There are infinite number of rational numbers between any two rational number. Which one of the following rational number lies between \[\frac{2}{3}\] and\[\frac{4}{5}\]?
A)
\[\frac{11}{55}\]
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B)
\[\frac{29}{30}\]
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C)
\[\frac{41}{30}\]
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D)
\[\frac{2}{3}\]
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E)
None of these
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The value of the given expression\[\left[ \frac{156}{24}+\left\{ \frac{-24}{56}+\frac{26}{112} \right\}\times \frac{112}{44} \right]\] is given by:
A)
\[\frac{1}{6}\]
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B)
\[\frac{2}{5}\]
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C)
\[\frac{36}{6}\]
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D)
\[216\]
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E)
None of these
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Which one of the following rational numbers has no reciprocal?
A)
\[\frac{4}{7}\]
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B)
\[\frac{9}{3}\]
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C)
\[0\]
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D)
\[\frac{5}{9}\]
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E)
None of these
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Which one of the following is a natural number has no reciprocal?
A)
\[\frac{14}{56}\]
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B)
\[\frac{19}{57}\]
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C)
\[\frac{91}{13}\]
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D)
\[\frac{45}{135}\]
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E)
None of these
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Find the value of \[x\] such that \[{{\left( \frac{64}{125} \right)}^{2}}{{\left( \frac{4}{5} \right)}^{4}}{{\left( \frac{16}{25} \right)}^{2x+1}}={{\left( \frac{256}{625} \right)}^{3x}}\]
A)
\[\frac{3}{2}\]
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B)
\[\frac{2}{5}\]
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C)
\[\frac{1}{3}\]
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D)
\[\frac{1}{2}\]
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E)
None of these
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Find the value of m such that \[\frac{{{(16)}^{2m}}\,{{(64)}^{4}}}{{{(256)}^{2}}}={{(256)}^{3m}}\]
A)
1
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B)
0.5
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C)
4
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D)
5
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E)
None of these
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Find the product of \[5{{m}^{2}}n,\]\[-\,3mnp\] and \[-\,5{{n}^{2}}p\].
A)
\[75\,{{m}^{3}}{{n}^{3}}{{p}^{2}}\]
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B)
\[75\,{{m}^{3}}{{n}^{4}}{{p}^{2}}\]
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C)
\[75\,m{{n}^{3}}{{p}^{3}}\]
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D)
\[75\,{{m}^{3}}n{{p}^{2}}\]
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E)
None of these
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Evaluate \[{{\left[ {{\left( \sqrt{\frac{2}{3}} \right)}^{2}}-\sqrt[3]{\frac{8}{27}} \right]}^{1000}}\]
A)
\[0\]
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B)
\[1\]
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C)
\[2\]
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D)
\[-1\]
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E)
None of these
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What is the value of\[\sqrt{3018+\,\,\sqrt{36+\sqrt{169}}}\] ?
A)
65
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B)
25
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C)
35
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D)
55
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E)
None of these
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Find the value of \[y\]such that \[\sqrt{1+\sqrt{1-\frac{2176}{2401}}}=1+\frac{y}{7}\]
A)
\[(1,-15)\]
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B)
\[(-1,-15)\]
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C)
\[(1,15)\]
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D)
\[(-1,15)\]
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E)
None of these
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What is the least number that should be added to the smallest 6 digit number to make it a perfect square?
A)
389
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B)
489
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C)
289
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D)
139
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E)
None of these
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Find the unit digit in the cube of the number 3331.
A)
1
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B)
8
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C)
4
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D)
9
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E)
None of these
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Find the value of \[{{\left[ {{\left( {{5}^{2}}+{{12}^{2}} \right)}^{\frac{1}{2}}} \right]}^{3}}\]
A)
2197
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B)
169
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C)
1693
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D)
289
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E)
None of these
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Find the least number by which 3087 must be multiplied to make it a perfect cube.
A)
3
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B)
4
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C)
9
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D)
7
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E)
None of these
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Find the sum of the given algebraic expression. \[2{{p}^{2}}{{q}^{2}}-3pq+4,\]\[5+7{{p}^{2}}{{q}^{2}}-8pq,\]\[5{{p}^{2}}{{q}^{2}}-8+9pq\]
A)
\[1{{p}^{2}}{{q}^{2}}-5pq+5\]
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B)
\[14{{p}^{2}}{{q}^{2}}-2pq+1\]
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C)
\[11{{p}^{2}}{{q}^{2}}+5pq+10\]
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D)
\[14{{p}^{2}}{{q}^{2}}+19pq+17\]
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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_________.
A)
\[12x{{y}^{2}}+9{{x}^{2}}{{y}^{2}}-12{{x}^{4}}y+15{{x}^{3}}{{y}^{3}}\]
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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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Find the quotient of polynomial if\[{{y}^{3}}-{{y}^{2}}+9y-2\] is divided by\[y-2\].
A)
\[{{y}^{2}}+y+11\]
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B)
\[{{y}^{2}}-y+11\]
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C)
\[{{Y}^{2}}\,+\,Y\,-\,11\]
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D)
\[{{y}^{2}}-y-11\]
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E)
None of these
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Simplify the given expression: \[\frac{0.86\times 0.86\times 0.86+0.14\times 0.14\times 0.14}{0.86\times 0.86-0.86\times 0.14+0.14\times 0.14}\]
A)
\[1\]
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B)
\[0\]
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C)
\[2\]
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D)
\[-1\]
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E)
None of these
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Find the solution of the given linear equation \[\frac{6m+7}{3m+2}=\frac{4m+5}{2m+3}\].
A)
\[-\frac{11}{9}\]
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B)
\[\frac{11}{9}\]
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C)
\[\frac{9}{11}\]
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D)
\[-\frac{9}{11}\]
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E)
None of these
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Solve the equation \[\frac{0.5\,\,(z-0.4)}{3.5}-\frac{0.6\,\,(z-2.7)}{4.2}=z+6.1\]
A)
\[\frac{202}{35}\]
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B)
\[\frac{197}{70}\]
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C)
\[\frac{70}{197}\]
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D)
\[\frac{-70}{197}\]
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E)
None of these
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A store has provision which would last for a certain number of men for 21 days. For one seventh of the men it will last for how many days?
A)
147
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B)
158
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C)
129
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D)
174
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E)
None of these
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If 4 women or 3 men earn Rs. 480 in a day, then the earning of 11 women and 7 men in a day will be:
A)
Rs. 2440
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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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There are two neighbours, one has 6 oxen and other has 8 cows, and they have common field for the grazing of the cattle. They use the field for their cattle turn wise for feeding them. The 6 oxen or the 8 cows can graze the field in 25 days. In how much time will 1 ox and 2 cows graze the same field if left together?
A)
40 days
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B)
60 days
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C)
50 days
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D)
55 days
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E)
None of these
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Robert can finish the writing of the book in 8 days while James can finish the same work in 10 days. If they work together then how long they will take to finish the same work?
A)
\[10\,\,\frac{1}{2}\,\,days\]
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B)
\[6\,\,\frac{2}{3}\,\,days\]
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C)
\[\frac{4}{9}\,\,days\]
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D)
\[4\,\,\frac{4}{9}\,\,days\]
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E)
None of these
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Three friends Paul, Harish and Thomas take up the work of fencing the garden in their back yard and decide to help each other in their work to finish. Paul and Harish can finish the fencing work in 15 days, while Harish and Thomas can finish the work in 18 days and Thomas and Paul can finish in 20 days. If they decide to do the work separately, in how many, days will Harish finish the work?
A)
\[27\,\,\frac{9}{13}\,\,day\]
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B)
\[32\,\,\frac{8}{11}\,\,day\]
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C)
\[25\,day\]
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D)
\[40\,\,\frac{1}{12}\,\,day\]
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E)
None of these
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The two numbers M and N are such that 80% of M is equal to the 40% of N, then N =? % of M.
A)
200
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B)
300
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C)
400
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D)
100
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E)
None of these
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The population of the city is 5500 and \[\frac{5}{11}th\] of the population is male and rest of them are female. If the 40% of the male are married, then the percentage of married female in the city is:
A)
\[33\,\,\frac{1}{3}%\]
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B)
\[42%\]
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C)
\[45.5%\]
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D)
\[25\,\,\frac{1}{2}%\]
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E)
None of these
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The four number are such that \[x\] is 15% of y, y is 10% of z, and z is 5% of w. If the value of\[x=450,\] then find the value of w.
A)
600
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B)
6,00,000
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C)
60,000
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D)
6000
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E)
None of these
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If the cost price of 10 greeting cards is equal to the selling price of 8 greeting cards, find the gain or loss percent.
A)
20%
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B)
25%
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C)
30%
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D)
40%
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E)
None of these
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Codi borrows Rs. 8000 for 60 days at 5% simple interest per year from his friend Lorentz for admission of his son in the school. Find the interest he has to pay to his friend after 60 days.
A)
Rs. 82.20
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B)
Rs. 55.5
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C)
Rs. 65.75
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D)
Rs. 92.00
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E)
None of thee
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If the simple interest on a certain sum of money is one - ninth of the principal and rate of interest is equal to the time for which interest is found. Find the rate of interest on that sum of money.
A)
\[10%\]
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B)
\[\frac{10}{3}%\]
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C)
\[5.5%\]
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D)
\[7.25%\]
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E)
None of these
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Find the value of y form the figure given below.
A)
\[140{}^\circ \]
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B)
\[120{}^\circ \]
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C)
\[110{}^\circ \]
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D)
\[100{}^\circ \]
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E)
None of these
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The ratio between the length and breadth of a rectangular field is\[5:3\].The area of the field is \[960\,\,{{m}^{2}}\]. Find the difference between the length and width of the field.
A)
16 m
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B)
12 m
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C)
10 m
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D)
18 m
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E)
None of these
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A 'T' shape is made by sticking together 2 cuboids as shown in the diagram. What is the total volume of the letter 'T'?
A)
\[57\,c{{m}^{3}}\]
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B)
\[64\,c{{m}^{3}}\]
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C)
\[48\,c{{m}^{3}}\]
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D)
\[25\,c{{m}^{3}}\]
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E)
None of these
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Find the volume of the figure given below:
A)
\[267\,c{{m}^{3}}\]
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B)
\[284\,c{{m}^{3}}\]
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C)
\[228\,c{{m}^{3}}\]
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D)
\[240\,c{{m}^{3}}\]
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E)
None of these
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Which two activities are favored equally by the students?
A)
Visiting friends and computer
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B)
Playing Sports and earn money
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C)
Talking on the phone and play sports
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D)
Computer and visiting friends
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E)
None of these
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On which day of the week sale was maximum?
A)
Monday
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B)
Tuesday
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C)
Thursday
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D)
Friday
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E)
None of these
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Robert tosses a coin three times. The probability that he gets at least two head is:
A)
\[\frac{1}{2}\]
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B)
\[\frac{1}{3}\]
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C)
\[\frac{1}{4}\]
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D)
\[\frac{1}{5}\]
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E)
None of these
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A pair of dice is rolled. Find the sample space for getting the sum as eight.
A)
\[\frac{1}{2}\]
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B)
\[\frac{1}{36}\]
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C)
\[\frac{5}{36}\]
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D)
\[\frac{5}{6}\]
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E)
None of these
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Which one of the following numbers cannot be a probability?
A)
\[-\,0.00001\]
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B)
\[0.5\]
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C)
\[0.001\]
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D)
\[0\]
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E)
None of these
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