Question 16

Arrange the following in descending order :
A: $$\sqrt{401} -\sqrt{399}$$
B: $$\sqrt{301} -\sqrt{299}$$
C: $$\sqrt{101} -\sqrt{99}$$
D: $$\sqrt{201} -\sqrt{199}$$

A:Β $$\sqrt{401} -\sqrt{399}$$ =Β $$\dfrac{2}{\sqrt{\ 401}+\sqrt{\ 399}}$$

B:Β $$\sqrt{301} -\sqrt{299}$$ =Β $$\dfrac{2}{\sqrt{\ 301}+\sqrt{\ 299}}$$

C:Β $$\sqrt{101} -\sqrt{99}$$ =Β $$\dfrac{2}{\sqrt{\ 101}+\sqrt{\ 99}}$$

D:Β $$\sqrt{201} -\sqrt{199}$$ =Β $$\dfrac{2}{\sqrt{\ 201}+\sqrt{\ 199}}$$

Now,Β $$\sqrt{\ 401}+\sqrt{\ 399}>\sqrt{\ 301}+\sqrt{\ 299}>\sqrt{\ 201}+\sqrt{\ 199}>\sqrt{\ 101}+\sqrt{\ 99}$$

or,Β $$\dfrac{2}{\sqrt{\ 401}+\sqrt{\ 399}}<\dfrac{2}{\sqrt{\ 301}+\sqrt{\ 299}}<\dfrac{2}{\sqrt{\ 201}+\sqrt{\ 199}}<\dfrac{2}{\sqrt{\ 101}+\sqrt{\ 99}}$$

So, $$A<B<D<C$$

or, $$C>D>B>A$$

So, option D is the correct answer.

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