131.
383 ÃÂÃÂÃÂÃÂÃÂÃÂ 38 ÃÂÃÂÃÂÃÂÃÂÃÂ 3.8 = ?
(A) 55305.2
(B) 56305.4
(C) 57305.6
(D) 58305.8
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Solution:
383 × 38 × 38 = 553052 Number of decimal place = 1 ∴ 383 × 38 × 3.8 = 55305.2
132.
Find the value of the following expression upto four places of decimals.
(A) 1.6414
(B) 1.6415
(C) 1.6416
(D) 1.6428
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Solution:
Given expression : $$\eqalign{ & \left[ {1 + \frac{1}{{1 \times 2}} + \frac{1}{{1 \times 2 \times 4}} + \frac{1}{{1 \times 2 \times 4 \times 8}} + \frac{1}{{1 \times 2 \times 4 \times 8 \times 16}}} \right] \cr & = \frac{{2 \times 4 \times 8 \times 16 + 4 \times 8 \times 16 + 8 \times 16 + 16 + 1}}{{2 \times 4 \times 8 \times 16}} \cr & = \frac{{1024 + 512 + 128 + 16 + 1}}{{1024}} \cr & = \frac{{1681}}{{1024}} \cr & = 1.6416 \cr} $$
133.
$$5.5 - \left[ {6.5 - \left\{ {3.5 \div \left( {6.5 - \overline {5.5 - 2.5} } \right)} \right\}} \right]$$ ÃÂÃÂ ÃÂÃÂ ÃÂÃÂ is equal to :
(A) - 1
(B) 0
(C) 0.1
(D) 1
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Solution:
Given expression : = 5.5 - [6.5 - {3.5 ÷ (6.5 - 3)}] = 5.5 - [6.5 - {3.5 ÷ 3.5}] = 5.5 - [6.5 - 1] = 5.5 - 5.5 = 0
134.
Solve : $$\frac{17292}{33}$$ÃÂàÃÂÃÂÃÂ÷ 8 = ?
(A) 23.5
(B) 53.5
(C) 65.5
(D) 33.5
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Solution:
= $$\frac{17292}{33}$$ × $$\frac{1}{8}$$ = $$\frac{17292}{33 × 8}$$ = 65.5
135.
32.4 ÃÂÃÂÃÂÃÂÃÂÃÂ 11.5 ÃÂÃÂÃÂÃÂÃÂÃÂ 8.5 = ?
(A) 3149.5
(B) 3129.1
(C) 3167.1
(D) 3162.5
Show Answer
Solution:
324 × 115 × 85 = 3167100 Sum of decimal place = 3 ∴ 32.4 × 11.5 × 8.5 = 3167.1
136.
The expression (11.98 ÃÂÃÂÃÂÃÂÃÂÃÂ 11.98 + 11.98 ÃÂÃÂÃÂÃÂÃÂÃÂ X + 0.02 ÃÂÃÂÃÂÃÂÃÂÃÂ 0.02) will be a perfect square for X equal to:
(A) 0.02
(B) 0.2
(C) 0.04
(D) 0.4
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Solution:
Given expression = (11.98)2 + (0.02)2 + 11.98 × X For the given expression to be a perfect square, (a + b)2 = a2 + b2 + 2ab we must have 11.98 × X = 2 × 11.98 × 0.02 ∴ X = 0.04
137.
$$1.\overline {27} $$ ÃÂÃÂ in the from $$\frac{p}{q}$$ is equal to :
(A) $$\frac{127}{100}$$
(B) $$\frac{14}{11}$$
(C) $$\frac{73}{100}$$
(D) $$\frac{11}{14}$$
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Solution:
$$\eqalign{ & = 1.\overline {27} \cr & = 1 + 0.\overline {27} \cr & = 1 + \frac{{27}}{{99}} \cr & = 1 + \frac{3}{{11}} \cr & = \frac{{11 + 3}}{{11}} \cr & = \frac{{14}}{{11}} \cr} $$
138.
Solve : $$7\frac{1}{2} - $$ ÃÂà$$\left[ {2\frac{1}{4} ÃÂÃÂÃÂ÷ \left\{ {1\frac{1}{4} - \frac{1}{2}\left( {1\frac{1}{2} - \frac{1}{3} - \frac{1}{6}} \right)} \right\}} \right]$$ ÃÂàÃÂàÃÂà= ?
(A) $$\frac{2}{9}$$
(B) $$4\frac{1}{2}$$
(C) $$9\frac{1}{2}$$
(D) $$1\frac{77}{228}$$
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Solution:
$$ = 7\frac{1}{2} - $$ $$\left[ {2\frac{1}{4} \div \left\{ {1\frac{1}{4} - \frac{1}{2}\left( {1\frac{1}{2} - \frac{1}{3} - \frac{1}{6}} \right)} \right\}} \right]$$ $$ = \frac{{15}}{2} - $$ $$\left[ {\frac{9}{4} \div \left\{ {\frac{5}{4} - \frac{1}{2}\left( {\frac{3}{2} - \frac{1}{3} - \frac{1}{6}} \right)} \right\}} \right]$$ $$ = \frac{{15}}{2} - $$ $$\left[ {\frac{9}{4} \div \left\{ {\frac{5}{4} - \frac{1}{2}\left( {\frac{{9 - 2 - 1}}{6}} \right)} \right\}} \right]$$ $$\eqalign{ & = \frac{{15}}{2} - \left[ {\frac{9}{4} \div \left\{ {\frac{5}{4} - \frac{1}{2}} \right\}} \right] \cr & = \frac{{15}}{2} - \left[ {\frac{9}{4} \div \left\{ {\frac{{5 - 2}}{4}} \right\}} \right] \cr & = \frac{{15}}{2} - \left[ {\frac{9}{4} \div \frac{3}{4}} \right] \cr & = \frac{{15}}{2} - \left[ {\frac{9}{4} \times \frac{4}{3}} \right] \cr & = \frac{{15}}{2} - 3 \cr & = \frac{{15 - 6}}{2} \cr & = \frac{9}{2} \cr & = 4\frac{1}{2} \cr} $$
139.
Solve this : $$\frac{0.0203 ÃÂÃÂÃÂÃÂÃÂÃÂ 2.92}{0.0073 ÃÂÃÂÃÂÃÂÃÂÃÂ 14.5 ÃÂÃÂÃÂÃÂÃÂÃÂ 0.7}$$ ÃÂÃÂÃÂÃÂ ÃÂÃÂÃÂÃÂ = ?
(A) 0.8
(B) 1.45
(C) 2.40
(D) 3.25
Show Answer
Solution:
= $$\frac{0.0203 × 2.92}{0.0073 × 14.5 × 0.7}$$ = $$\frac{203 × 292}{73 × 145 × 7}$$ = $$\frac{4}{5}$$ = 0.8
140.
One hundredth of centimetre when written in fractions of kilometres, is equal to :
(A) 0.0000001
(B) 0.000001
(C) 0.0001
(D) 0.001
Show Answer
Solution:
Required fraction : $$\eqalign{ & = \frac{{\frac{1}{{100}}{\text{ cm}}}}{{1{\text{ km}}}} \cr & = \frac{{\left( {\frac{1}{{100}}} \right){\text{ cm}}}}{{\left( {1000 \times 100} \right){\text{ cm}}}} \cr & = \frac{1}{{100 \times 1000 \times 100}} \cr & = \frac{1}{{10000000}} \cr & = 0.0000001 \cr} $$