MAH-CET 2025 — Mathematics PYQ

Solution

1. Equation ko Samajhna

Humein diya gaya hai:

Jahan $x,y\in \mathbb{Z}$ (integers).

2. Domain ki Definition

Relation $R$ ka Domain un sabhi $x$ values ka set hota hai jiske liye equation solve ho sake.

Equation se hum $y^2$ ki value nikaalte hain:

3. Integers ki Values Check Karna

Kyuki $y^2$ hamesha positive ya zero hota hai ($y^2\ge 0$), iska matlab:

Ab hum $x$ ki alag-alag integer values rakh kar check karte hain ki kya humein $y$ ke liye ek integer mil raha hai:

• Agar $x=0$:

  $0^2+y^2=9⟹y^2=9⟹y=\pm 3$ (Integers hain)

• Agar $x=\pm 1$:

  $1^2+y^2=9⟹y^2=8⟹y=\pm \sqrt{8}$ (Integer nahi hai)

• Agar $x=\pm 2$:

  $2^2+y^2=9⟹y^2=5⟹y=\pm \sqrt{5}$ (Integer nahi hai)

• Agar $x=\pm 3$:

  $3^2+y^2=9⟹y^2=0⟹y=0$ (Integer hai)

• Agar x > 3 ya x < -3:

  $x^2$ ki value $9$ se zyada ho jayegi, jisse $y^2$ negative ho jayega (Jo possible nahi hai).

Final Domain

Sirf $0,3,$ aur $-3$ hi aisi integer values hain jo humein $y$ ke liye integer output de rahi hain.