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JEE Advanced 2025 — Paper 2 (Mathematics) Solutions

Step-by-step mathematical proofs, multi-correct partial marking evaluation, and interactive practice for Paper 2.

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Mathematics Questions (17 Questions)

Interactive Partial Marking Mode
Q35Paper 2MathematicsOne or More Correct (Partial Marking)Tough / Advanced
Advanced Calculus & Differential Equations
Scoring Scheme: +4 Full Marks • -2 Negative Marks • Partial Marking Enabled
[JEE Advanced 2025 Paper 2 Mathematics Q35] Let a family of orthogonal trajectories be defined by the second order nonlinear differential equation y′′+(y′)2+y=0y'' + (y')^2 + y = 0. Evaluate the analytical solution properties:
Select one or more options, then click "Submit Choices":
Q36Paper 2MathematicsOne or More Correct (Partial Marking)Tough / Advanced
Advanced Calculus & Differential Equations
Scoring Scheme: +4 Full Marks • -2 Negative Marks • Partial Marking Enabled
[JEE Advanced 2025 Paper 2 Mathematics Q36] Let a family of orthogonal trajectories be defined by the second order nonlinear differential equation y′′+(y′)2+y=0y'' + (y')^2 + y = 0. Evaluate the analytical solution properties:
Select one or more options, then click "Submit Choices":
Q37Paper 2MathematicsOne or More Correct (Partial Marking)Tough / Advanced
Advanced Calculus & Differential Equations
Scoring Scheme: +4 Full Marks • -2 Negative Marks • Partial Marking Enabled
[JEE Advanced 2025 Paper 2 Mathematics Q37] Let a family of orthogonal trajectories be defined by the second order nonlinear differential equation y′′+(y′)2+y=0y'' + (y')^2 + y = 0. Evaluate the analytical solution properties:
Select one or more options, then click "Submit Choices":
Q38Paper 2MathematicsOne or More Correct (Partial Marking)Tough / Advanced
Advanced Calculus & Differential Equations
Scoring Scheme: +4 Full Marks • -2 Negative Marks • Partial Marking Enabled
[JEE Advanced 2025 Paper 2 Mathematics Q38] Let a family of orthogonal trajectories be defined by the second order nonlinear differential equation y′′+(y′)2+y=0y'' + (y')^2 + y = 0. Evaluate the analytical solution properties:
Select one or more options, then click "Submit Choices":
Q39Paper 2MathematicsOne or More Correct (Partial Marking)Tough / Advanced
Advanced Calculus & Differential Equations
Scoring Scheme: +4 Full Marks • -2 Negative Marks • Partial Marking Enabled
[JEE Advanced 2025 Paper 2 Mathematics Q39] Let a family of orthogonal trajectories be defined by the second order nonlinear differential equation y′′+(y′)2+y=0y'' + (y')^2 + y = 0. Evaluate the analytical solution properties:
Select one or more options, then click "Submit Choices":
Q40Paper 2MathematicsOne or More Correct (Partial Marking)Tough / Advanced
Advanced Calculus & Differential Equations
Scoring Scheme: +4 Full Marks • -2 Negative Marks • Partial Marking Enabled
[JEE Advanced 2025 Paper 2 Mathematics Q40] Let a family of orthogonal trajectories be defined by the second order nonlinear differential equation y′′+(y′)2+y=0y'' + (y')^2 + y = 0. Evaluate the analytical solution properties:
Select one or more options, then click "Submit Choices":
Q41Paper 2MathematicsNumerical Value TypeTough / Advanced
Advanced Calculus & Differential Equations
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2025 Paper 2 Mathematics Q41] Let a family of orthogonal trajectories be defined by the second order nonlinear differential equation y′′+(y′)2+y=0y'' + (y')^2 + y = 0. Evaluate the analytical solution properties:
Q42Paper 2MathematicsNumerical Value TypeTough / Advanced
Advanced Calculus & Differential Equations
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2025 Paper 2 Mathematics Q42] Let a family of orthogonal trajectories be defined by the second order nonlinear differential equation y′′+(y′)2+y=0y'' + (y')^2 + y = 0. Evaluate the analytical solution properties:
Q43Paper 2MathematicsNumerical Value TypeTough / Advanced
Advanced Calculus & Differential Equations
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2025 Paper 2 Mathematics Q43] Let a family of orthogonal trajectories be defined by the second order nonlinear differential equation y′′+(y′)2+y=0y'' + (y')^2 + y = 0. Evaluate the analytical solution properties:
Q44Paper 2MathematicsNumerical Value TypeTough / Advanced
Advanced Calculus & Differential Equations
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2025 Paper 2 Mathematics Q44] Let a family of orthogonal trajectories be defined by the second order nonlinear differential equation y′′+(y′)2+y=0y'' + (y')^2 + y = 0. Evaluate the analytical solution properties:
Q45Paper 2MathematicsNumerical Value TypeTough / Advanced
Advanced Calculus & Differential Equations
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2025 Paper 2 Mathematics Q45] Let a family of orthogonal trajectories be defined by the second order nonlinear differential equation y′′+(y′)2+y=0y'' + (y')^2 + y = 0. Evaluate the analytical solution properties:
Q46Paper 2MathematicsNumerical Value TypeTough / Advanced
Advanced Calculus & Differential Equations
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2025 Paper 2 Mathematics Q46] Let a family of orthogonal trajectories be defined by the second order nonlinear differential equation y′′+(y′)2+y=0y'' + (y')^2 + y = 0. Evaluate the analytical solution properties:
Q47Paper 2MathematicsSingle Correct OptionTough / Advanced
Advanced Calculus & Differential Equations
Scoring Scheme: +3 Full Marks • -1 Negative Marks
[JEE Advanced 2025 Paper 2 Mathematics Q47] Let a family of orthogonal trajectories be defined by the second order nonlinear differential equation y′′+(y′)2+y=0y'' + (y')^2 + y = 0. Evaluate the analytical solution properties:
Q48Paper 2MathematicsSingle Correct OptionTough / Advanced
Advanced Calculus & Differential Equations
Scoring Scheme: +3 Full Marks • -1 Negative Marks
[JEE Advanced 2025 Paper 2 Mathematics Q48] Let a family of orthogonal trajectories be defined by the second order nonlinear differential equation y′′+(y′)2+y=0y'' + (y')^2 + y = 0. Evaluate the analytical solution properties:
Q49Paper 2MathematicsSingle Correct OptionTough / Advanced
Advanced Calculus & Differential Equations
Scoring Scheme: +3 Full Marks • -1 Negative Marks
[JEE Advanced 2025 Paper 2 Mathematics Q49] Let a family of orthogonal trajectories be defined by the second order nonlinear differential equation y′′+(y′)2+y=0y'' + (y')^2 + y = 0. Evaluate the analytical solution properties:
Q50Paper 2MathematicsSingle Correct OptionTough / Advanced
Advanced Calculus & Differential Equations
Scoring Scheme: +3 Full Marks • -1 Negative Marks
[JEE Advanced 2025 Paper 2 Mathematics Q50] Let a family of orthogonal trajectories be defined by the second order nonlinear differential equation y′′+(y′)2+y=0y'' + (y')^2 + y = 0. Evaluate the analytical solution properties:
Q51Paper 2MathematicsSingle Correct OptionTough / Advanced
Advanced Calculus & Differential Equations
Scoring Scheme: +3 Full Marks • -1 Negative Marks
[JEE Advanced 2025 Paper 2 Mathematics Q51] Let a family of orthogonal trajectories be defined by the second order nonlinear differential equation y′′+(y′)2+y=0y'' + (y')^2 + y = 0. Evaluate the analytical solution properties: