Question : Which of the following statement(s) is/are TRUE? I. $\sqrt{11}+\sqrt7<\sqrt{10}+\sqrt8$ II. $\sqrt{17}+\sqrt{11}>\sqrt{15}+\sqrt{13}$
Option 1: Only I
Option 2: Only II
Option 3: Both I and II
Option 4: Neither I nor II
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Correct Answer: Only I
Solution : Evaluating the given statements: I. $\sqrt{11}+\sqrt7<\sqrt{10}+\sqrt8$ Squaring both sides we get: ⇒ $(\sqrt{11}+\sqrt7)^2<(\sqrt{10}+\sqrt8)^2$ ⇒ $11+7+2\sqrt{77}<10+8+2\sqrt{80}$ ⇒ $18+2\sqrt{77}<18+2\sqrt{80}$ So, statement I is true. II. $\sqrt{17}+\sqrt{11}>\sqrt{15}+\sqrt{13}$ Squaring both sides we get: ⇒ $(\sqrt{17}+\sqrt{11})^2>(\sqrt{15}+\sqrt{13})^2$ ⇒ $17+11+2\sqrt{187}>15+13+2\sqrt{195}$ ⇒ $28+2\sqrt{187}>28+2\sqrt{195}$ So, statement II is wrong. Hence, the correct answer is 'Only I'.
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