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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Let Z be the set of all integers, and consider the sets $X=\{(x,y)\colon{x}^2+2{y}^2=3,\, x,y\in Z\}$ and $Y=\{(x,y)\colon x{\gt}y,\, x,y\in Z\}$. Then the number of elements in $X\cap Y$ is:
Solution
Given: $$x^2 + 2y^2 = 3 \text{ and } x > y \text{ with } x, y \in \mathbb{Z}$$
Solutions to the equation are: $$\{(1,1), (1,-1), (-1,1), (-1,-1)\}$$
Among them, only \( (1, -1) \) satisfies \( x > y \).
Answer: $$\boxed{1}$$
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