Simplify: \[1-\left[ 1+\frac{1}{3}\{18\div 6-3\,(1-\overline{9-7})\} \right]\]
A)
0
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B)
\[-1\]
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C)
\[-2\]
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D)
4
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E)
None of these
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The product of given 15 fractions is: \[\left( 1-\frac{1}{5} \right)\left( 1-\frac{1}{6} \right)\left( 1-\frac{1}{7} \right).......\left( 1-\frac{1}{19} \right)\]
A)
\[\frac{1}{19}\]
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B)
\[\frac{18}{19}\]
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C)
\[\frac{4}{19}\]
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D)
\[\frac{6}{19}\]
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E)
None of these
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In the given magic square, each row, column and diagonal have the same sum. Find the value of \[A-B\]
\[-3\] 2 \[-5\] A \[-2\] 0 1 \[-6\] B
A)
3
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B)
\[-3\]
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C)
\[-5\]
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D)
5
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E)
None of these
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Which one is correct for the given statement?
Statement 1: A fraction \[\frac{a}{b}\,\]can be expressed as a terminating decimal, if b has no prime factors other than 2 and 5. Statement 2: Every fraction is a rational number but every integer is not a rational number.
A)
Statement 1 is true and 2 is false.
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B)
Statement 2 is true and 1 is false.
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C)
Both statements 1 and 2 are true.
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D)
Both statements 1 and 2 are false.
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E)
None of these
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If \[\sqrt{4489}=67,\] then the value of \[\sqrt{44.89}+\sqrt{0.4489}+\sqrt{0.004489}\] is:
A)
7.773
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B)
7.943
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C)
7.883
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D)
7.437
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E)
None of these
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Which one of the following numbers is exactly divisible by 99?
A)
121969
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B)
121869
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C)
121672
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D)
120781
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E)
None of these
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How many prime numbers are there in the given prime factorization? \[({{39}^{6}}\times {{21}^{28}}\times {{55}^{7}})\]
A)
51
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B)
102
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C)
87
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D)
72
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E)
82
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The value of \[\left( \frac{{{1000}^{38}}+{{1000}^{100}}}{{{1000}^{38}}}-1 \right)\] is equal to ______.
A)
\[{{100}^{93}}\]
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B)
\[{{100}^{95}}\]
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C)
\[{{100}^{98}}\]
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D)
\[{{100}^{96}}\]
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E)
None of these
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In the given multiplication, * stands for a digit. If the unit digit of whole product is 6 then the missing digit * is: \[(29987\times 6015*\times 72082)\]
A)
2 or 6
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B)
4 or 9
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C)
5 or 7
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D)
1 or 8
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E)
None of these
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What is the least number which when divided by 7, 8 and 18 leaves remainder 4 in each case?
A)
500
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B)
504
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C)
508
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D)
512
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E)
None of these
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In the figure given below, product of fractions represented by shaded parts and unshaded parts in its simplest form is:
A)
\[\frac{8}{25}\]
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B)
\[\frac{12}{25}\]
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C)
\[\frac{6}{25}\]
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D)
\[\frac{14}{25}\]
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E)
None of these
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If \[{{x}^{2}}+\frac{1}{{{x}^{2}}}=23,\] then the value of \[{{x}^{3}}+\frac{1}{{{x}^{3}}}\]is:
A)
130
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B)
120
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C)
\[\sqrt{396}\]
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D)
115
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E)
None of these
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By how much is \[2\,{{x}^{4}}+8\,{{x}^{2}}{{y}^{2}}+{{y}^{4}}\] more than \[{{x}^{4}}-16\,{{x}^{2}}{{y}^{2}}+{{y}^{4}}?\]
A)
\[3\,{{x}^{4}}+24\,{{x}^{2}}{{y}^{2}}\]
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B)
\[-{{x}^{4}}+8\,{{x}^{2}}{{y}^{2}}\]
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C)
\[{{x}^{4}}+24\,{{x}^{2}}{{y}^{2}}\]
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D)
\[{{x}^{4}}-8\,{{x}^{2}}{{y}^{2}}\]
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E)
None of these
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Thrice a number when decreased by 7 gives 113. If 25% of the number is added to 113, the sum is:
A)
117
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B)
123
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C)
127
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D)
133
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E)
None of these
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Two numbers are 20% and 45% less than a third number. By how much per cent is the second number less than the first number?
A)
\[34\frac{1}{4}\]%
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B)
\[31\frac{1}{4}\]%
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C)
\[21\frac{1}{4}\]%
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D)
\[25\frac{1}{4}\]%
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E)
None of these
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What number should be added to each of the numbers 3, 4, 12 and 14 so that the numbers are in proportion?
A)
4
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B)
6
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C)
8
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D)
3
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E)
None of these
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Find the difference between the Compound Interest and Simple Interest on the sum of Rs. 10000 at 20% per annum for 3 years.
A)
Rs. 1280
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B)
Rs. 1440
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C)
Rs. 1160
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D)
Rs. 1620
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E)
None of these
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If \[3A=4B=9C,\]then \[A:B:C=?\]
A)
3 : 4 : 9
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B)
9 : 4 : 3
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C)
12 : 9 : 4
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D)
6 : 3 : 2
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E)
None of these
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Simplify:\[\frac{3.2\times {{10}^{-3}}+2.5\times {{10}^{-4}}+4.5\times {{10}^{-5}}}{5}\]
A)
\[4.79\times {{10}^{-4}}\]
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B)
\[6.78\times {{10}^{-3}}\]
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C)
\[7.64\times {{10}^{-3}}\]
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D)
\[6.99\times {{10}^{-4}}\]
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E)
None of these
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600 soldiers in a fort had enough food for 14 days. After 2 days, some soldiers were transferred to another fort and thus the food lasted for an extra 16 days. How many soldiers left the fort?
A)
300
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B)
150
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C)
125
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D)
75
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E)
None of these
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In the figure given below, ABC is an isosceles triangle in which AB = AC. AP is the angle bisector of\[\angle BAC\]. If \[\angle BAC=74{}^\circ ,\] then find the measure of\[\angle ABC.\]
A)
\[51{}^\circ \]
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B)
\[53{}^\circ \]
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C)
\[54{}^\circ \]
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D)
\[57{}^\circ \]
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E)
None of these
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In the figure given below, QORM is a straight line and PQ = OQ. Find the value of\[x\].
A)
\[31{}^\circ \]
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B)
\[26{}^\circ \]
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C)
\[29{}^\circ \]
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D)
\[32{}^\circ \]
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E)
None of these
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Which of the following triangles is practically not possible?
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 given triangle ABC, the sides AB and AC are produced to P and Q, respectively. The bisector of \[\angle PBC\] and \[\angle QCB\] intersect at O then \[\angle BOC\] is equal to:
A)
\[90{}^\circ +\frac{\angle A}{2}\]
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B)
\[90{}^\circ -\frac{\angle A}{2}\]
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C)
\[90{}^\circ -\frac{\angle A}{4}\]
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D)
\[45{}^\circ +\frac{\angle A}{2}\]
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E)
None of these
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Four horses are tethered at four corners of a square plot of side 28 m so that the adjacent horses can just reach one another. What is the area of field which remains ungrazed? \[\left( \text{Use}\,\,\pi \,\,\frac{22}{7} \right)\]
A)
\[168\,\,{{m}^{2}}\]
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B)
\[172\,\,{{m}^{2}}\]
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C)
\[142\,\,{{m}^{2}}\]
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D)
\[184\,\,{{m}^{2}}\]
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E)
None of these
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Area of the largest square that can be cut out of a circle of radius 18 cm is:
A)
\[576\,\,c{{m}^{2}}\]
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B)
\[624\,\,c{{m}^{2}}\]
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C)
\[648\,\,c{{m}^{2}}\]
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D)
\[598\,\,c{{m}^{2}}\]
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E)
None of these
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A dice is tossed 100 times and the number 6 is obtained 66 times. Now, the dice is tossed at random, then the probability of getting any number other than 6 is:
A)
\[\frac{33}{50}\]
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B)
\[\frac{17}{50}\]
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C)
\[\frac{11}{50}\]
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D)
\[\frac{11}{100}\]
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E)
None of these
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Direction: Given pie chart shows the number of employees in different departments of an organization where the total number of employees is 2400. Read the pie chart and answer the following questions.
If 72 new employees are hired in Accounts department, then what is the ratio of the number of employees of Accounts department to the number of employees of IT department?
A)
2 : 5
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B)
3 : 5
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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: Given pie chart shows the number of employees in different departments of an organization where the total number of employees is 2400.
Read the pie chart and answer the following questions.
When 72 new employees are hired in Accounts department, the new percentage of employees in the Marketing department is:
A)
\[\frac{2400}{100}\]%
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B)
\[\frac{1800}{103}\]%
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C)
\[\frac{1500}{103}\]%
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D)
\[\frac{2100}{103}\]%
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E)
None of these
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If \[A=\left\{ 1,\text{ }5,\text{ }6,\text{ }7,\text{ }8,\text{ }10 \right\}\] and \[B=\left\{ 2,\text{ }4,\text{ }6,\text{ }8 \right\},\]then which one of the following is incorrect?
A)
\[A\cup B=\,\,\left\{ 1,\,\,2,\,\,4,\,\,5,\,\,6,\,\,7,\,\,8,\,\,10 \right\}\]
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B)
\[A\cap B=\left\{ 6,\,\,8 \right\}\]
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C)
\[A-B=\left\{ 1,\,\,5,\,\,7,\,\,10 \right\}\]
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D)
\[B-A=\left\{ 1,\,\,2,\,\,4,\,\,10 \right\}\]
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E)
None of these
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Find the missing term in place of question mark (?) in the number series given below. \[102,\,\,96,\,\,89,\,\,81,\,\,72,\,\,\underline{?},\,\,51\]
A)
63
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B)
61
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C)
60
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D)
62
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E)
None of these
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Pointing towards a person in a photograph, Lalita said, "He is the only son of the father of my sister's brother." How is that person is related to Lalita?
A)
Maternal uncle
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B)
Brother
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C)
Mother
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D)
Father
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E)
None of these
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If \[M=13,\]\[ME=9,\] and \[MAY=13,\] then \[MIND=?\]
A)
12
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B)
10
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C)
11
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D)
8
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E)
None of these
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In a certain analogy, if 'True' is related to 'False' as 'Stress' is related to:
A)
Attach
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B)
Disregard
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C)
Relax
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D)
Indifferent
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E)
None of these
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How many rectangles are there in the figure given below?
A)
12
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B)
16
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C)
13
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D)
11
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E)
None of these
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In a certain language, if 'EFNE' is coded as 'CHLG', then how 'LTNE' is written in the same code?
A)
TLLG
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B)
JVLG
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C)
UMLG
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D)
VJLG
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E)
None of these
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Anushka faces towards South. Turning to her left, she walks 30 metres. She then turns to her right and walks 40 metres. Next, she moves 30 metres to her left. She then turns to her right again and walks 80 metres. Finally, she turns to the left and moves 30 metres. In which direction is she now from her starting point?
A)
South - West
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B)
North - West
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C)
South - East
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D)
North - East
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E)
None of these
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A dice has A, B, C, D written in anticlockwise order on the adjacent faces while E and F at the top and bottom, respectively. When D is at top, what will be at its bottom?
A)
C
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B)
A
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C)
B
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D)
F
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E)
None of these
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There is a certain relationship between the figures (i) and (ii). Establish the same relationship between figures (iii) and (iv) by selecting a suitable figure from the options that will replace the question mark (?) in figure (iv).
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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Find the water image of the given figure.
A)
done
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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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When 918 is divided by a certain positive number, which is \[44\,\,\frac{4}{9}%\] of the quotient, it leaves 18 as remainder. Find the divisor.
A)
45
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B)
20
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C)
22
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D)
24
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E)
None of these
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In the figure given below, ABCD is outer square made by arranging the inner square PQRS surrounded by four congruent rectangles. If the area of outer square is \[324\,\,c{{m}^{2}},\] find the perimeter of one rectangle.
A)
32 cm
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B)
18 cm
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C)
36 cm
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D)
24 cm
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E)
None of these
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A labour is engaged for 25 days on the condition that he will receive Rs. 90 for each day he works and will be fined for Rs. 15 for each day he is absent. If he receives Rs. 1305 in total, for how many days he remained absent?
A)
7 days
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B)
8 days
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C)
9 days
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D)
6 days
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E)
None of these
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\[P=\frac{5\times {{(81)}^{x+1}}-{{3}^{4x+5}}}{3\times {{3}^{4x}}+{{81}^{x}}}\] and \[Q={{\left( \frac{2}{9} \right)}^{2}},\] then \[P\times Q\]is equal to:
A)
1
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B)
2
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C)
9
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D)
81
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E)
None of these
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Observe the given data of the weights of 15 students (in kg). 19, 17, 15, 17, 23, 17, 19, 24, 24, 19, 22, 24, 26, 24, 25
Match the following: Column I Column II (I) Range of the data A. 22 kg (II) Median of the data B. 11 Kg (III) Mode of the data C. 21 kg (IV) Mean weight of the students D. 24 kg
A)
(I - B), (II - D), (III - C), (IV - A)
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B)
(I - B), (II - A), (III - D), (IV - C)
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C)
(I - B), (II - D), (III - A), (IV - C)
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D)
(I - B), (II - A), (III - C), (IV - D)
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E)
None of these
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In the given\[\Delta \,ABC,\] the ratio of\[\angle A,\] \[\angle B\] and \[\angle C\] is \[4:3:2\] \[DE||AB\] and \[GF||AC\]. If GP is angle bisector of\[\angle FGE,\] find the value of\[x\].
A)
\[120{}^\circ \]
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B)
\[95{}^\circ \]
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C)
\[110{}^\circ \]
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D)
\[100{}^\circ \]
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E)
None of these
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In the figure given below, all line segments of shaded portion are of the same length and at right angles to each other. Find the area of unshaded portion.
A)
\[588\text{ }c{{m}^{2}}\]
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B)
\[637\,c{{m}^{2}}\]
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C)
\[539\text{ }c{{m}^{2}}\]
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D)
\[475\text{ }c{{m}^{2}}\]
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E)
None of these
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Which one of the following is the correct arrangement of rational numbers?
A)
\[\frac{3}{8}>\frac{8}{15}>-\,0.875>\frac{-\,5}{6}\]
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B)
\[\frac{-5}{6}<-\,0.875<\frac{3}{8}<\frac{8}{15}\]
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C)
\[\frac{3}{8}>\frac{8}{15}>\frac{-\,5}{6}>-\,0.875\]
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D)
\[-\,0.875<\frac{-\,5}{6}<\frac{3}{8}<\frac{8}{15}\]
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E)
None of these
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A contractor employed 180 men to build a house in 50 days. After 8 days, he was joined by 36 more men. In how many days will the remaining work be finished?
A)
28 days
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B)
36 days
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C)
35 days
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D)
42 days
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E)
None of these
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Find the reciprocal of the fraction represented by shaded parts in the given figure.
A)
\[\frac{32}{9}\]
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B)
\[\frac{32}{11}\]
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C)
\[\frac{32}{13}\]
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D)
\[\frac{96}{41}\]
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E)
None of these
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