{3364}\].
A)
\[\frac{289}{58}\]
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B)
\[\frac{271}{58}\]
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C)
\[\frac{281}{58}\]
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D)
\[\frac{291}{58}\]
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E)
None of these
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Find the cube root of 91125.
A)
35
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B)
25
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C)
15
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D)
45
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E)
None of these
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Find the sum of \[5{{x}^{2}}-\frac{x}{3}+\frac{5}{2},\frac{-1}{2}{{x}^{2}}+\frac{x}{2}-\frac{1}{3}\]and \[-2{{x}^{2}}-\frac{x}{5}-\frac{1}{6}\]
A)
\[\frac{2}{3}{{x}^{2}}-\frac{7x}{11}+1\]
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B)
\[\frac{5}{2}{{x}^{2}}+\frac{11}{30}x+2\]
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C)
\[\frac{1}{5}{{x}^{2}}+\frac{13x}{30}+3\]
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D)
\[\frac{1}{3}{{x}^{2}}+\frac{2}{3}x+5\]
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E)
None of these
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Factorise:\[\frac{16}{25}{{x}^{2}}+\frac{9}{16}{{y}^{2}}+9{{z}^{2}}-\frac{6}{5}xy-\frac{9}{2}yz+\frac{24}{5}zx\]
A)
\[{{\left( \frac{4}{5}x+\frac{3}{4}y-3z \right)}^{2}}\]
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B)
\[{{\left( \frac{4}{5}x-\frac{3}{4}y+3z \right)}^{2}}\]
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C)
\[\frac{48y-64}{3}\]
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D)
\[{{\left( \frac{4}{5}x+\frac{3}{4}y+3z \right)}^{2}}\]
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E)
None of these
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The average of three numbers is 27. If the largest number is replaced by the number 34, then the average becomes 30. The original number that is replaced is:
A)
25
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B)
22
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C)
23
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D)
24
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E)
None of these
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A gardener uses pipes to water his garden from a tank. For his entire garden he uses 6 pipes to water and it takes him 1 hour 20 minutes to completely empty the tank. How much time will one pipe take to empty the tank?
A)
8 hours
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B)
8 hours and 36 min
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C)
7 hours and 45 min
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D)
9 hours and 55 min
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E)
None of these
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Three friends James, Harry and Smith are working in a restaurant and together earn Rs.360 per day, while James and Harry together earn Rs. 250 and James and Smith together earn Rs. 210 per day. The earning of James per day is:
A)
Rs. 100
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B)
Rs. 180
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C)
Rs. 130
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D)
Rs. 150
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E)
None of these
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The production of rice increases by 10% in the first year, 15% in the second year, and decreases by 14% in the third year. Find the production of rice in the first year if at the end of third year it was 20,000 kg.
A)
18,384 kg
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B)
18,300 kg
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C)
19,740 kg
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D)
18,474 kg
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E)
None of these
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I f the cost price of 25 chairs is equal to the selling price of 30 chairs, then find the loss percent.
A)
\[16\frac{1}{3}%\]
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B)
\[17\frac{2}{3}%\]
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C)
\[16\frac{2}{3}%\]
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D)
\[16%\]
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E)
None of these
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Find the weight of a cubical wooden block of length 60 Cm if weight of 1 cubic metre of wooden block is 900 kg.
A)
192.36 kg
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B)
198 kg
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C)
196.5 kg
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D)
194.4 kg
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E)
None of these
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The value of \[y+y({{y}^{y}})\] when\[y=2\]is:
A)
8
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B)
10
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C)
18
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D)
4
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E)
None of these
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Find the value of \[({{3}^{0}}+{{4}^{-1}})\times {{2}^{2}}\]
A)
7
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B)
11
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C)
5
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D)
3
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E)
None of these
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Find the value of m for which \[{{5}^{m}}\div {{5}^{-1}}={{5}^{5}}\]
A)
5
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B)
25
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C)
3
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D)
2
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E)
None of these
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Standard form of 0.0000000000085.
A)
\[8.5\times {{10}^{12}}\]
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B)
\[8.5\times {{10}^{-}}^{12}\]
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C)
\[8.5\times {{10}^{11}}\]
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D)
\[8.5\times {{10}^{-}}^{11}\]
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E)
None of these
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Simplify: \[\frac{(x-1)(x-2)({{x}^{2}}-9x+14)}{(x-7)({{x}^{2}}-3x+2)}\]
A)
\[(x-1)\]
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B)
\[(x-2)\]
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C)
\[(x-7)\]
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D)
\[(x-1)(x-2)\]
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E)
None of these
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Solve for\[x:\frac{{{x}^{2}}-14x+49}{{{x}^{2}}-49}=\frac{3}{17}\]
A)
\[-1\]
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B)
0
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C)
10
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D)
13
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E)
None of these
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If 30% of \[140=x%\]of 840, then find the value of x.
A)
24
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B)
5
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C)
11
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D)
33
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E)
None of these
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Find the value of \[\sqrt[3]{\frac{0.027}{0.008}}-\sqrt{\frac{0.09}{0.04}}-1\]
A)
0
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B)
1
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C)
\[-1\]
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D)
\[\frac{3}{2}\]
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E)
None of these
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If \[4{{x}^{2}}+{{y}^{2}}=40\]and \[xy=6,\]then find the value of\[2x+y\].
A)
\[\pm \,6\]
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B)
\[\pm \,2\]
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C)
\[\pm \,8\]
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D)
\[\pm \,10\]
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E)
None of these
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Which of the following is a factor of\[6-y-2{{y}^{2}}\]?
A)
\[y-3\]
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B)
\[y-2\]
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C)
\[y+3\]
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D)
\[3-2y\]
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E)
None of these
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Which\[P:Q:R\] \[=2:3:4\] and \[{{P}^{2}}+{{Q}^{2}}+{{R}^{2}}\]\[=11600,\]then find\[P+Q-R\], where P, Q and R are whole numbers.
A)
16
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B)
18
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C)
20
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D)
22
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E)
None of these
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