Find the rational number which lies between \[\frac{5}{6}\] and \[\frac{6}{7}\].
A)
\[\frac{71}{84}\]
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B)
\[\frac{73}{84}\]
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C)
\[\frac{23}{28}\]
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D)
\[\frac{37}{42}\]
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E)
None of these
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Simplify: \[{{5}^{-3}}\times {{5}^{-6}}\]
A)
\[{{5}^{-\,7}}\]
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B)
\[{{5}^{-\,8}}\]
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C)
\[{{5}^{-\,9}}\]
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D)
\[{{9}^{-\,5}}\]
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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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Find the value of \[\sqrt[3]{{{8}^{4}}}\]
A)
2
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B)
8
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C)
16
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D)
64
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E)
None of these
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The product of\[(-3{{x}^{2}}y)\,\,(4{{x}^{2}}y-3x{{y}^{2}}+4x-5y)\]is equal to:
A)
\[12{{x}^{3}}{{y}^{2}}+9{{x}^{2}}{{y}^{2}}-12{{x}^{4}}y+15{{x}^{3}}{{y}^{3}}\]
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B)
\[-12{{x}^{4}}{{y}^{2}}+9{{x}^{3}}{{y}^{3}}-12{{x}^{3}}y+15{{x}^{2}}{{y}^{2}}\]
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C)
\[-12x{{y}^{2}}\,+\,9{{x}^{3}}\,{{y}^{2}}\,-\,12{{x}^{3}}y\,+\,15xy\]
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D)
\[-12x{{y}^{3}}+9xy-12x{{y}^{2}}+15{{x}^{2}}y\]
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E)
None of these
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Factories: \[8{{y}^{2}}+36y+36\]
A)
\[(4y+12)\,\,(2y+3)\]
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B)
\[(4y+12)\,\,(2y-3)\]
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C)
\[(4y-12)\,\,(2y+3)\]
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D)
\[(4y-12)\,\,(2y-3)\]
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E)
None of these
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The scientific notation of 216000000000000 is given by:
A)
\[21.6\times {{10}^{13}}\]
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B)
\[216\times {{10}^{12}}\]
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C)
\[2160\times {{10}^{11}}\]
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D)
\[2.16\times {{10}^{14}}\]
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E)
None of these
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\[45\,xyz\,\,(xy+yz+{{z}^{2}})(z+x)\]\[\div \,\,105\,xy\,(xy+xz+yz+{{z}^{2}})\]when simplified is equal to:
A)
\[\frac{3z\,(3z+x)}{7}\]
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B)
\[\frac{z\,(z-x)}{7}\]
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C)
\[\frac{3z\,(z-x)}{7}\]
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D)
\[\frac{3z\,(z+x)}{7}\]
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E)
None of these
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72 % of 25 students are good in Mathematics. How many are not good at it?
A)
10
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B)
7
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C)
18
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D)
25
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E)
None of these
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10% of A is equal to 5% of B, then 25% of B is ________.
A)
25% of A
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B)
20% of A
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C)
50% of A
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D)
40% of A
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E)
None of these
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If\[\sqrt{{{2}^{n}}}=32,\]then the value of n is:
A)
3
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B)
5
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C)
10
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D)
8
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E)
None of these
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If 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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A retailer purchased 300 kg of potatoes at the rate of Rs. 12 per kg and sold it at a profit of 6 %. Find the selling price of 300 kg of potatoes.
A)
Rs. 3958
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B)
Rs. 3816
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C)
Rs. 3769
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D)
Rs. 3896
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E)
None of these
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If \[f(x)=3{{x}^{4}}+5{{x}^{3}}-6{{x}^{2}}+7x+9,\] then \[f(-1)\] is equal to:
A)
\[-\,5\]
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B)
\[-\,6\]
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C)
\[-\,7\]
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D)
1
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E)
None of these
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If \[x-y=3\]and\[{{x}^{2}}+{{y}^{2}}=29,\]then the value of\[xy\] is:
A)
5
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B)
10
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C)
15
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D)
20
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E)
None of these
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Factorise \[{{m}^{3}}-64\] and choose the correct option.
A)
\[(m-4)\,\,({{m}^{2}}-4m-16)\]
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B)
\[(m-4)\,\,({{m}^{2}}+4m+16)\]
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C)
\[(m+4)\,\,({{m}^{2}}+4m+16)\]
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D)
\[(m-4)\,\,({{m}^{2}}-4m+16)\]
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E)
None of these
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Which one of the following is a rational number?
A)
\[7-\sqrt{56}\]
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B)
\[8-\sqrt{25}\]
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C)
\[6-\sqrt{31}\]
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D)
\[2-\sqrt{73}\]
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E)
None of these
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View Answer play_arrow
Simplify: \[\frac{25\times {{a}^{-\,4}}}{{{5}^{-\,3}}\times 10\times {{a}^{-\,8}}}\]
A)
\[\frac{5\,{{a}^{2}}}{2}\]
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B)
\[\frac{25\,{{a}^{3}}}{2}\]
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C)
\[\frac{125\,{{a}^{4}}}{2}\]
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D)
\[\frac{625\,{{a}^{4}}}{2}\]
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E)
None of these
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What is the value of \[\sqrt{15368+\sqrt{52+\sqrt{144}}}\] ?
A)
124
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B)
112
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C)
96
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D)
91
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E)
None of these
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Find the value of\[y\]such that\[\frac{y}{10}+\frac{2y}{5}-\frac{16}{25}=\frac{1}{25}\].
A)
\[\frac{17}{25}\]
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B)
\[\frac{42}{25}\]
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C)
\[\frac{45}{25}\]
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D)
\[\frac{34}{25}\]
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E)
None of these
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Martin purchased 12 shirts for Rs. 1920. Find the number of shirts he can purchase for Rs. 3680.
A)
21
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B)
22
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C)
23
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D)
25
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E)
None of these
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There are 320 people in a cinema hall. If 20 % are females, then total number of females in the Cinema hall are:
A)
70
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B)
80
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C)
60
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D)
40
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E)
None of these
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If principal is x and rate of interest is y% annually for five years then which one of the following is correct for calculating the compound interest?
A)
\[x\left\{ {{\left( 1+\frac{5}{100} \right)}^{y}}-1 \right\}\]
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B)
\[y\,\,\left\{ {{\left( 1+\frac{5}{100} \right)}^{x}}-1 \right\}\]
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C)
\[x\left\{ {{\left( 1+\frac{y}{100} \right)}^{5}}-1 \right\}\]
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D)
All of these
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E)
None of these
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A is thrice as good as B and therefore is able to finish a work in 80 days less than B. Find the number of days required to complete the work if they are working together.
A)
20 days
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B)
24 days
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C)
32 days
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D)
40 days
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E)
None of these
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Find the value of\[\sqrt{\left( 7+3+\sqrt{5} \right)\left( 7-3\sqrt{5} \right)}\].
A)
2
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B)
4
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C)
\[\sqrt{5}\]
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D)
\[2\sqrt{5}\]
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E)
None of these
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The Pythagorean triplet whose smallest number is 12 is:
A)
12, 32 and 35
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B)
12, 35 and 37
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C)
12, 32 and 37
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D)
12, 39 and 42
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E)
None of these
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Arrange\[\frac{4}{5},\]\[\frac{7}{10}\] and \[\frac{13}{20}\] in ascending order.
A)
\[\frac{4}{5}<\frac{7}{10}<\frac{13}{20}\]
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B)
\[\frac{7}{10}<\frac{13}{20}<\frac{4}{5}\]
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C)
\[\frac{7}{10}<\frac{4}{5}<\frac{13}{20}\]
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D)
\[\frac{13}{20}<\frac{7}{10}<\frac{4}{5}\]
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E)
None of these
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If \[{{3}^{(x-y)}}=27\] and \[{{3}^{(x+y)}}=243,\]then x is equal to:
A)
0
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B)
2
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C)
4
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D)
6
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E)
None of these
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Find the value of \[{{\left[ {{({{6}^{2}}+{{8}^{2}})}^{\frac{1}{2}}} \right]}^{3}}\].
A)
2197
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B)
1690
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C)
1000
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D)
2890
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E)
None of these
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If 5 women or 4 men earn Rs. 600 is a day, then the earning of 10 women and 8 men in a day will be:
A)
Rs. 2400
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B)
Rs. 2200
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C)
Rs. 1860
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D)
Rs. 1480
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E)
None of these
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Find the volume of a cylindrical can whose radius is 3.2 cm and height is 5.6 cm.
A)
\[180.22\,\,c{{m}^{3}}\]
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B)
\[175.96\,\,c{{m}^{3}}\]
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C)
\[178.2\,\,c{{m}^{3}}\]
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D)
\[174.56\,\,c{{m}^{3}}\]
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E)
None of these
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To satisfy must \[\frac{6{{x}^{2}}+13x-4}{2x+5}=\frac{12{{x}^{2}}+5x-2}{4x+3},\] be equal to:
A)
1
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B)
2
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C)
0
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D)
3
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E)
None of these
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Mary can finish an art work in 5 days and Martin can do the same work in 8 days. Find the time taken to finish the same work if both of them work together.
A)
\[8\,\,\frac{1}{2}\,\,days\]
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B)
\[9\,\,\frac{2}{3}\,\,days\]
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C)
\[4\,\,\frac{4}{9}\,\,days\]
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D)
\[3\,\,\frac{1}{13}\,\,days\]
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E)
None of these
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Martin went to a shop and purchased a toy for his son for Rs. 550. The cost price of the toy is Rs. 485. Find the gain percent on the toy earned by the shopkeeper.
A)
\[10.25%\]
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B)
\[5\,\,\frac{1}{4}%\]
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C)
\[13.4%\]
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D)
\[15\,\,\frac{2}{3}%\]
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E)
None of these
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What sum of money will produce Rs. 1770 simple interest in\[7\,\,\frac{1}{2}\]years at 8% per annum?
A)
Rs. 2900
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B)
Rs. 2950
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C)
Rs. 3000
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D)
Rs. 2800
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E)
None of these
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What is the measure of each angle of a regular hexagon?
A)
\[108{}^\circ \]
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B)
\[150{}^\circ \]
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C)
\[120{}^\circ \]
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D)
\[156{}^\circ \]
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E)
None of thee
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Find the area of the polygon given below if AP = 10 cm, BP = 20 cm, CP = 50 cm, DP = 60 cm and PS = 90 cm.
A)
\[4080\,c{{m}^{2}}\]
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B)
\[5050\,c{{m}^{2}}\]
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C)
\[6060\,c{{m}^{2}}\]
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D)
\[7070\,c{{m}^{2}}\]
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E)
None of these
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The area of the trapezium is 210\[c{{m}^{2}}\]and its height is 14 cm. If one of the parallel sides is longer than the other by 6 cm, find the two parallel sides.
A)
(12, 20) cm
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B)
(16, 18) cm
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C)
(12, 18) cm
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D)
(10, 15) cm
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E)
None of these
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Find the value of y from the figure given below.
A)
\[{{140}^{o}}\]
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B)
\[{{120}^{o}}\]
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C)
\[{{110}^{o}}\]
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D)
\[{{100}^{o}}\]
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E)
None of these
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In a quadrilateral ABCD shown in given figure, \[AB||DC\]and\[AD\bot AB\]. Also AB = 10 cm, DC = BC = 6 cm. Find the area of the quadrilateral.
A)
\[26\,c{{m}^{2}}\]
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B)
\[24\,c{{m}^{2}}\]
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C)
\[34\,c{{m}^{2}}\]
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D)
\[20\,c{{m}^{2}}\]
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E)
None of these
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