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JEE Advanced 2016 — Paper 1 (Mathematics) Solutions

Step-by-step mathematical proofs, multi-correct partial marking evaluation, and interactive practice for Paper 1.

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Mathematics Questions (17 Questions)

Interactive Partial Marking Mode
Q35Paper 1MathematicsOne or More Correct (Partial Marking)Hard
Integral Calculus (Definite Integrals & Differential Equations)
Scoring Scheme: +4 Full Marks • -2 Negative Marks • Partial Marking Enabled
[JEE Advanced 2016 Paper 1 Mathematics Q35] Let f:(0,∞)→Rf: (0, \infty) \to \mathbb{R} be a differentiable function satisfying f(1)=1f(1) = 1 and x∫1xf(t)dt=(x+1)∫1xtf(t)dtx \int_1^x f(t) dt = (x+1) \int_1^x t f(t) dt for all x>0x > 0. Which of the following statements is/are CORRECT?
Select one or more options, then click "Submit Choices":
Practice JEE Main Level (Integral Calculus (Definite Integrals & Differential Equations))
Q36Paper 1MathematicsNumerical Value TypeMedium
Vectors and 3D Geometry
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2016 Paper 1 Mathematics Q36] Find the shortest distance between the two skew straight lines L1:r⃗1=(i^+2j^+3k^)+λ(2i^+3j^+4k^)L_1: \vec{r}_1 = (\hat{i} + 2\hat{j} + 3\hat{k}) + \lambda (2\hat{i} + 3\hat{j} + 4\hat{k}) and L2:r⃗2=(2i^+4j^+5k^)+μ(3i^+4j^+5k^)L_2: \vec{r}_2 = (2\hat{i} + 4\hat{j} + 5\hat{k}) + \mu (3\hat{i} + 4\hat{j} + 5\hat{k}). Give the exact distance squared (d2d^2).
Practice JEE Main Level (Vectors and 3D Geometry)
Q37Paper 1MathematicsOne or More Correct (Partial Marking)Hard
Complex Numbers & Quadratic Equations
Scoring Scheme: +4 Full Marks • -2 Negative Marks • Partial Marking Enabled
[JEE Advanced 2016 Paper 1 Mathematics Q37] Let the mathematical relation governing Geometry of Circles and Apollonius Circles in Complex Plane in Complex Numbers & Quadratic Equations be defined over its maximal domain. Evaluate the mathematical properties:
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Practice JEE Main Level (Complex Numbers & Quadratic Equations)
Q38Paper 1MathematicsOne or More Correct (Partial Marking)Tough / Advanced
Matrices and Determinants
Scoring Scheme: +4 Full Marks • -2 Negative Marks • Partial Marking Enabled
[JEE Advanced 2016 Paper 1 Mathematics Q38] Let the mathematical relation governing Cayley-Hamilton Theorem and Inverse of Orthogonal Matrices in Matrices and Determinants be defined over its maximal domain. Evaluate the mathematical properties:
Select one or more options, then click "Submit Choices":
Practice JEE Main Level (Matrices and Determinants)
Q39Paper 1MathematicsOne or More Correct (Partial Marking)Hard
Probability & Statistics
Scoring Scheme: +4 Full Marks • -2 Negative Marks • Partial Marking Enabled
[JEE Advanced 2016 Paper 1 Mathematics Q39] Let the mathematical relation governing Bayes Theorem in Multi-Urn Sampling with Replacement in Probability & Statistics be defined over its maximal domain. Evaluate the mathematical properties:
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Practice JEE Main Level (Probability & Statistics)
Q40Paper 1MathematicsOne or More Correct (Partial Marking)Tough / Advanced
Permutations and Combinations
Scoring Scheme: +4 Full Marks • -2 Negative Marks • Partial Marking Enabled
[JEE Advanced 2016 Paper 1 Mathematics Q40] Let the mathematical relation governing Derangements and Multinomial Distribution Coefficients in Permutations and Combinations be defined over its maximal domain. Evaluate the mathematical properties:
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Practice JEE Main Level (Permutations and Combinations)
Q41Paper 1MathematicsOne or More Correct (Partial Marking)Hard
Differential Calculus (Continuity & AOD)
Scoring Scheme: +4 Full Marks • -2 Negative Marks • Partial Marking Enabled
[JEE Advanced 2016 Paper 1 Mathematics Q41] Let the mathematical relation governing Lagrange Mean Value Theorem and Monotonicity Intervals in Differential Calculus (Continuity & AOD) be defined over its maximal domain. Evaluate the mathematical properties:
Select one or more options, then click "Submit Choices":
Practice JEE Main Level (Differential Calculus (Continuity & AOD))
Q42Paper 1MathematicsNumerical Value TypeTough / Advanced
Application of Derivatives (Maxima & Minima)
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2016 Paper 1 Mathematics Q42] Let the mathematical relation governing Optimization on Parametric Curves with Constraint Geometry in Application of Derivatives (Maxima & Minima) be defined over its maximal domain. Evaluate the mathematical properties:
Practice JEE Main Level (Application of Derivatives (Maxima & Minima))
Q43Paper 1MathematicsNumerical Value TypeHard
Definite Integration
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2016 Paper 1 Mathematics Q43] Let the mathematical relation governing King Rule and Reduction Formula for Trigonometric Powers in Definite Integration be defined over its maximal domain. Evaluate the mathematical properties:
Practice JEE Main Level (Definite Integration)
Q44Paper 1MathematicsNumerical Value TypeTough / Advanced
Differential Equations
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2016 Paper 1 Mathematics Q44] Let the mathematical relation governing Bernoulli Differential Equation with Variable Substitution in Differential Equations be defined over its maximal domain. Evaluate the mathematical properties:
Practice JEE Main Level (Differential Equations)
Q45Paper 1MathematicsNumerical Value TypeHard
Coordinate Geometry - Parabola
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2016 Paper 1 Mathematics Q45] Let the mathematical relation governing Co-normal Points and Locus of Point of Intersection of Tangents in Coordinate Geometry - Parabola be defined over its maximal domain. Evaluate the mathematical properties:
Practice JEE Main Level (Coordinate Geometry - Parabola)
Q46Paper 1MathematicsNumerical Value TypeTough / Advanced
Coordinate Geometry - Ellipse & Hyperbola
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2016 Paper 1 Mathematics Q46] Let the mathematical relation governing Director Circle and Asymptotes of Conjugate Hyperbolas in Coordinate Geometry - Ellipse & Hyperbola be defined over its maximal domain. Evaluate the mathematical properties:
Practice JEE Main Level (Coordinate Geometry - Ellipse & Hyperbola)
Q47Paper 1MathematicsSingle Correct OptionHard
Trigonometry & Inverse Trigonometric Functions
Scoring Scheme: +3 Full Marks • -1 Negative Marks
[JEE Advanced 2016 Paper 1 Mathematics Q47] Let the mathematical relation governing Summation of Inverse Trigonometric Series via Telescoping in Trigonometry & Inverse Trigonometric Functions be defined over its maximal domain. Evaluate the mathematical properties:
Practice JEE Main Level (Trigonometry & Inverse Trigonometric Functions)
Q48Paper 1MathematicsSingle Correct OptionTough / Advanced
Binomial Theorem
Scoring Scheme: +3 Full Marks • -1 Negative Marks
[JEE Advanced 2016 Paper 1 Mathematics Q48] Let the mathematical relation governing Double Summation and Coefficients of Generalized Multinomial Series in Binomial Theorem be defined over its maximal domain. Evaluate the mathematical properties:
Practice JEE Main Level (Binomial Theorem)
Q49Paper 1MathematicsSingle Correct OptionHard
Limits, Continuity and Differentiability
Scoring Scheme: +3 Full Marks • -1 Negative Marks
[JEE Advanced 2016 Paper 1 Mathematics Q49] Let the mathematical relation governing Evaluation of 1∞1^\infty Indeterminate Form and Squeeze Theorem in Limits, Continuity and Differentiability be defined over its maximal domain. Evaluate the mathematical properties:
Practice JEE Main Level (Limits, Continuity and Differentiability)
Q50Paper 1MathematicsSingle Correct OptionTough / Advanced
Functions & Relations
Scoring Scheme: +3 Full Marks • -1 Negative Marks
[JEE Advanced 2016 Paper 1 Mathematics Q50] Let the mathematical relation governing Functional Equations and Injective/Surjective Mapping Properties in Functions & Relations be defined over its maximal domain. Evaluate the mathematical properties:
Practice JEE Main Level (Functions & Relations)
Q51Paper 1MathematicsSingle Correct OptionHard
Sequences and Series
Scoring Scheme: +3 Full Marks • -1 Negative Marks
[JEE Advanced 2016 Paper 1 Mathematics Q51] Let the mathematical relation governing Arithmetico-Geometric Progression (AGP) and Infinite Sum Convergence in Sequences and Series be defined over its maximal domain. Evaluate the mathematical properties:
Practice JEE Main Level (Sequences and Series)