If a, b, c, d are four distinct numbers chose | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) To minimize the sum $\frac{a}{b} + \frac{c}{d}$ where $a, b, c, d$ are distinct elements from $\{1, 2, 3, \ldots, 9\}$,we should choose the smalle

Vedclass · Accepted Answer

$\frac{25}{72}$

Vedclass · Answer

(D) To minimize the sum $\frac{a}{b} + \frac{c}{d}$ where $a, b, c, d$ are distinct elements from $\{1, 2, 3, \ldots, 9\}$,we should choose the smallest possible values for the numerators $a$ and $c$ and the largest possible values for the denominators $b$ and $d$.Let the set of values be $S = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$.We choose $a=1, c=2$ (or vice versa) and $b=9, d=8$ (or vice versa).Then,the sum is $\frac{1}{9} + \frac{2}{8} = \frac{1}{9} + \frac{1}{4} = \frac{4+9}{36} = \frac{13}{36}$.Alternatively,if we choose $a=2, c=1$ and $b=9, d=8$,we get $\frac{2}{9} + \frac{1}{8} = \frac{16+9}{72} = \frac{25}{72}$.Comparing the values,$\frac{13}{36} = \frac{26}{72}$,which is greater than $\frac{25}{72}$.Thus,the minimum value is $\frac{25}{72}$.

If $a, b, c, d$ are four distinct numbers chosen from the set $\{1, 2, 3, \ldots, 9\}$,then the minimum value of $\frac{a}{b} + \frac{c}{d}$ is

Similar Questions

$A$ regular polygon of $n$ sides has $170$ diagonals,then $n$ is equal to

$110$ triangles can be formed by joining $10$ points as vertices,in which $n$ points are collinear. Then the value of $n$ is:

If the number of diagonals in a polygon with $n$ sides is $275$,then $n = .....$

Let $p_n$ denote the total number of triangles formed by joining the vertices of an $n$-sided regular polygon. If $p_{n+1} - p_n = 66$, then the sum of all distinct prime divisors of $n$ is:

If a polygon has $44$ diagonals,then it has ...... sides.

Vedclass Test Series

Exam Paper Generator

Online Exam Module