9:{"metadata":[["$","title","0",{"children":"CUET Mathematics 2024 - The area of the region bounded by the lines x+2 y=12, x=2, x=6 and x-axis is : | PYQs + Solutions | AfterBoards"}],["$","meta","1",{"name":"description","content":"undefined Identifying the region by finding the intersection points: - The x-axis corresponds to y=0 - When y=0 in x+2y=12, we >=t x=12 - Our region is bounded by x=2 and x=6, which are vertical lines

Expressing y in terms of x for the sloped boundary: From x+2y=12, I can solve for y: 2y = 12-x y = 12-x2 = 6-x2

Finding intersection points to define the region comp<=tely: At x=2: y = 6-22 = 5 At x=6: y = 6-62 = 3

Calculating the area using integration: Area = _2^6 (6-x2) dx Area = [6x - x^24]_2^6 Area = (6(6) - 6^24) - (6(2) - 2^24) Area = (36 - 364) - (12 - 44) Area = (36 - 9) - (12 - 1) Area = 27 - 11 = 16

Alternatively, using the trapezoid formula: Area = 12 width (height_1 + height_2) = 12 4 (5 + 3) = 16 Therefore, the area of the region is 16 square units."}],["$","link","2",{"rel":"manifest","href":"https://www.afterboards.in/manifest.json","crossOrigin":"$undefined"}],["$","meta","3",{"name":"keywords","content":"CUETMAT,MAT,Calculus,Application of Integrals"}],["$","meta","4",{"name":"robots","content":"index, follow"}],["$","meta","5",{"name":"category","content":"education"}],["$","meta","6",{"name":"google-site-verification","content":"google"}],["$","meta","7",{"property":"og:title","content":"CUET Mathematics 2024 - The area of the region bounded by the lines x+2 y=12, x=2, x=6 and x-axis is : | PYQs + Solutions"}],["$","meta","8",{"property":"og:description","content":"undefined Identifying the region by finding the intersection points: - The x-axis corresponds to y=0 - When y=0 in x+2y=12, we >=t x=12 - Our region is bounded by x=2 and x=6, which are vertical lines

Expressing y in terms of x for the sloped boundary: From x+2y=12, I can solve for y: 2y = 12-x y = 12-x2 = 6-x2

Finding intersection points to define the region comp<=tely: At x=2: y = 6-22 = 5 At x=6: y = 6-62 = 3

Calculating the area using integration: Area = _2^6 (6-x2) dx Area = [6x - x^24]_2^6 Area = (6(6) - 6^24) - (6(2) - 2^24) Area = (36 - 364) - (12 - 44) Area = (36 - 9) - (12 - 1) Area = 27 - 11 = 16

Alternatively, using the trapezoid formula: Area = 12 width (height_1 + height_2) = 12 4 (5 + 3) = 16 Therefore, the area of the region is 16 square units."}],["$","meta","9",{"property":"og:url","content":"https://www.afterboards.in/cuet-past-year-questions/cuet-mat-2024-01/4"}],["$","meta","10",{"property":"og:site_name","content":"AfterBoards | CUET Preparation"}],["$","meta","11",{"property":"og:image","content":"https://www.afterboards.in/pyp/AfterBoards%20CUET%20Past%20Year%20Papers%20with%20Solutions.webp"}],["$","meta","12",{"property":"og:type","content":"website"}],["$","meta","13",{"name":"twitter:card","content":"summary_large_image"}],["$","meta","14",{"name":"twitter:site","content":"afterboards.in"}],["$","meta","15",{"name":"twitter:title","content":"CUET Mathematics 2024 - The area of the region bounded by the lines x+2 y=12, x=2, x=6 and x-axis is : | PYQs + Solutions"}],["$","meta","16",{"name":"twitter:description","content":"undefined Identifying the region by finding the intersection points: - The x-axis corresponds to y=0 - When y=0 in x+2y=12, we >=t x=12 - Our region is bounded by x=2 and x=6, which are vertical lines

Expressing y in terms of x for the sloped boundary: From x+2y=12, I can solve for y: 2y = 12-x y = 12-x2 = 6-x2

Finding intersection points to define the region comp<=tely: At x=2: y = 6-22 = 5 At x=6: y = 6-62 = 3

Calculating the area using integration: Area = _2^6 (6-x2) dx Area = [6x - x^24]_2^6 Area = (6(6) - 6^24) - (6(2) - 2^24) Area = (36 - 364) - (12 - 44) Area = (36 - 9) - (12 - 1) Area = 27 - 11 = 16

Alternatively, using the trapezoid formula: Area = 12 width (height_1 + height_2) = 12 4 (5 + 3) = 16 Therefore, the area of the region is 16 square units."}],"$L18","$L19","$L1a","$L1b","$L1c","$L1d","$L1e","$L1f","$L20","$L21"],"error":null,"digest":"$undefined"}

CUET Mathematics 2024 PYQs

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