Mary had to do typing work of some pages for her project. So she share the work with her three friends. She gave one-fourth to first, one- third to the second and one-fifth to her third friend and types the remaining by herself. If she typed 65 pages, then find the number of pages that was typed by her first friend.
A)
66
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B)
52
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C)
75
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D)
55
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E)
None of these
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Evaluate: \[{{\left( \frac{-1728}{2744} \right)}^{\frac{2}{3}}}\,\,{{\left( \frac{4096}{9216} \right)}^{\frac{1}{2}}}\,\,-\,\,{{\left( \frac{729}{343} \right)}^{\frac{2}{3}}}\]
A)
0
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B)
\[\frac{4208}{2152}\]
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C)
\[-\frac{57}{49}\]
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D)
\[\frac{2152}{4208}\]
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E)
None of these
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3600 when expressed in its simplest form will be equal to:
A)
\[{{2}^{4}}\times {{3}^{3}}\times {{5}^{2}}\]
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B)
\[{{2}^{3}}\times {{3}^{3}}\times {{5}^{3}}\]
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C)
\[{{2}^{4}}\times {{3}^{2}}\times {{5}^{2}}\]
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D)
\[{{2}^{4}}\times {{3}^{4}}\times {{5}^{4}}\]
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E)
None of these
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Express \[8\div 2000000\] in standard form.
A)
\[25\times {{10}^{4}}\]
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B)
\[4\times 10{{\,}^{6}}\]
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C)
\[4\times {{10}^{-\,\,6}}\]
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D)
\[16\times {{10}^{-\,6}}\]
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E)
None of these
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If \[a=\frac{\sqrt{2+1}}{2-1}\] and \[b=\frac{\sqrt{2-1}}{2+1}\]then \[\frac{{{a}^{2}}+ab+{{b}^{2}}}{{{a}^{2}}-ab+{{b}^{2}}}\] is equal to:
A)
\[32-4\sqrt{2}\]
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B)
\[32+4\sqrt{2}\]
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C)
\[\frac{35}{33}\]
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D)
\[\frac{33}{35}\]
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E)
None of these
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The value of \[\sqrt{7+2\sqrt{10}}\]is equal to:
A)
\[1+\sqrt{6}\]
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B)
\[2+\sqrt{5}\]
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C)
\[\sqrt{2}+\sqrt{5}\]
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D)
\[\sqrt{3}+\sqrt{4}\]
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E)
None of these
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Find the least number by which 1568 must be multiplied to make it a perfect cube.
A)
13
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B)
14
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C)
19
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D)
17
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E)
None of these
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Three numbers are in the ratio\[1:2:3\], if the sum of their cubes is 98784, then the numbers are the successive multiples of:
A)
12
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B)
16
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C)
14
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D)
24
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E)
None of these
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Simplify:\[{{x}^{3}}-2{{x}^{2}}-x+2\]
A)
\[(x+1)\,\,{{(x-1)}^{2}}\]
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B)
\[(x-2)\,\,{{(x+1)}^{2}}\]
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C)
\[(x-2)\,\,(x-1)\,\,(x+1)\]
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D)
\[(x+2)\,\,(x-1)\,\,(x+1)\]
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E)
None of these
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The value of\[{{a}^{3}}-3\sqrt{3}\,{{b}^{3}}\]:
A)
\[(a+b\sqrt{3})\,\,({{a}^{2}}-ab\sqrt{3}+3{{b}^{2}})\]
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B)
\[(a-b\sqrt{3})\,\,({{a}^{2}}+ab\sqrt{3}+3{{b}^{2}})\]
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C)
\[(a-b\sqrt{3})\,\,({{a}^{2}}-ab\sqrt{3}+3{{b}^{2}})\]
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D)
\[(a-b\sqrt{3})\,\,({{a}^{2}}+3ab+3{{b}^{2}})\]
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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)
\[\frac{48\,y-64}{3}\]
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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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Find the remainder when\[5\,{{m}^{3}}-13\,{{m}^{2}}+15\,m+7\] is divided by\[4-3\,m+{{m}^{2}}\].
A)
\[m-1\]
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B)
\[m+1\]
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C)
\[2\,m+1\]
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D)
\[2\,m-1\]
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E)
None of these
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The angles of a triangle are in the ratio of \[5:6:7\]What is the sum of the smallest and largest angles together?
A)
\[150{}^\circ \]
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B)
\[120{}^\circ \]
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C)
\[110{}^\circ \]
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D)
\[140{}^\circ \]
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E)
None of these
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If \[A=\frac{1}{4}B\] and \[B=\frac{1}{2}C,\] then find the value of \[A:B:C\].
A)
\[8:4:1\]
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B)
\[4:2:1\]
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C)
\[1:4:8\]
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D)
\[1:2:4\]
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E)
None of these
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A bag contains Rs. 1, 50 p and 25 p coins in the ratio of \[8:9:11\]. If the total money in the bag is Rs. 366, find the number of 25 p coins.
A)
264
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B)
364
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C)
241
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D)
245
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E)
None of these
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One angle of a right angled triangle is\[35{}^\circ \]. Which of the following is one of its angles?
A)
\[45{}^\circ \]
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B)
\[60{}^\circ \]
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C)
\[55{}^\circ \]
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D)
Couldn't be determined
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E)
None of these
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The base of a parallelogram is twice its height. If the area of a parallelogram is 722 sq. cm, find its height.
A)
21 cm
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B)
18 cm
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C)
19 cm
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D)
17 cm
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E)
None of these
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A trader buys some goods for Rs. 150. If the overhead expenses be 12 % of the cost price, at what price should it be sold to earn 10 %?
A)
Rs. 184.80
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B)
Rs. 185.80
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C)
Rs. 187.8
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D)
Rs. 188.80
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E)
None of these
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30 % of a three-digit number is 190.8. What will be 125 % of that number?
A)
759
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B)
785
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C)
795
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D)
779
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E)
None of these
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The total number of employees in a bank is 5350 out of which 28 % are females. What is the respective ratio between the numbers of female employees to the number of male employees?
A)
\[7:8\]
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B)
\[5:18\]
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C)
\[7:16\]
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D)
\[7:17\]
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E)
None of these
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Evaluate \[\sqrt{16}+\sqrt{\frac{9.5\times 0.0085\times 18.9}{0.021\times 0.0017\times 1.9}}\]
A)
154
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B)
158
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C)
160
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D)
169
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E)
None of these
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If \[\sqrt{3}=1.732\], find the value of \[4\left( \sqrt{192}-\frac{1}{2}\sqrt{48}-\sqrt{75} \right)\] correct to 3 places of decimal.
A)
6.928
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B)
5.928
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C)
2.732
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D)
3.732
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E)
None of these
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Find the value of x in the figure given below.
A)
\[35{}^\circ \]
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B)
\[50{}^\circ \]
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C)
\[55{}^\circ \]
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D)
\[60{}^\circ \]
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E)
None of these
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If \[\frac{7.2}{\sqrt[3]{0.729}}=\frac{{{(x)}^{3}}}{{{(2)}^{3}}},\]find the value of\[x\].
A)
4
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B)
5
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C)
6
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D)
8
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E)
None of these
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If \[{{a}^{2}}+{{b}^{2}}=234\] and \[ab=108\], find the value of\[\frac{a+b}{a-b}\].
A)
10
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B)
8
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C)
5
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D)
4
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E)
None of these
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\[\frac{0.5\times 0.5\times 0.5-0.2\times 0.2\times 0.2+\,\,0.3\times 0.3\times 0.3+3\times 0.5\times 0.3\times 0.2}{0.5\times 0.5\times 0.2\times 0.2+0.3\times 0.3+\,0.5\times 0.2+0.2\times 0.3-0.5\times 0.3}=?\]
A)
1
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B)
0.6
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C)
0.4
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D)
0.03
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E)
None of these
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If \[a+\frac{1}{b}=1\]and \[b+\frac{1}{c}=1,\] then find the value of\[c+\frac{1}{a}\].
A)
4
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B)
24
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C)
3
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D)
1
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E)
None of these
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One - third of Rahul's marks in Mathematics exceeds one - half of his marks in Hindi by 30. If he got 480 marks in the two subjects together, how many marks did he get in Hindi?
A)
200
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B)
294
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C)
186
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D)
196
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E)
None of these
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If\[2x+3y=29\] and\[y=x+3,\]what is the value of\[x\]?
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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Deepak has some hens and some goats. If the total number of animal heads is 90 and the total number of animal feet is 248, what is the total number of goats Deepak has?
A)
32
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B)
36
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C)
34
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D)
Couldn't determined
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E)
None of these
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The sum of two numbers is 80. If three times of one number is equal to five times of the other number, find the numbers.
A)
20, 60
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B)
50, 30
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C)
10, 70
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D)
25, 55
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E)
None of these
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In an examination, a student scores 4 marks for every correct answer and losses 1 mark for every wrong answer. A student attempted all the 200 questions and scored 200 marks. Find the number of questions, he answered correctly.
A)
82
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B)
80
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C)
68
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D)
60
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E)
None of these
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12 men can do a piece of work in 24 days. How many days are needed to complete the work if 8 men do this work?
A)
28
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B)
36
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C)
48
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D)
52
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E)
None of these
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A and B can do a piece of work in 72 days. B and C can do it in 120 days. A and C can do it in 90 days. In what time can A alone do it?
A)
80 days
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B)
100 days
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C)
120 days
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D)
150 days
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E)
None of these
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If a man wants to sell his chair for Rs. 720 he gets 25 % loss. To gain 25 % , he should sell it for
A)
Rs. 1200
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B)
Rs. 1000
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C)
Rs. 960
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D)
Rs. 900
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E)
None of these
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The compound interest on a sum of Rs. 4000 becomes Rs. 630.50 in 9 months. Find the rate of interest, if interest is compounded quarterly.
A)
20%
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B)
23%
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C)
19%
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D)
21%
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E)
None of these
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At what percent annual compound interest rate, a certain sum amounts to its 27 times in 3 yr?
A)
100%
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B)
150%
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C)
75%
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D)
200%
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E)
None of these
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The area of a rectangle is 1.8 times the area of a square. The length of the rectangle is 5 times the breadth. The side of the square is 20 cm. What is the perimeter of the rectangle?
A)
145 cm
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B)
144 cm
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C)
133 cm
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D)
135 cm
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E)
None of these
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Find the area of a rhombus one side of which measures 20 cm and one diagonal is 24 cm.
A)
98 sq cm
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B)
384 sq cm
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C)
250 sq cm
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D)
584 sq cm
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E)
None of these
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A river 3 m deep and 40 m wide is flowing at the rate of 2 km/h. How much water will fall into the sea in a minute?
A)
\[4000\,{{m}^{3}}\]
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B)
\[3000\,{{m}^{3}}\]
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C)
\[2500\,{{m}^{3}}\]
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D)
\[5000\,{{m}^{3}}\]
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E)
None of these
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