CUET UG 2025 — General Test Quantitative Reasoning

Two lines are parallel when they have the same slope.

Line 1: $px + 3y + 5 = 0$px+3y+5=0

Line 2: $8x + 2y - 3 = 0$8x+2y−3=0

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Converting Line 2 to slope-intercept form:

$$8x + 2y - 3 = 0$$8x+2y−3=0

$$2y = -8x + 3$$2y=−8x+3

$$y = -4x + \dfrac{3}{2}$$y=−4x+23​

Slope of Line 2 is $-4$−4.

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Converting Line 1 to slope-intercept form:

$$px + 3y + 5 = 0$$px+3y+5=0

$$3y = -px - 5$$3y=−px−5

$$y = -\dfrac{p}{3}x - \dfrac{5}{3}$$y=−3p​x−35​

Slope of Line 1 is $-\dfrac{p}{3}$−3p​.

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For the lines to be parallel, their slopes must be equal:

$$-\dfrac{p}{3} = -4$$−3p​=−4

$$p = 12$$p=12

Therefore, $p = 12$p=12.