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Arithmetic Ability
Simplification
Quiz 4
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Q.1
By what least number should 675 be multiplied so as to obtain a perfect cube number ?
3
5
24
40
Q.2
The least fraction to be subtracted from the expression $$\frac{{3\frac{1}{4} - \frac{4}{5}{\text{ of }}\frac{5}{6}}}{{4\frac{1}{3} \div \frac{1}{5} - \left( {\frac{3}{{10}} + 21\frac{1}{5}} \right)}}$$ to make it an integer?
$$\frac{1}{2}$$
$$\frac{5}{6}$$
$$\frac{1}{4}$$
$$\frac{3}{{10}}$$
Q.3
The simplified value of $$\sqrt {5 + \sqrt {11 + \sqrt {19 + \sqrt {29 + \sqrt {49} } } } } $$ = ?
3
2
4
6
Q.4
The value of $${\text{1 + }}\frac{1}{{4 \times 3}} + \frac{1}{{4 \times {3^2}}} + \frac{1}{{4 \times {3^2}}} = ?$$
$$\frac{{121}}{{108}}$$
$$\frac{3}{2}$$
$$\frac{{31}}{2}$$
None of these
Q.5
$$\frac{1}{{1.2.3}} + \frac{1}{{2.3.4}} + \frac{1}{{3.4.5}} + \frac{1}{{4.5.6}}$$ is equal to = ?
$$\frac{7}{{30}}$$
$$\frac{{11}}{{30}}$$
$$\frac{{13}}{{30}}$$
$$\frac{{17}}{{30}}$$
Q.6
If x = y = 2z and xyz = 256, then x = ?
2
4
8
None of these
Q.7
The value of $$\left( {1 - \frac{1}{{{3^2}}}} \right)$$ $$\left( {1 - \frac{1}{{{4^2}}}} \right)$$ $$\left( {1 - \frac{1}{{{5^2}}}} \right)$$ . . . . . $$\left( {1 - \frac{1}{{{{11}^2}}}} \right)$$ $$\left( {1 - \frac{1}{{{{12}^2}}}} \right)$$ $$ = ?$$
$$\frac{{11}}{{20}}$$
$$\frac{{13}}{{15}}$$
$$\frac{{13}}{{18}}$$
$$\frac{{15}}{{16}}$$
None of these
Q.8
What is the maximum number of half - pint bottles of cream that can be filled with a 4-gallon can of cream? (2pt. = 1qt. and 4qt. = 1gal.)
16
24
30
64
Q.9
Which of the following values of x and y satisfy the following equations i and ii?
i. 3x + y = 19
ii. x - y = 9
-7, -2
-7, 2
7, -2
7, 2
Q.10
The value of $$\frac{2}{3} \times \frac{3}{{\frac{5}{6} \div \frac{2}{3}{\text{ of 1}}\frac{1}{4}}} = ?$$
2
1
$$\frac{1}{2}$$
$$\frac{2}{3}$$
Q.11
The value (1001)
3
is = ?
1003003001
100303001
100300301
103003001
Q.12
The value of (0.98)
3
+ (0.02)
3
+ 3 × 0.98 × 0.02 - 1 = ?
1.98
1.09
1
0
Q.13
The smallest number that must be subtracted from 1000 to make the resulting number a perfect square is = ?
37
38
39
40
Q.14
$$\sqrt {\frac{{0.009 \times 0.036 \times 0.016 \times 0.08}}{{0.002 \times 0.0008 \times 0.0002}}} $$ is equal to = ?
34
36
38
39
Q.15
$$\left[ {2\sqrt {54} - 6\sqrt {\frac{2}{3}} - \sqrt {96} } \right]$$ is equal to = ?
0
1
2
$$\sqrt 6 $$
Q.16
$$\frac{{{{\left( {7.5} \right)}^3} + 1}}{{{{\left( {7.5} \right)}^2} - 6.5}}$$ is equal to = ?
2.75
$$\frac{9}{5}$$
4.75
8.5
Q.17
Given that $$\sqrt {13} $$ = 3.6 and $$\sqrt {130} $$ = 11.4, then the value of $$\sqrt {13} $$ + $$\sqrt {1300} $$ + $$\sqrt {0.013} $$ is equal to = ?
36.164
637.254
39.714
37.154
Q.18
If the sum of the squares three consecutive natural numbers is 110, then the smallest of these natural numbers is = ?
8
6
7
5
Q.19
$$\root 3 \of {{{\left( {333} \right)}^3} + {{\left( {333} \right)}^3} + {{\left( {334} \right)}^3} - 3 \times 333 \times 333 \times 334} $$ is equal to = ?
12
11
10
15
Q.20
$$\frac{2}{{2 + \frac{2}{{3 + \frac{2}{{3 + \frac{2}{3}}}}} \times 0.39}}$$ is simplified to = ?
$$\frac{1}{3}$$
2
6
None of these
Q.21
The simplified value of $${\left[ {{{\left( {0.111} \right)}^3} + {{\left( {0.222} \right)}^3} - {{\left( {0.333} \right)}^3} + {{\left( {0.333} \right)}^2}\left( {0.222} \right)} \right]^3} = ?$$
0.999
0
0.888
0.111
Q.22
The value of $$\sqrt {400} $$ + $$\sqrt {0.0400} $$ + $$\sqrt {0.000004} $$ = ?
0.222
20.22
20.202
2.022
Q.23
If $$\sqrt 3 {\text{ = 1}}{\text{.7321,}}$$ then the value of $$\sqrt {192} - \frac{1}{2}\sqrt {48} - \sqrt {75} {\text{,}}$$ correct to 3 place of decimal, is = ?
8.661
4.331
1.732
-1.732
Q.24
(71 × 29 + 27 × 15 + 8 × 4) equals = ?
3450
3458
2496
None of these
Q.25
A canteen requires 798 bananas for a week. Total how many bananas did it require for the months of January, February and March 2008?
10277
10374
10480
10586
None of these
Q.26
Find the sum : $$\frac{1}{2} + $$ $$\frac{1}{6} + $$ $$\frac{1}{{12}} + $$ $$\frac{1}{{20}} + $$ $$\frac{1}{{30}} + $$ $$\frac{1}{{42}} + $$ $$\frac{1}{{56}} + $$ $$\frac{1}{{72}} + $$ $$\frac{1}{{90}} + $$ $$\frac{1}{{110}} + $$ $$\frac{1}{{132}}$$ $$ = ?$$
$$\frac{7}{8}$$
$$\frac{{11}}{{12}}$$
$$\frac{{11}}{{12}}$$
$$\frac{{17}}{{18}}$$
Q.27
If 4x = p(x + 3) + q(x - 1) is an identity, then the values of p and q are?
1, -3
1, 3
1, 1
3, 1
Q.28
If $$a + \frac{1}{b} = 1$$ and $$b + \frac{1}{c} = 1{\text{,}}$$ then $$c + \frac{1}{a}$$ is equal to = ?
0
$$\frac{1}{2}$$
1
2
Q.29
If $$\frac{x}{{\left( {2x + y + z} \right)}}$$ = $$\frac{y}{{\left( {x + 2y + z} \right)}}$$ = $$\frac{z}{{\left( {x + y + 2z} \right)}} = a{\text{,}}$$ then find a, If x + y + z ≠ 0
$$\frac{1}{3}$$
$$\frac{1}{4}$$
$$\frac{1}{2}$$
$$\frac{1}{8}$$
Q.30
The number, whose square is equal to the difference of the squares of 75.15 and 60.12, is = ?
46.09
48.09
45.09
47.09
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