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STD 11 - 5. linear inequalities — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 5. linear inequalities4 Marks
MCQ
Let $a, b, c, d, e$ be real numbers such that $a + b < c + d$, $b + c < d + e, c + d < e + a, d + e < a + b$. Then,
  • ✓
    the largest is $a$ and the smallest is $b$.
  • B
    the largest is $a$ and the smallest is $c$.
  • C
    the largest is $c$ and the smallest is $e$.
  • D
    the largest is $c$ and the smallest is $b$.
✓

Answer

Correct option: A.
the largest is $a$ and the smallest is $b$.
a
(a)

Given,

$a + b < c + d \ldots \text { (i) }$

$b + c < d + e \ldots \text { (ii) }$

$c + d < e + a \ldots \text { (iii) }$

$d + e < a + b \ldots \text { (iv) }$

From Eqs.$(i)$ and $(iii)$, we get

$a + b + c + d  < c + d + e + a$

$b < e$

From Eqs.$(ii)$ and $(iv)$, we get

$b + c + d + e$ $ < d + c < a + b$

$c < a$

$\text { From Eqs. (i) and (iv), we get }$

$a + b + d + e$ $< c + d + a + b$

$e < c$

From Eqs. $(v), (vi), (vii)$, we get

$a > c > e > b$

$\therefore$ Largest value is $a$ and smallest value is $b$.

 

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