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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: $$\sqrt{401} -\sqrt{399}$$ = $$\dfrac{2}{\sqrt{\ 401}+\sqrt{\ 399}}$$
B: $$\sqrt{301} -\sqrt{299}$$ = $$\dfrac{2}{\sqrt{\ 301}+\sqrt{\ 299}}$$
C: $$\sqrt{101} -\sqrt{99}$$ = $$\dfrac{2}{\sqrt{\ 101}+\sqrt{\ 99}}$$
D: $$\sqrt{201} -\sqrt{199}$$ = $$\dfrac{2}{\sqrt{\ 201}+\sqrt{\ 199}}$$
Now, $$\sqrt{\ 401}+\sqrt{\ 399}>\sqrt{\ 301}+\sqrt{\ 299}>\sqrt{\ 201}+\sqrt{\ 199}>\sqrt{\ 101}+\sqrt{\ 99}$$
or, $$\dfrac{2}{\sqrt{\ 401}+\sqrt{\ 399}}<\dfrac{2}{\sqrt{\ 301}+\sqrt{\ 299}}<\dfrac{2}{\sqrt{\ 201}+\sqrt{\ 199}}<\dfrac{2}{\sqrt{\ 101}+\sqrt{\ 99}}$$
So, $$A<B<D<C$$
or, $$C>D>B>A$$
So, option D is the correct answer.
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