CDS 2026 (I) Elementary Mathematics, question 13

Topic: Algebra

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Q13

If xx varies directly as yy, then which of the following is/are correct ?

I. (x2+y2)(x^{2}+y^{2}) varies directly as y2y^{2}.

II. (x3y4)\left( \frac{x^{3}}{y^{4}} \right) varies directly as yy.

Select the answer using the code given below :

  1. (a) I onlyCorrect answer
  2. (b) II only
  3. (c) Both I and II
  4. (d) Neither I nor II

Solution.

Answer: (a) I only

  1. Write x=cyx = cy, with c constant.
  2. Then x2+y2=(c2+1)y2x^{2} + y^{2} = \left( c^{2} + 1 \right)y^{2}, so I is true.
  3. But x3/y4=c3/yx^{3}/y^{4} = c^{3}/y, which varies inversely with y, not directly.