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# Decimal Fraction Questions for RRB JE PDF

Download Top 15 RRB JE Decimal Fraction Questions and Answers PDF. RRB JE Maths questions based on asked questions in previous exam papers very important for the Railway JE exam.

Question 1: Which of the following fractions is the smallest?

a) $\dfrac{2}{7}$

b) $\dfrac{1}{6}$

c) $\dfrac{2}{9}$

d) $\dfrac{1}{8}$

Question 2: Which of the following is greatest ?
$\frac{43}{44},\frac{117}{120},\frac{132}{135},\frac{120}{123}$

a) $\frac{43}{44}$

b) $\frac{117}{120}$

c) $\frac{150}{153}$

d) $\frac{120}{123}$

Question 3: When 0.728728728.… is converted into fraction, then what is its value?

a) $\dfrac{7}{10}$

b) $\dfrac{728}{999}$

c) $\dfrac{72}{99}$

d) None of these

Question 4: Which of the following fractions is the second smallest?
$\frac{23}{35}$, $\frac{31}{43}$, $\frac{47}{59}$, $\frac{53}{65}$

a) $\frac{23}{35}$

b) $\frac{31}{43}$

c) $\frac{47}{59}$

d) $\frac{53}{65}$

Question 5: If $\frac{2a+b}{a+4b}$ = 3, then find the value of $\frac{a+b}{a+2b}$

a) $\frac{2}{7}$

b) $\frac{9}{7}$

c) $\frac{5}{3}$

d) $\frac{10}{9}$

Question 6: $\frac{3}{4}\times \frac{16}{27} \div \frac{2}{3} = ?$

a) 2/3

b) 3/2

c) 9/4

d) 4/9

Question 7: $\frac{75\times75-26\times26}{101}=?$

a) 59

b) 39

c) 29

d) 49

Question 8: By how much is $\ \frac{3}{5}$th of 75 greater than $\ \frac{4}{7}$th of 77?

a) 0

b) 5

c) 1

d) None of these

Question 9: If x=y=z, then $\ \frac{(x+y+z)^{2}}{x^{2}+y^{2}+z^{2}}\$is:

a) 2

b) 3

c) 1

d) 4

Question 10: Which of the following fractions is the largest?

a) $\dfrac{2}{5}$

b) $\dfrac{3}{11}$

c) $\dfrac{1}{6}$

d) $\dfrac{4}{13}$

Question 11: The Vulgar fraction of 0.3939…… is:

a) $\frac{11}{39}$

b) $\frac{17}{39}$

c) $\frac{13}{33}$

d) $\frac{15}{33}$

Question 12: If $\frac{a}{b}=\frac{c}{d}=5$, then $\frac{3a+4c}{3b+4d}$ is equal to

a) 60

b) 15

c) 5

d) 20

Question 13: Find the value of $n+n+\frac{3n}{2}+\frac{9n}{4}+………\infty$

a) 0

b) 1

c) 2

d) Infinity

Question 14: The sum of a fraction and its reciprocal is $\frac{113}{56}$. Find the fraction.

a) $\frac{7}{8}$

b) $\frac{5}{8}$

c) $\frac{8}{9}$

d) $\frac{3}{7}$

Question 15: If $a^{2}+b^{2}=80$ and $ab=32$, then calculate the value of $\frac{a-b}{a+b}$

a) 0.337

b) 0.339

c) 0.333

d) 0.335

$\dfrac{2}{7} = 0.285$
$\dfrac{1}{6} = 0.166$
$\dfrac{2}{9} = 0.222$
$\dfrac{1}{8} = 0.125$
Hence, $\dfrac{1}{8}$ is the smallest.

The values of the fractions are
$\frac{43}{44}$=0.977
$\frac{117}{120}$=0.975
$\frac{150}{153}$=0.98
$\frac{120}{123}$=0.909

Let x = 0.728728728…. → (1)
Here, 3 digits are repeating. Hence, 1000 should be multiplied on both sides.
1000x = 728.728728728… → (2)
Subtracting (1) from (2)
⇒ 1000x – x = 728.728728728… – 0.728728728…
⇒ 999x = 728
⇒ x = $\dfrac{728}{999}$

The difference between the numerator and the denominator for each fraction is 12. The lower the numerator, the closer it will be to zero and higher the numerator, the closer it will be to 1. So, the smallest fraction is $\frac{23}{35}$.
The second smallest is $\frac{31}{43}$.

Given $\frac{2a+b}{a+4b}$=3

=>$2a+3b=3a+12b$

$=>a=-11b$

Substituting this in $\frac{a+b}{a+2b}$

=$\frac{-10b}{9b}$

=$\frac{10}{9}$

$\frac{3}{4}\times \frac{16}{27} \div \frac{2}{3}$ = $\frac{3}{4}\times \frac{16}{27} \times \frac{3}{2}$ = $\frac{4}{9} \times \frac{3}{2} = \frac{2}{3}$

So the answer is option A.

$\frac{75\times75-26\times26}{101}$ = $\frac{75^{2}-26^{2}}{101}$

==>$\frac{(75+26)(75-26)}{101}$ ( $\because a^{2}-b^{2}=(a+b)(a-b)$)

= $\frac{101\times49}{101} = 49$

$\frac{3}{5}\times75$ = 45

$\frac{4}{5}\times 77$ = 44

$\therefore$ 45 is greater than 44 by 1

Given : $x=y=z$

Let $x=y=z=k$

To find : $\ \frac{(x+y+z)^{2}}{x^{2}+y^{2}+z^{2}}\$

= $\frac{(k+k+k)^2}{k^2+k^2+k^2}$

= $\frac{(3k)^2}{3k^2}$

= $\frac{9k^2}{3k^2}=3$

=> Ans – (B)

$\dfrac{2}{5}$ = 0.4

$\dfrac{3}{11}$ = 0.27

$\dfrac{1}{6}$ = 0.16

$\dfrac{4}{13}$ = 0.30

Hence, $\dfrac{4}{13}$ is the largest.

Number = $0.\overline{39}$

Let $x=0.\overline{39}$ ————(i)

=> $100x=39.\overline{39}$ ————(ii)

Subtracting equation (i) from (ii),

=> $100x-x=39.39-0.39$

=> $99x=39$

=> $x=\frac{39}{99}=\frac{13}{33}$

=> Ans – (C)

Given : $\frac{a}{b}=\frac{c}{d}=5$

Let $a=c=5$ and $b=d=1$

To find : $\frac{3a+4c}{3b+4d}$

= $\frac{3(5)+4(5)}{3(1)+4(1)}$

= $\frac{15+20}{3+4}$

= $\frac{35}{7}=5$

=> Ans – (C)

Expression = $n+n+\frac{3n}{2}+\frac{9n}{4}+………\infty$

= $n+(n+\frac{3n}{2}+\frac{9n}{4}+………\infty)$

It is a geometric progression with common ratio, $r=\frac{3}{2}$ and first term, $a=n$

$\because$ The common ratio is greater than 1, => Sum will tend to infinity.

=> Ans – (D)

Let the fraction be $x$

According to ques,

=> $x+\frac{1}{x}=\frac{113}{56}$

=> $\frac{x^2+1}{x}=\frac{113}{56}$

=> $56x^2-113x+56=0$

=> $56x^2-49x-64x+56=0$

=> $7x(8x-7)-8(8x-7)=0$

=> $(7x-8)(8x-7)=0$

=> $x=\frac{8}{7},\frac{7}{8}$

=> Ans – (A)

Given : $a^{2}+b^{2}=80$ ———-(i) and $ab=32$

=> $2ab=64$ ———–(ii)

Adding equations (i) and (ii), we get :

=> $a^2+b^2+2ab=80+64$

=> $(a+b)^2=144$

=> $(a+b)=\sqrt{144}=12$

Similarly, $(a-b)=4$

$\therefore$ $\frac{a-b}{a+b}$

= $\frac{4}{12}=0.333$

=> Ans – (C)

We hope this Decimal Fraction Questions for RRB JE Exam will be highly useful for your preparation