Practice Problems based on continued fraction - quantitative aptitude Online Quiz (set-1) For All Competitive Exams
Q-1) Find the value of $2/{1+1/{1-{1/2}}} × 3/{{5/6} of {3/2} ÷ 1{1/4}}$
(a)
(b)
(c)
(d)
$2/{1+1/{1-{1/2}}} × 3/{{5/6} of {3/2} ÷ 1{1/4}}$
$2/{1+1/{1/2}} × 3/{({5/6 × 3/2}) ÷ {5/4}}$
= $2/{1 + 2} × 3/{{5/4}÷{5/4}}$
= $2/3×3/{{5/4}×{4/5}} = {2/3}×3 = 2$
Q-2) The value of $1 - a/{1-1/{1+{a/{1 - a}}}}$ is
(a)
(b)
(c)
(d)
Expression = $1 - a/{1-1/{1+{a/{1 - a}}}}$
= $1 - a/{1-{1/{{1 - a+a}/{1 - a}}}}$
= $1 - a/{1 - {1/{1/{1 - a}}}}$
= $1 - a/{1 - (1 - a)} = 1-a/{1 - 1+a}$
= 1 - 1 = 0
Q-3) If x = $1+1/{1+1/{1+1/{1+{1/2}}}}$ then, the value of $2x + 7/4$ is :
(a)
(b)
(c)
(d)
$x = 1+1/{1+1/{1+1/{1+{1/2}}}}$
= $1+1/{1+1/{1+1/{3/2}}} = 1+1/{1+1/{1+{2/3}}}$
= $1 + 1/{1 + {1/{5/3}}} = 1 + 1/{1+{3/5}}$
= $1 + 1/{8/5} = 1 + {5/8} = 13/8$
$2x + 7/4 = 2 ×13/8 + 7/4$
= ${13 + 7}/4 = 20/4 =5$
Q-4) $√{{4{1/7} - 2{1/4}}/{3{1/2} + 1{1/7}} ÷ {2/{2+1/{2+1/{5-{1/5}}}}}}$ is equal to
(a)
(b)
(c)
(d)
${4{1/7} - 2{1/4}}/{3{1/2}+1{1/7}} = {29/7 - 9/4}/{7/2 +8/7}$
= ${{116 - 63}/28}/{{49+16}/14} = 53/28 ×14/65 = 53/130$
Again,
$1/{2+1/{2+{1/{{25 - 1}/5}}}} =1/{2+1/{2+{5/24}}}$
= $1/{2+{1/{{48+5}/24}}} = 1/{2+{24/53}}$
$1/{{106+24}/53} = 53/130$
Expression = $√{{53/130} ÷ {53/130}} = 1$
Q-5) The value of $1/{3 + 1/{2 - 1/{7/9}}} + 17/22$ is :
(a)
(b)
(c)
(d)
$1/{3 + 1/{2 - {1/{7/9}}}} + 17/22$
= $1/{3 + 1/{2 - {9/7}}} + 17/22$
= $1/{3 + 1/{{14 - 9}/7}} + 17/22$
= $1/{3 + {1/{5/7}}} + 17/22 = 1/{3 + {7/5}} + 17/22$
= $1/{{15+7}/5} + 17/22$
= $5/22 + 17/2 = 22/22 = 1$
Q-6) ${5{9/14}}/{5 + 3/{3 + {1/{3/5}}}}$ is equal to
(a)
(b)
(c)
(d)
${79/14}/{5 + 3/{3 + {5/3}}}$
= ${79/14}/{5 + 3/{{9 + 5}/3}}$
= ${79/14}/{5 + {9/14}} = {79/14}/{{70 + 9}/14}$
= $79/14 × 14/79 = 1$
Q-7) ${4{2/7} - {1/2}}/{3{1/2} + 1{1/7}}$ ÷ $1/{2+1/{2+1/{5-{1/5}}}}$ is equal to
(a)
(b)
(c)
(d)
First part = ${30/7 - 1/2}/{7/2 + 8/7}$
= ${{60 - 7}/14}/{{49+16}/14} = {53/14} × 14/65 = 53/65$
Second part = $1/{2+1/{2+{1/{{25 - 1}/5}}}}$
= $1/{2+1/{2+{5/24}}} = 1/{2+{1/{{48+5}/24}}}$
= $1/{2+{24/53}} = 1/{{106+24}/53} = 53/130$
Expression = ${53/65} ÷ {53/130} = 53/65 × 130/53 = 2$
Q-8) The value of $1+1/{1+1/{1+1/{1+1/{1+{2/3}}}}$ is
(a)
(b)
(c)
(d)
Expression
$1+1/{1+1/{1+1/{1+1/{1+{2/3}}}}$
= $1+1/{1+1/{1+1/{1+{1/{3+2}/3}}}}$
= $1+1/{1+1/{1+1/{1+ {3/5}}}}$
= $1+1/{1+1/{1+{1/{{5+3}/5}}}}$
= $1+1/{1+1/{1+{5/8}}}$
= $1+1/{1+{1/{{8+5}/8}}}$
= $1+1/{1+{8/13}} = 1+1/{{13+8}/13}$
= $1+{13/21} = {21+13}/21 = 34/21$
Q-9) The simplification of $5/{3+3/{1-{2/3}}}$ gives
(a)
(b)
(c)
(d)
$5/{3+3/{1-{2/3}}}$
$5/{3+3/{{3 - 2}/3}} = 5/{3 + {3/{1/3}}}$
$5/{3 + 3 × 3} = 5/{3 + 9} = 5/12$
Q-10) $1 + 1/{1+{1/2}}$ is equal to
(a)
(b)
(c)
(d)
Expression = $1 + 1/{1 + {1/2}}$
= $1 + 1/{{2+1}/2} = 1+{2/3}$
= ${3 + 2}/3 = 5/3$