CUET UG 2025 — Mathematics Algebra

The region is bounded by $y = x + 2$y=x+2, $x = 0$x=0, $x = 1$x=1, and $y = 0$y=0.

Key points on the line $y = x + 2$y=x+2:

When $x = 0$x=0:

$$y = 0 + 2 = 2$$y=0+2=2

Point: $(0, 2)$(0,2)

When $x = 1$x=1:

$$y = 1 + 2 = 3$$y=1+2=3

Point: $(1, 3)$(1,3)

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The bounded region forms a trapezoid with:

Bottom side: along the x-axis from $(0,0)$(0,0) to $(1,0)$(1,0)

Left side: vertical line from $(0,0)$(0,0) to $(0,2)$(0,2) with height $= 2$=2

Right side: vertical line from $(1,0)$(1,0) to $(1,3)$(1,3) with height $= 3$=3

Top side: line $y = x + 2$y=x+2

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Using the trapezoid area formula:

Area $= \dfrac{1}{2} \times (\text{sum of parallel sides}) \times \text{width}$=21​×(sum of parallel sides)×width

Sum of parallel sides $= 2 + 3 = 5$=2+3=5

Width $= 1 - 0 = 1$=1−0=1

Area $= \dfrac{1}{2} \times 5 \times 1$=21​×5×1

Area $= \dfrac{5}{2}$=25​ sq. units