Choose the greatest number among the following: \[{{\left[ {{(5+5)}^{2}} \right]}^{2}},\]\[{{\left[ 5\times 5\times 5 \right]}^{2}},\]\[{{\left[ 5+5+5 \right]}^{3}},\]\[\left[ {{5}^{5}}+{{5}^{5}} \right],\]\[\left[ {{5}^{5}}+{{5}^{5}}+{{5}^{5}}+{{5}^{5}} \right]\]
A)
\[{{\left[ {{(5+5)}^{2}} \right]}^{2}}\]
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B)
\[{{\left[ 5\times 5\times 5 \right]}^{2}}\]
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C)
\[{{\left[ 5+5+5 \right]}^{3}}\]
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D)
\[[{{5}^{5}}+{{5}^{5}}]\]
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E)
None of these
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Find the sum of \[{{5}^{3}}+{{6}^{3}}+{{7}^{3}}+----------\,\,+\,\,{{12}^{3}}\]
A)
5984
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B)
5944
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C)
5994
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D)
5934
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E)
None of these
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What must be added to the following algebraic expression to make it a perfect square? \[\frac{5{{x}^{2}}}{64}-\frac{3\sqrt{40}\,x}{20}+\frac{22}{25}\]
A)
\[\frac{28}{25}\]
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B)
\[1\]
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C)
\[2\]
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D)
\[\frac{51}{25}\]
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E)
None of these
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Which one among the following statements is correct?
A)
An equation is not true for all the values of the variables used in it.
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B)
An identity is true for only some certain values of the variable.
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C)
Polynomial is an algebraic expression containing one or more terms with non- zero coefficients and the variables used in it have integer exponents.
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D)
All the above
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E)
None of these
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The excise duty on a certain item has been reduced to Rs. 800 from Rs. 1024. Find the percentage reduction in the excise duty.
A)
\[28%\]
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B)
\[26%\]
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C)
\[21\,\,\frac{7}{8}%\]
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D)
\[24\,\,\frac{3}{8}%\]
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E)
None of these
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Vipin and Shubham run a race. Vipin gives Shubham a start of 20 metres and is beaten by almost 20 metres. Who has higher speed between the two?
A)
Vipin
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B)
Shubham
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C)
Both have equal speed
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D)
Cannot be determined
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E)
Either (a) or (b)
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In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in Physics. Then, the number of students who have passed in Physics only is ________.
A)
22
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B)
33
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C)
10
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D)
45
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E)
None of these
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In a group of students, 8 students like reading a book and 5 students like watching a cartoon channel. If 3 of them like both reading a book and watching a cartoon channel, then how many students are there in the group?
A)
16
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B)
22
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C)
10
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D)
19
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E)
None of these
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A room is in the form of a cuboid of measures\[60\,m\times 40\,m\times 30\,m\]. How many cuboidal boxes can be stored in it if the volume of one box \[0.8\,\,{{m}^{3}}\]?
A)
75000
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B)
65000
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C)
60000
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D)
90000
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E)
None of these
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The wheels of a car are 80 cm in diameter. How many complete revolutions does each wheel will make in 8 minutes if car is travelling at a speed of 33 km/ h? \[\left[ Take\,\pi =\frac{22}{7} \right]\]
A)
1600
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B)
1800
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C)
1750
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D)
1850
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E)
None of these
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Direction : Study the following pie-chart carefully to answer the questions that follow: Degree wise break-up of expenditure of a family in a month.
If total amount spent in a month is Rs. 48600, then find the amount spent by the family on Entertainment.
A)
Rs. 4820
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B)
Rs. 6228
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C)
Rs. 5940
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D)
Rs. 5820
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E)
None of these
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Direction : Study the following pie-chart carefully to answer the questions that follow: Degree wise break-up of expenditure of a family in a month.
If the amount spent by the family on Groceries, Entertainment and Others together is Rs. 25920, then the amount spent on Investments is ______.
A)
Rs. 5184
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B)
Rs. 6280
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C)
Rs. 5340
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D)
Rs. 6224
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E)
None of these
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Direction : Study the following pie-chart carefully to answer the questions that follow: Degree wise break-up of expenditure of a family in a month.
If the difference of the amount spent by the family on the Medicine and the amount spent on others is Rs. 1500, then the amount spent on Medicine is __________.
A)
Rs. 8120
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B)
Rs. 9020
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C)
Rs. 9340
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D)
Rs. 9250
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E)
None of these
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Direction : Study the following pie-chart carefully to answer the questions that follow: Degree wise break-up of expenditure of a family in a month.
The difference of squares of two consecutive numbers is 61. What will be the sum of these numbers?
A)
81
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B)
41
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C)
61
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D)
51
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E)
None of these
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If the eight digit number 5671\[\alpha \]118 is exactly divisible by 222, then find the least possible value of\[\alpha \].
A)
0
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B)
2
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C)
3
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D)
4
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E)
5
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If \[K=\sqrt{49-12\sqrt{5}},\]then find the value of\[K+2\].
A)
\[2+3\sqrt{3}\]
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B)
\[3\sqrt{5}\]
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C)
\[5\sqrt{2}\]
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D)
\[2\sqrt{7}\]
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E)
\[2\sqrt{5}\]
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Which one among the following is a perfect square?
A)
343396
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B)
300302
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C)
407043
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D)
427718
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E)
4225000
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If \[\frac{1}{p}-\frac{1}{q}-\frac{1}{r}=\frac{1}{36}\] and \[pq-qr=pr,\]then find the value of \[r\].
A)
\[0\]
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B)
\[1\]
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C)
\[-72\]
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D)
\[-36\]
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E)
None of these
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The sum of the digits of a two digit number is 13. If 45 is subtracted from the number, the resultant number becomes the number obtained on reversing the digits of the original number. Find the number which is nine times the original number.
A)
765
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B)
846
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C)
684
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D)
603
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E)
None of these
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90 persons can dig a well in 40 days. After they have worked for 10 days, how many more persons should be employed so as to complete the work in another 20 days?
A)
125
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B)
35
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C)
45
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D)
135
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E)
None of these
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If p : q = 3 : 4, q : r = 6 : 5 and r: s = 7 : 2, then on dividing Rs. 12324 among p, q, r and s, find the amount of r.
A)
Rs. 3640
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B)
Rs. 4268
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C)
Rs. 3320
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D)
Rs. 4638
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E)
None of these
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A sum amounts to Rs. 32000 in 4 years and Rs. 38000 in 6 years at a certain rate of simple interest. Find the sum.
A)
Rs. 18000
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B)
Rs. 20000
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C)
Rs. 24000
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D)
Rs. 25000
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E)
None of these
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John borrowed a sum of Rs. 15625 from Donald at the rate of 16% per annum under simple interest. Immediately John gave this money to Bush at the same rate under compound interest, compounded quarterly. Find the profit of John in doing so after 9 months.
A)
Rs. 38
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B)
Rs. 76
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C)
Rs. 57
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D)
Rs. 95
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E)
None of these
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A batsman makes a score of 148 in his 29th innings and therefore his average increases by 4. His average after 29 innings is ________.
A)
32
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B)
34
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C)
36
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D)
38
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E)
None of these
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If \[U=\{1,\,\,3,\,\,5,\,\,7,\,\,9,\,\,a,\,\,b,\,\,c,\,\,d\}\] and \[A=\{1,\,\,3,\,\,5\}\]and\[B=\{a,\,\,b,\,\,c\}\] then\[(A\cup B)'\]=________.
A)
\[\{1,\,\,3,\,\,5,\,\,a,\,\,b,\,\,c\}\]
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B)
\[1,\,\,3,\,\,5\]
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C)
\[\{a,\,\,b,\,\,c\}\]
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D)
\[\{7,\,\,9,\,\,d\}\]
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E)
None of these
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Which among the following Venn diagram represents\[(P\cup Q)'\]?
A)
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B)
done
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C)
done
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D)
done
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E)
None of these
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In the figure given below, PQRS and QMNO are two identical squares with side length of 8 cm, and A is the mid- point of PS and MN, find the area of the hexagon QRSANOQ.
A)
\[80\,c{{m}^{2}}\]
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B)
\[96\,\,c{{m}^{2}}\]
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C)
\[112\,\,c{{m}^{2}}\]
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D)
\[112\,\,c{{m}^{2}}\]
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E)
None of these
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The shopkeeper marks the price of a shirt 50% more than the cost price and allows a discount of 40% on the mark price of the shirt. Find the gain or the loss percent the shopkeeper has made on whole transaction.
A)
10% loss
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B)
10% gain
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C)
20% loss
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D)
20% gain
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E)
None of these
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The rectangular hall of length 'I', width 'b' and height 'h' contains sufficient amount of air for the number of people in the hall. If the volume of air contained in the hall is \[260\,\,c{{m}^{3}}\]. Also /+b + h = 22 and if each side of the hall is 3 cm or more in length such that each length is in whole number, then the largest possible area of a face of the hall is __________.
A)
\[65\,c{{m}^{2}}\]
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B)
\[40\,\,c{{m}^{2}}\]
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C)
\[40\,\,c{{m}^{2}}\]
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D)
\[50\,\,c{{m}^{2}}\]
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E)
None of these
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On a payment order of Rs. 10000 John has choice between three successive discounts of 10%, 10% and 30% and three successive discount of 40%, 5% and 5%. By choosing the better one, John can save Rs._______.
A)
433
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B)
400
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C)
255
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D)
200
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E)
None of these
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DAZE is written as 41265 in a certain code. How will BOY be written in the same code?
A)
41425
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B)
5120
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C)
21525
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D)
359
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E)
None of these
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If 'mud' is called 'water', 'water' is called 'heat', 'heat' is called 'gas', 'gas' is called 'air', 'air' is called 'fire', where do fishes swim?
A)
water
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B)
air
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C)
heat
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D)
fire
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E)
None of these
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In a certain code FINGER is written as DGLECP, similarly what will be the code for KIDNEY?
A)
IGBLCW
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B)
IGCLBW
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C)
IBCGLE
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D)
IGBKCV
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E)
None of these
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Following figures are given in a certain pattern. You have to identify the figure which is not following the pattern.
A)
I
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B)
II
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C)
III
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D)
IV
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E)
None of these
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Aditya is Bhavi's brother, Bharat is Jayant's father. Ella is Bhavi's mother. Aditya and Jayant are brothers. What is Ella's relationship with Bharat?
A)
Sister
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B)
Mother
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C)
Daughter
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D)
Wife
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E)
None of these
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Find the missing number in place of the question mark (?) in the given table:
6 6 8 5 7 5 4 3 ? 120 126 320
A)
4
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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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Which one among the following correctly represents the relationship among triangles, scalene triangles and right angled triangles?
A)
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B)
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C)
done
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D)
All the above
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E)
None of these
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Examine the following three figures given below in which the number follows a specific pattern: The missing number in the third figure given above is _______.
A)
65
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B)
75
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C)
30
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D)
68
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E)
None of these
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Find the number that does not follow the pattern of the series: 720, 360, 24, 6, 2, 1
A)
720
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B)
360
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C)
24
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D)
6
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E)
None of these
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Students line up in a queue in which Alam stands eighteenth from the left and Vinod is seventh from the right. If they interchange their places, Vinod would be nineteenth from the right. How many number of students are there in the queue?
A)
46
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B)
32
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C)
36
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D)
37
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E)
None of these
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Read the statements given below:
Statement I: \[(123456\times 123460)>{{(123458)}^{2}}\] Statement II: \[{{(64)}^{13}}>{{(127)}^{11}}\] Statement III: \[{{4}^{32}}>{{64}^{11}}\] Based on the above statements choose the correct option:
A)
Only statement I is true
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B)
Only statement II is true
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C)
All the statements I, II and III are true
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D)
All the statements I, II and III are false
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E)
None of these
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Put numbers 1, 3, 4, 5, 6, 7 and 8 at the vertices of a cuboid such that the sum of any three numbers on any face is not less than 10. Find the minimum sum of the four numbers on a face.
A)
17
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B)
18
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C)
19
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D)
20
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E)
None of these
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The rightmost non-zero digits of the number \[{{(70)}^{1560}}\] is ________.
A)
1
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B)
9
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C)
3
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D)
7
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E)
None of these
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If \[p={{13}^{3}}+{{15}^{3}}+{{17}^{3}}+{{19}^{3}},\] then what will be the remainder if \[p\] is divided by 32?
A)
1
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B)
31
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C)
29
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D)
0
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E)
None of these
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Which one among the following statements is incorrect?
A)
If \[(n+1)\] is divisible by 3, then \[8+14n\] is also divisible by 3.
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B)
If \[(3+n)\] and \[(36-m)\] both are divisible by 11, then \[(n+m)\] is not divisible by 11.
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C)
The last digit of the number \[{{2}^{50}}\]is 4.
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D)
The remainder of \[{{2}^{100}}\]when divided by 3 is 4.
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E)
None of these
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Natural numbers starting from 1 are written in a row as given below:
1 2 3 4 5 6 7 8 9 10 11 12 13........
What will be the 3000th digit in the sequence?
A)
0
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B)
1
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C)
2
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D)
3
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E)
None of these
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If a, b, m and n are four different positive integers selected from 1 to 100, then find the highest possible value of \[\frac{(a+b)+(m+n)}{(a+b)+(m-n)}\].
A)
201
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B)
200
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C)
101
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D)
100
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E)
None of these
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A cube of side 4 cm is painted on all its side. If it is cut into 1 cubic centimeter cubes, how many 1 cubic centimeter cubes will have exactly two of their sides painted?
A)
8
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B)
16
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C)
24
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D)
12
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E)
None of these
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How many pairs of positive integers p and q satisfy \[\frac{1}{p}+\frac{3}{q}=\frac{1}{15},\] where q is an even integer less than 60?
A)
0
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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 sides of a triangle are 3 cm, 4 cm and 5 cm. Find the area of the largest square that can be inscribed in it.
A)
\[2\,\,\frac{36}{49}\,\,c{{m}^{2}}\]
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B)
\[3\,\,\frac{33}{64}\,\,c{{m}^{2}}\]
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C)
\[2\,\,\frac{46}{49}\,\,c{{m}^{2}}\]
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D)
\[4\,\,\frac{76}{81}\,\,c{{m}^{2}}\]
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E)
None of these
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