Previous-year questions organized for practice. Solutions prepared by Statstrive.
Question list
Question 1Consumer Theory / Cobb--Douglas utility maximizationEasyQuestion 2Consumer Theory / Linear utility and corner solutionsEasyQuestion 3Consumer Theory / Weak Axiom of Revealed PreferenceModerateQuestion 4Production and Cost / Leontief technology cost minimizationEasyQuestion 5Market Structure / Cournot duopoly with asymmetric costsModerateQuestion 6Consumer Theory / Marginal utility vs.\ marginal rate of substitutionModerateQuestion 7Consumer Theory / Representation of preferencesEasyQuestion 8Consumer Theory / Compensating and Equivalent Variations (Leontief)ModerateQuestion 9Optimization / Bliss point with binding budget constraintEasyQuestion 10Production Theory / Marginal product under Leontief technologyModerateQuestion 11Consumer Theory / Aggregation of individual elasticitiesModerateQuestion 12Market Structure / Competitive industry short-run equilibriumModerateQuestion 13Market Structure / Monopoly pricing and elasticityModerateQuestion 14Macroeconomics / Solow steady-state capital--output ratioEasyQuestion 15Combinatorics / Arrangements with a block constraintEasyQuestion 16Algebra / Functions / Roots of related polynomialsModerateQuestion 17Functions / Function compositionEasyQuestion 18Calculus / Monotonicity and convexity of compositionModerateQuestion 19Calculus / Mean Value Theorem and strict convexityModerateQuestion 20Linear Algebra / Similar matrices and determinantsEasyQuestion 21Calculus / Limits and L'H\^opitalEasyQuestion 22Calculus / Monotonicity of $f(x)/x$ for convex $f$ with $f(0)=0$ModerateQuestion 23Combinatorics / Number of onto functionsEasyQuestion 24Functions / Range of $x/(1+x^2)$EasyQuestion 25Linear Algebra / Rank of a product of full row/column rank matricesEasyQuestion 26Linear Algebra / Eigenvalues of a specific matrixModerateUnder reviewQuestion 27Linear Algebra / Null space of a singular matrixEasyQuestion 28Probability / Conditional probabilityEasyQuestion 29Probability / Total probabilityEasyQuestion 30Functions / Injectivity / surjectivityEasy