CUET PG 2025 — Mathematics PYQ

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Question

CUET PG 2025 — Mathematics PYQ

CUET PG | Mathematics | 2025

If the line through (3, y) and (2, 7) is parallel to the line through (-2, 4) and (0, 6), then the value of y is:

Choose the correct answer:

Explanation

1. Slope ka Formula

Kisi bhi do points $(x_1, y_1)$ aur $(x_2, y_2)$ se guzarne wali line ka slope ( $m$ ) nikaalne ka formula hai:

m = \frac{y_2 - y_1}{x_2 - x_1}

2. Step-by-Step Solution

Pehli line ka slope ( $m_1$ ):

Points hain $(3, y)$ aur $(2, 7)$ .

m_1 = \frac{7 - y}{2 - 3}

m_1 = \frac{7 - y}{-1} = y - 7

Dusri line ka slope ( $m_2$ ):

Points hain $(-2, 4)$ aur $(0, 6)$ .

m_2 = \frac{6 - 4}{0 - (-2)}

m_2 = \frac{2}{0 + 2} = \frac{2}{2} = 1

3. Value nikaalna

Kyunki dono lines parallel hain, isliye unke slopes barabar honge ( $m_1 = m_2$ ):

y - 7 = 1

Ab $7$ ko barabar ke dusri taraf le jaane par:

y = 1 + 7

y = 8

Answer:

$y$ ki value $8$ hai.