\[\frac{3}{4}\,\,\times \,\,\left( \frac{-8}{3}\,\,+\,\,\frac{-13}{12} \right)\,\,=\,\,\frac{3}{4}\,\,\times \,\,\frac{-8}{3}\,\,+\,\,\frac{3}{4}\,\,\times \,\,\frac{-13}{12}\] is illustrated by which of the following property?
A)
Commutativity
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B)
Associativity of multiplication
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C)
Distributivity of multiplication over addition
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D)
Existence of identity
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E)
None of these
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\[\frac{2}{5}\] people in a joint family are students, \[\frac{1}{4}\] people are house wives and rest are working. If there are 20 members in the family, then the number of working persons in the family are:
A)
3
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B)
7
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C)
9
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D)
11
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E)
None of these
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Simplify: \[1\div \left\{ {{\left( \frac{2}{3} \right)}^{6}}\times {{\left( \frac{1}{3} \right)}^{-\,4}}\times {{3}^{-\,1}}\times {{6}^{-\,1}} \right\}\]\[+\,\,\left[ {{\left( \frac{1}{3} \right)}^{-\,3}}-\,\,{{\left( \frac{1}{2} \right)}^{-\,3}} \right]\div \,\,{{\left( \frac{1}{4} \right)}^{-\,3}}\]
A)
\[\frac{181}{64}\]
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B)
\[\frac{151}{64}\]
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C)
\[\frac{172}{21}\]
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D)
\[\frac{147}{32}\]
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E)
None of these
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Find the value of \[x\]such that \[{{\left( \frac{5}{3} \right)}^{-\,5}}\times \,\,{{\left( \frac{5}{3} \right)}^{-\,11}}={{\left( \frac{5}{3} \right)}^{8x}}\]
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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If \[x={{\left( \frac{4}{3} \right)}^{2}}\times {{\left( \frac{3}{4} \right)}^{-\,4}},\] then the value of \[{{x}^{-\,\,3}}\]is equal to:
A)
\[{{\left( \frac{3}{4} \right)}^{12}}\]
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B)
\[{{\left( \frac{3}{4} \right)}^{-12}}\]
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C)
\[{{\left( \frac{3}{4} \right)}^{18}}\]
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D)
\[{{\left( \frac{3}{4} \right)}^{-18}}\]
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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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Find the value of \[x\] in\[\frac{x}{\sqrt{128}}=\frac{\sqrt{162}}{x}\]
A)
12
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B)
14
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C)
16
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D)
18
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E)
None of these
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On selling 120 things, it results a profit equal to the selling price of 30 things. What is the profit percentage?
A)
\[11\,\,\frac{1}{9}%\]%
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B)
\[25\]%
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C)
\[20\]%
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D)
\[33\,\,\frac{1}{3}\]%
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E)
None of these
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Three numbers are in the ratio 2 : 3 : 4 , and sum of their cubes is 33957. Find the sum of these numbers.
A)
14
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B)
63
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C)
21
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D)
28
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E)
None of these
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The product of : \[(2{{x}^{2}}-5{{x}^{-2}}-x+7)\] and\[(3-2x+{{x}^{2}})\]is
A)
\[-3{{x}^{4}}+5{{x}^{3}}-17x+21\]
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B)
\[{{x}^{5}}+24{{x}^{4}}+5{{x}^{2}}+x+21\]
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C)
\[8{{x}^{5}}+{{x}^{4}}-12+7x+1\]
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D)
\[3{{x}^{5}}-4{{x}^{4}}+1{{x}^{3}}-5{{x}^{2}}-7x+2\]
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E)
None of these
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If \[x+\frac{1}{x}=3,\]then find the value of\[x-\frac{1}{x}\] .
A)
\[\pm \,\,1\]
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B)
\[\pm \,\sqrt{2}\]
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C)
\[\pm \,\sqrt{5}\]
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D)
0
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E)
None of these
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Factorise the expression:
A)
\[(un+vm)\,\,(um-vn)\]
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B)
\[(un+vm)\,\,(um+vn)\]
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C)
\[(un-vm)\,\,(um-vn)\]
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D)
\[(un-vm)\,\,(um+vn)\]
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E)
None of these
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\[{{x}^{4}}+{{x}^{2}}-20,\] when divided by \[(x-2)\] leaves a remainder of:
A)
0
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B)
1
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C)
2
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D)
\[x+2\]
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E)
None of these
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The ratio of ages of a father and his son at present is \[6:1\]. After 5 years the ratio will be\[7:2\]. The present age of the father is:
A)
25 years
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B)
28 years
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C)
30 years
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D)
35 years
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E)
None of these
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Find the value of \['x'\] if \[\frac{6}{{{x}^{2}}-9x+20}\,\,=\,\,\frac{2}{x-4}\,\,-\,\,\frac{4}{x-5}\]
A)
1
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B)
0
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C)
5
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D)
9
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E)
None of these
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There is a work of levelling the ground. 10 labours can level the ground in 15 days. After 5 days, 5 labours left the work. In how many days, remaining labours can finish the rest of the work?
A)
10 days
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B)
20 days
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C)
15 days
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D)
25 days
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E)
None of these
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A private taxi charges a fare of Rs. 260 for 200 km. How much will it travel for Rs. 279.50?
A)
200 km
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B)
220 km
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C)
215 km
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D)
210 km
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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, 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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If 34 men can complete a work in 8 days working 9 hours a day, then find the number of men required to finish the work in 2 days, if they work 9 hours in a day.
A)
100 men
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B)
200 men
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C)
300 men
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D)
136 men
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E)
None of these
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When 5 lemons are purchased at the rate of Rs. 4 and sold them at the rate of 4 for Rs. 5, what is the profit per cent?
A)
\[22\]%
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B)
\[56\,\,\frac{1}{4}\]%
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C)
\[56\]%
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D)
\[55\,\,\frac{1}{4}\]%
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E)
None of these
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Two numbers are such that 60% of one is equal to 40% of the other and sum of the numbers is 320. Find the larger number.
A)
192
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B)
156
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C)
128
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D)
184
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E)
None of these
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If the sum of a number and its cube is 520, then the number will be:
A)
6
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B)
8
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C)
12
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D)
16
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E)
None of these
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Rishi requires 40% to pass. He gets 185 marks and fails by 15 marks, what has been the maximum marks that he could get?
A)
450
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B)
550
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C)
500
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D)
510
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E)
None of these
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A train moving with the speed of 54 km/hr reaches its destination in 14 hr. If the speed of a train is 70 km/hr, then how much time would it take to cover the same distance (in hr)?
A)
11
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B)
9.8
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C)
11.8
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D)
10.8
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E)
None of these
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On selling an article for Rs. 250, it earns a profit of 25%. For what amount it should be sold to have a loss of 20%?
A)
Rs. 190
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B)
Rs. 160
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C)
Rs. 200
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D)
Rs. 180
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E)
None of these
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What is the time period for which amount Rs. 8000 will be Rs. 12000 at 20% per annum of simple interest?
A)
4 years
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B)
2.5 years
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C)
3.25 years
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D)
6 years
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E)
None of these
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A sum of money which doubles itself in 8 years at simple interest will triple itself at the same rate in:
A)
12 years
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B)
16 years
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C)
14 years
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D)
4 years
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E)
None of these
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Two cylinders of same volume have their radii in the ratio\[\sqrt{3}:1\]. What will be the ratio of their height?
A)
\[2:3\]
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B)
\[1:3\]
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C)
\[3:4\]
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D)
\[1:2\]
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E)
None of these
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The sum of two natural numbers is 64. Which of the following cannot be the ratio of these two numbers?
A)
\[3:5\]
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B)
\[1:3\]
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C)
\[7:9\]
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D)
\[3:4\]
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E)
None of these
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The reflex angle between the hands of a clock at 10.25 is.
A)
\[180{}^\circ \]
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B)
\[192\,\,\frac{1{}^\circ }{2}\]
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C)
\[195{}^\circ \]
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D)
\[197\,\,\frac{1{}^\circ }{2}\]
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E)
None of these
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Direction: The following pie graph shows the number of certain players of a particular country playing different games. Study the pie graph carefully and answer the following questions:
Which sports is played most?
A)
Cricket
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B)
Football
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C)
Tennis
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D)
Hockey
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E)
None of these
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Direction: The following pie graph shows the number of certain players of a particular country playing different games. Study the pie graph carefully and answer the following questions:
The ratio between the number of person playing Golf to that of the persons playing Hockey is:
A)
\[1:2\]
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B)
\[1:3\]
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C)
\[3:4\]
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D)
\[2:3\]
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E)
None of these
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Direction: The following pie graph shows the number of certain players of a particular country playing different games. Study the pie graph carefully and answer the following questions:
If the total number of persons is 90000, then the difference between the number of persons playing only Tennis and Hockey is:
A)
11250
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B)
8250
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C)
7500
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D)
6750
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E)
None of these
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The length of a rectangle is 1 cm more than its breadth. The diagonal is 29 cm. Find the area of the rectangle.
A)
\[481\,c{{m}^{2}}\]
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B)
\[841\,c{{m}^{2}}\]
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C)
\[420\,c{{m}^{2}}\]
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D)
\[870\,c{{m}^{2}}\]
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E)
None of these
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A room is 16 m long 7 m broad and 8 m high. Find the cost of white washing the four walls of room at Rs.\[7.5\,\,per\,{{m}^{2}}\]. White washing is not to toe done on the doors and windows, which occupy.
A)
Rs. 2272.5
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B)
Rs. 2278.5
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C)
Rs. 2575
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D)
Rs. 3575.8
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E)
None of these
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A sum of money in 3 years becomes Rs. 1344 and in 7 years it becomes Rs. 1536. What is the principal sum where simple rate of interest is to be charged?
A)
Rs. 4000
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B)
Rs. 1500
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C)
Rs. 1200
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D)
Rs. 2800
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E)
None of these
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Introducing Lily, Raghav said, "Her father is my mother's only son". How is Lily related to Raghav?
A)
Aunt
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B)
Daughter
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C)
Mother
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D)
Sister
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E)
None of these
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A cyclist goes 30 km to North, then 40 km to East. Now he takes a right turn and goes 20 km. Then again he turns his right and goes 40 km. How far is the cyclist from his starting point?
A)
40 km
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B)
50 km
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C)
25 km
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D)
10 km
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E)
None of these
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In a certain code MATTER is written as TAMRET and FOREST is written as ROFTSE. What will be the code for DOCTOR?
A)
DOCROT
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B)
ROTCOD
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C)
CODROT
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D)
CODTOR
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E)
None of these
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Insert the missing number:
A)
2
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B)
5
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C)
20
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D)
25
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E)
None of these
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