What must be added to\[9{{x}^{2}}-24x+10\]to make it a perfect square?
A)
6
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B)
5
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C)
10
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D)
0
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E)
None of these
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The sum of the interior angles of a polygon is twice the sum of its exterior angles. How many sides does the polygon have?
A)
8 sides
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B)
9 sides
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C)
12 sides
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D)
6 sides
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E)
None of these
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Sam said to Rita "Your mother's husband's sister is my aunt". How is Rita related to Sam?
A)
Daughter
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B)
Niece
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C)
Sister
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D)
Mother
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E)
None of these
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X gives \[\frac{1}{2}\] of his property to his wife and \[\frac{1}{2}\] of the rest to his son. The remainder is divided equally to his two daughters. The share of each daughter is :
A)
\[\frac{1}{8}\]
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B)
\[\frac{1}{6}\]
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C)
\[\frac{1}{4}\]
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D)
\[\frac{2}{3}\]
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E)
None of these
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The area of the base of a right cone is \[154\,{{m}^{2}}\] and its volume is \[308\,{{m}^{3}}\]. The height of the cone is
A)
8 m
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B)
6 m
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C)
7 m
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D)
9 m
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E)
None of these
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The L.C.M. of two numbers is 12 times their H.C.F. The sum of the H.C.F. and L.C.M. is 403. If one number is 93, then the other number is:
A)
134
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B)
124
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C)
128
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D)
310
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E)
None of these
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All natural numbers and 0 are called the ________ numbers.
A)
whole
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B)
prime
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C)
integer
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D)
rational
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E)
None of these
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Person sells an article for Rs. 550, gaining \[\frac{1}{10}\]_________ of its cost price. Find gain percent.
A)
10%
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B)
12%
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C)
8%
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D)
15%
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E)
None of these
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The multiplicative inverse of \[-\,2\frac{2}{3}\] is:
A)
\[\frac{3}{8}\]
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B)
\[\frac{-3}{8}\]
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C)
\[2\frac{2}{3}\]
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D)
\[4\frac{2}{3}\]
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E)
None of these
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If x, y are non-zero rational numbers and n is an integer, then \[{{(xy)}^{n}}\] is equal to :
A)
\[{{x}^{n}}{{y}^{n}}\]
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B)
\[{{(xy)}^{\frac{n}{2}}}\]
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C)
\[\frac{{{x}^{n}}}{{{y}^{n}}}\]
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D)
\[{{(x+y)}^{n}}\]
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E)
None of these
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Simplify \[{{(-\,4)}^{3}}\times {{(-\,5)}^{-\,3}}\times {{(-\,5)}^{-\,3}}\] and write the answer in exponential form :
A)
\[{{2}^{6}}\times {{10}^{-\,2}}\]
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B)
\[{{2}^{6}}\times {{10}^{-\,4}}\]
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C)
\[{{2}^{12}}\times {{10}^{-\,5}}\]
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D)
\[{{2}^{12}}\times {{10}^{-\,6}}\]
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E)
None of these
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If\[{{3}^{(x-y)}}=27\]and \[{{3}^{(x+y)}}=243\], then x 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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Find the value of m in: \[\frac{{{(25)}^{2m+1}}\times {{(125)}^{5}}}{{{(625)}^{2}}}={{(3125)}^{3m}}\]
A)
1
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B)
0
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C)
\[\frac{9}{11}\]
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D)
\[\frac{11}{9}\]
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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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If \[a=\frac{\sqrt{2}+1}{\sqrt{2}-1}\] and \[b=\frac{\sqrt{2}-1}{\sqrt{2}+1}\] 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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Simplify the expression: \[\sqrt{\frac{0.256\times 0.081\times 4.356\times 625}{1.5625\times 0.0121\times 129.6\times 64}}\]
A)
3
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B)
5
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C)
\[\frac{3}{5}\]
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D)
\[\frac{5}{3}\]
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E)
None of these
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The smallest natural number whose square is exactly divisible by 4, 5, 6 and 18 is:
A)
15
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B)
19
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C)
20
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D)
30
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E)
None of these
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Find the smallest number by which 864 must be multiplied so that the product will be a perfect cube.
A)
3
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B)
2
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C)
8
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D)
5
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E)
None of these
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If \[y=\sqrt[3]{2\frac{80}{216}}\], then find the value of y.
A)
\[\frac{4}{6}\]
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B)
\[\frac{4}{3}\]
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C)
\[\frac{3}{4}\]
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D)
\[\frac{6}{4}\]
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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, then the sum of these numbers is:
A)
27
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B)
63
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C)
81
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D)
99
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E)
None of these
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Evaluate:\[\sqrt[3]{1372}\,\,\times \,\,\sqrt[3]{1458}\]
A)
63
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B)
126
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C)
93
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D)
186
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E)
None of these
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The area of the figure ABCEFGA is \[84\,{{m}^{2}}\]AH=HC=AG=6m. CE=HF = 4m. If angles marked in the figure are\[90{}^\circ \]ten the length of DB will be:
A)
2.5 m
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B)
5 m
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C)
6 m
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D)
12 m
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E)
None of these
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The value of\[(5\,{{a}^{6}})\,\,\times \,\,(-\,10a{{b}^{2}})\,\,\times \,\,(2.1\,{{a}^{2}}{{b}^{3}})\] for \[a=1\]and \[b\frac{1}{2}\]is:
A)
\[-\frac{105}{32}\]
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B)
\[\frac{105}{64}\]
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C)
\[\frac{150}{32}\]
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D)
1
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E)
None of these
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In the figure, find the value of \[2x+y+z\].
A)
\[360{}^\circ \]
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B)
\[450{}^\circ \]
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C)
\[650{}^\circ \]
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D)
\[720{}^\circ \]
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E)
None of these
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If \[a+\frac{1}{a}=x+y\] and \[a-\frac{1}{a}=x-y,\]then:
A)
\[xy=1\]
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B)
\[x=y\]
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C)
\[xy=2\]
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D)
\[x+y=0\]
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E)
None of these
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The value of \[{{a}^{3}}-3\sqrt{3}\,{{b}^{3}}\]is:
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 the expression given by \[27{{x}^{3}}{{y}^{3}}-18{{x}^{2}}{{y}^{3}}+36{{x}^{3}}{{y}^{2}}\].
A)
\[9{{x}^{2}}{{y}^{2}}\,(3xy-2y+4x)\]
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B)
\[9{{x}^{2}}{{y}^{2}}\,(2xy+3y+4x)\]
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C)
\[9{{x}^{2}}{{y}^{2}}\,(2xy-3y+4x)\]
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D)
\[9{{x}^{2}}{{y}^{2}}\,(3xy+2y-4x)\]
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E)
None of these
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What must be added to\[({{x}^{4}}+2{{x}^{3}}-2{{x}^{2}}-2x-1)\] to obtain a polynomial which is exactly divisible by \[(x-1)(x+3)\]?
A)
\[2x+4\]
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B)
\[2x-4\]
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C)
\[4x+2\]
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D)
\[4x-2\]
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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 become\[7:2\]. The present age of the son is:
A)
5 years
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B)
8 years
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C)
10 years
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D)
12 years
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E)
None of these
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The average of three numbers is 27. If the largest number is replaced by the number 34, then the average becomes 30. The original number that is replaced is :
A)
25
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B)
22
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C)
23
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D)
24
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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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4 men or 9 women can earn Rs. 864 per day. How much would 15 men and 10 women can earn in a day?
A)
Rs. 3250
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B)
Rs. 3475
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C)
Rs. 4200
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D)
Rs. 4800
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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 other and sum of 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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There are 300 cats in a village, and 75 of them are black, 65 of them are brown, 90 of them are white and rest of them are of mixed colours. What is the percentage of mixed colour cats in the village?
A)
\[23\,\,\frac{1}{3}%\]
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B)
\[25\,\,\frac{1}{5}%\]
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C)
\[30%\]
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D)
\[28\,\,\frac{2}{5}%\]
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E)
None of these
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A nursery have 5000 plants in which 5% are roses and 1% are sunflowers. What is the total number of other plants?
A)
4700
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B)
5000
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C)
2500
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D)
4500
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E)
None of these
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A sum of Rs. 232 is made up of 672 coins which are either 50 paise or 25 paise coins. The number of 50 paise coins is:
A)
256
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B)
334
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C)
416
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D)
464
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E)
None of these
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A dishonest dealer professes to sell his goods at cost price, but he uses a weight of 960 g for 1 kg. Find his gain percent.
A)
\[5\,\,\frac{2}{3}%\]
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B)
\[3\,\,\frac{1}{3}%\]
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C)
\[4\,\,\frac{1}{4}%\]
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D)
\[4\,\,\frac{1}{6}%\]
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E)
None of these
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After allowing a discount of 12% on the marked price of an article, it is sold for Rs. 880. Find its marked price.
A)
Rs. 1000
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B)
Rs. 900
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C)
Rs. 1050
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D)
Rs. 950
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E)
None of these
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If a % discount is offered on the cost price of b, then find the selling price.
A)
\[\frac{b\,(100-a)}{100}\]
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B)
\[\frac{a\,(100-b)}{100}\]
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C)
\[a\,(100-b)\]
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D)
All of these
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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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