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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Factorise:\[8{{y}^{2}}+36y+36\]
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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\[45\,\,xyz\,\,(xy+yz+xz+{{z}^{2}})(z+x)\]\[\div \,105\,\,xy\,\,(xy+xz+yz+{{z}^{2}})\] 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 \[x-y=3\] 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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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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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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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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The cost of fencing a square field at 60 paise per metre is Rs. 1200. Find the cost of reaping the field at the rate of 50 paise per 100 sq m.
A)
Rs. 1250
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B)
Rs. 1450
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C)
Rs. 1350
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D)
Rs. 1950
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E)
None of these
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The diagonal of a rhombus are 6 cm & 8 cm. Find the length of a side of the rhombus.
A)
4
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B)
5
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C)
6
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D)
7
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E)
None of these
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Two adjacent angles of parallelogram are as 2 : 3. Find the ratio of other two angles.
A)
2 : 3
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B)
1 : 2
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C)
3 : 4
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D)
4 : 5
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E)
None of these
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If \[a+b+c=15\] & \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}=83,\] find the value of \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}\,-\,\,3abc\].
A)
120
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B)
140
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C)
160
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D)
180
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E)
None of these
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A steamer goes downstream & covers the distance in 4 hours, while it covers the same distance in 5 hours when going upstream. If the speed of stream is 2 km/hr, then find the speed of the steamer in still water.
A)
12 km/hr
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B)
14 km/hr
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C)
16 km/hr
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D)
18 km/hr
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E)
None of these
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To satisfy \[\frac{6\,{{x}^{2}}+13x-4}{2x+5}=\frac{12\,{{x}^{2}}+5x-2}{4x+3},\]\[x\] must 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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Find the smallest number by which 1152 is divided so that it becomes a perfect square.
A)
1
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B)
2
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C)
3
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D)
4
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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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How long will John take to make a round of a circular field of radius 21 m cycling at the speed of 8km/hr?
A)
34 sec
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B)
45 sec
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C)
59.4 sec
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D)
31 sec
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E)
None of these
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If the selling price of 18 oranges is equal to the cost of 16 oranges, find the loss or gain percent.
A)
110
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B)
(100/9) %
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C)
99%
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D)
29%
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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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Solve \[{{(2x+3)}^{2}}+{{(2x-3)}^{2}}=(8x+6)\,\,(x-1)+22\]
A)
\[-\,1\]
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B)
\[-\,2\]
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C)
\[-\,3\]
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D)
\[-\,4\]
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E)
None of these
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The side of an inscribed triangle have arcs measuring \[(2x-24){}^\circ ,\] \[(2x+12){}^\circ \] & \[(3x-36){}^\circ \]. What kind of triangle it is?
A)
Isosceles
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B)
Scalene
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C)
Right
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D)
All of these
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E)
None of these
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The area of four walls of a hall is \[320\,\,{{m}^{2}}\]. The length & breadth of the hall is \[12.5\,\,m\] & \[7.5\,\,m\]respectively. Find the height of the hall.
A)
8 m
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B)
9 m
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C)
3 m
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D)
5 m
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E)
None of these
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The ratio of the radii of two circles is 3 : 2. What is the ratio of their circumference?
A)
4 : 5
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B)
5 : 7
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C)
3 : 2
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D)
All
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E)
None of these
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In what time will Rs. 64000 amount to Rs. 68921 at 5% per annum, interest being compounded half - yearly?
A)
1 year
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B)
1.5 years
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C)
24 months
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D)
15 months
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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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A person sells an article for Rs. 770, gaining \[\frac{1}{10}\] of its C.P. Find gain percent.
A)
25%
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B)
10%
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C)
15%
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D)
5%
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E)
None of these
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The population of city increase at the rate of 15% per annum. If its population was 4000 at the end of year 2009. What will be its population at the end of year 2011?
A)
6250
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B)
5290
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C)
5550
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D)
4290
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E)
None of these
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If \[{{3}^{\left( x-y \right)}}=27\] and \[{{3}^{\left( x+y \right)}}=243,\]then 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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lf \[x+\frac{1}{x}=6,\]then the value of \[{{x}^{4}}+\frac{1}{{{x}^{4}}}=\]
A)
526
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B)
1154
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C)
1528
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D)
529
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E)
None of these
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