Calculus
135 questions across 6 topics.
Differential Calculus of one and two real variables, and Integral Calculus
- 2Integral function critical pointsIIT JAM 2026 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 12Piecewise function differentiabilityIIT JAM 2026 MSDifferential Calculus of one and two real variables, and Integral CalculusHard
- 13Saddle points of xy(5x+3y-6)IIT JAM 2026 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 14Continuity versus partials off axesIIT JAM 2026 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 15Washer volume of a parabolic regionIIT JAM 2026 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 41Taylor coefficients of 3 e^x cos 2xIIT JAM 2026 MSDifferential Calculus of one and two real variables, and Integral CalculusEasy
- 51Area between parabola and lineIIT JAM 2026 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 3Integral of an odd periodic functionIIT JAM 2025 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 11Roots of x plus pi cos xIIT JAM 2025 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 15Darboux property versus continuityIIT JAM 2025 MSDifferential Calculus of one and two real variables, and Integral CalculusHard
- 33Decay of a positive function at infinityIIT JAM 2025 MSDifferential Calculus of one and two real variables, and Integral CalculusHard
- 43Second-order difference of a sineIIT JAM 2025 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 52Area between a cubic and the line y=xIIT JAM 2025 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 53Volume of a truncated ellipsoidIIT JAM 2025 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 12Continuity of two oscillatory functionsIIT JAM 2024 MSDifferential Calculus of one and two real variables, and Integral CalculusEasy
- 14Local extrema of a strictly convex functionIIT JAM 2024 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 15Convergence of two improper integralsIIT JAM 2024 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 32Mean value conclusions from four function valuesIIT JAM 2024 MSDifferential Calculus of one and two real variables, and Integral CalculusHard
- 42Turning point of an integral functionIIT JAM 2024 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 51A scaled sine-exponential limitIIT JAM 2024 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 52Integral of radius over a circular sectorIIT JAM 2024 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 7Saddle point of bivariate quadraticIIT JAM 2023 MSDifferential Calculus of one and two real variables, and Integral CalculusEasy
- 16Number of curve intersectionsIIT JAM 2023 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 26Volume of truncated cylinderIIT JAM 2023 MSDifferential Calculus of one and two real variables, and Integral CalculusEasy
- 30Closest point on a sphereIIT JAM 2023 MSDifferential Calculus of one and two real variables, and Integral CalculusEasy
- 36Differentiability of rational bivariate functionIIT JAM 2023 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 38Double integral of maximum functionIIT JAM 2023 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 41Minimum number of roots of second derivativeIIT JAM 2023 MSDifferential Calculus of one and two real variables, and Integral CalculusEasy
- 43Limit of integral ratioIIT JAM 2023 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 51Limit of sum of derivative quotientsIIT JAM 2023 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 53Value of Gaussian integral constantIIT JAM 2023 MSDifferential Calculus of one and two real variables, and Integral CalculusEasy
- 2Derivative of x sin of reciprocalIIT JAM 2022 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 11Limit of a Riemann sumIIT JAM 2022 MSDifferential Calculus of one and two real variables, and Integral CalculusEasy
- 12Differentiability of bivariate functionIIT JAM 2022 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 13Arc length of an integral functionIIT JAM 2022 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 14Derivative of integral with floor functionIIT JAM 2022 MSDifferential Calculus of one and two real variables, and Integral CalculusHard
- 32Critical points of bivariate polynomialIIT JAM 2022 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 42Determining function from two-sided boundsIIT JAM 2022 MSDifferential Calculus of one and two real variables, and Integral CalculusEasy
- 51Extrema on a circleIIT JAM 2022 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 52Double integral with variable substitutionIIT JAM 2022 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 2Strictly increasing polynomial is bijectiveIIT JAM 2021 MSDifferential Calculus of one and two real variables, and Integral CalculusEasy
- 3Exponentials against a cosineIIT JAM 2021 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 11Cubic-over-quadratic partials at originIIT JAM 2021 MSDifferential Calculus of one and two real variables, and Integral CalculusHard
- 35What twice differentiability buysIIT JAM 2021 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 43Integral over a slanted triangleIIT JAM 2021 MSDifferential Calculus of one and two real variables, and Integral CalculusEasy
- 44Ordered simplex volume weightedIIT JAM 2021 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 50Length of the log-secant curveIIT JAM 2021 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 51Double integral over a slanted parallelogramIIT JAM 2021 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 57Area between sine and cosineIIT JAM 2021 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 58Counting real roots of an eleventh degreeIIT JAM 2021 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 60Integral quotient by L'HopitalIIT JAM 2021 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 2Differentiability determines two constantsIIT JAM 2020 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 3Area between a quartic and a parabolaIIT JAM 2020 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 13Alpha and beta from a limitIIT JAM 2020 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 14Cubics over quadratics at the originIIT JAM 2020 MSDifferential Calculus of one and two real variables, and Integral CalculusHard
- 15Iterated limits for a paraboloid solidIIT JAM 2020 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 16Polar double integral over a shifted discIIT JAM 2020 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 32Two saddles among four critical pointsIIT JAM 2020 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 33Arc length integrals for a parabolaIIT JAM 2020 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 42Global maximum of a rational functionIIT JAM 2020 MSDifferential Calculus of one and two real variables, and Integral CalculusEasy
- 43Iterated exponential integral by swapping orderIIT JAM 2020 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 51Pinned down by the derivative boundIIT JAM 2020 MSDifferential Calculus of one and two real variables, and Integral CalculusMedium
Integral calculus
- 3Derivative of an integral with variable lower limitIIT JAM 2019 MSIntegral calculusEasy
- 15Length of a fractional-power curveIIT JAM 2019 MSIntegral calculusMedium
- 16Volume of a solid of revolution about x equals 6IIT JAM 2019 MSIntegral calculusMedium
- 43Double integral by reversing the orderIIT JAM 2019 MSIntegral calculusMedium
- 53Volume between two planes inside a cylinderIIT JAM 2019 MSIntegral calculusHard
- 15Differentiability of an integral function at breakpointsIIT JAM 2018 MSIntegral calculusMedium
- 42Area between two tangent semicirclesIIT JAM 2018 MSIntegral calculusMedium
- 43Area of the region absolute x plus absolute y at most oneIIT JAM 2018 MSIntegral calculusEasy
- 54Double integral by reversing the orderIIT JAM 2018 MSIntegral calculusMedium
- 23Limits after reversing a double integralIIT JAM 2017 MSIntegral calculusMedium
- 28Bounds for an integral with a cubic under the rootIIT JAM 2017 MSIntegral calculusHard
- 30Arc length up to a vertical tangentIIT JAM 2017 MSIntegral calculusHard
- 48Area between two opposite parabolasIIT JAM 2017 MSIntegral calculusEasy
- 52Number of roots of an integral function on an intervalIIT JAM 2017 MSIntegral calculusHard
- 53Length of a closed curve formed by a curve and its tangentIIT JAM 2017 MSIntegral calculusHard
- 54Volume of a solid under a plane over a parabolic regionIIT JAM 2017 MSIntegral calculusHard
- 3Volume of a solid of revolution of a hyperbolaIIT JAM 2016 MSIntegral calculusMedium
- 4Volume of a region enclosed by a cylinder and planesIIT JAM 2016 MSIntegral calculusMedium
- 29Area under the second derivative of a convolution integralIIT JAM 2016 MSIntegral calculusMedium
- 50Arc length from a given derivativeIIT JAM 2016 MSIntegral calculusMedium
- 51Value of the upper limit from a triple integralIIT JAM 2016 MSIntegral calculusHard
- 53Lower angle limit from a polar double integralIIT JAM 2016 MSIntegral calculusMedium
- 47Volume of a solid of revolution of a lineIIT JAM 2015 MSIntegral calculusEasy
- 48Integral of the floor function over an intervalIIT JAM 2015 MSIntegral calculusEasy
- 57Length of an arc of a semicircleIIT JAM 2015 MSIntegral calculusMedium
- 60Area of a region bounded by a line and a curve in the first quadrantIIT JAM 2015 MSIntegral calculusMedium
- 17Area between a line and an absolute-value parabolaIIT JAM 2014 MSIntegral calculusMedium
- 21Order of integration after switching for a region between a parabola and a lineIIT JAM 2014 MSIntegral calculusMedium
- 3Function recovered from a given arc lengthIIT JAM 2013 MSIntegral calculusHard
- 2Volume of the solid generated by a square-root curveIIT JAM 2012 MSIntegral calculusEasy
- 3Order of integration reversed for a region between a parabola and a lineIIT JAM 2012 MSIntegral calculusMedium
Differential calculus of one variable
- 13Parameter for which a quartic has no real rootIIT JAM 2019 MSDifferential calculus of one variableHard
- 32Extrema and monotonicity around a pointIIT JAM 2019 MSDifferential calculus of one variableMedium
- 42Function satisfying a Holder condition of exponent 4/3IIT JAM 2019 MSDifferential calculus of one variableMedium
- 52Sum of floor and fractional-part terms near zeroIIT JAM 2019 MSDifferential calculus of one variableHard
- 11Discontinuities of a function with a floor termIIT JAM 2018 MSDifferential calculus of one variableHard
- 12Number of intersections of two curvesIIT JAM 2018 MSDifferential calculus of one variableHard
- 34Extremum, monotonicity and differentiability at zeroIIT JAM 2018 MSDifferential calculus of one variableHard
- 51Limit of scaled differences of a differentiable functionIIT JAM 2018 MSDifferential calculus of one variableMedium
- 53Limit of a power with a slowly growing base termIIT JAM 2018 MSDifferential calculus of one variableHard
- 24Second derivative of an integral at zeroIIT JAM 2017 MSDifferential calculus of one variableHard
- 27Parameter making a difference of reciprocals finiteIIT JAM 2017 MSDifferential calculus of one variableMedium
- 33A bijection of the unit interval defined by rationalityIIT JAM 2017 MSDifferential calculus of one variableHard
- 34Curve below two lines from a bounded derivativeIIT JAM 2017 MSDifferential calculus of one variableHard
- 47Coefficient combination from a local minimumIIT JAM 2017 MSDifferential calculus of one variableMedium
- 25Differentiability at zero of two oscillating functionsIIT JAM 2016 MSDifferential calculus of one variableHard
- 26Mean value theorem on adjacent intervalsIIT JAM 2016 MSDifferential calculus of one variableHard
- 33Limits of powers times a function with a cancelling expansionIIT JAM 2016 MSDifferential calculus of one variableHard
- 34Continuity at a point for functions involving a floor termIIT JAM 2016 MSDifferential calculus of one variableHard
- 49Minimum of an increasing function on an intervalIIT JAM 2016 MSDifferential calculus of one variableMedium
- 9Injectivity and surjectivity of a cubic polynomialIIT JAM 2015 MSDifferential calculus of one variableEasy
- 10Inequality between an exponential and a lineIIT JAM 2015 MSDifferential calculus of one variableEasy
- 23Monotonicity of the absolute value from a sign conditionIIT JAM 2015 MSDifferential calculus of one variableMedium
- 26Number of roots of a logarithmic functionIIT JAM 2015 MSDifferential calculus of one variableMedium
- 33Zeros of a continuous function from three valuesIIT JAM 2015 MSDifferential calculus of one variableMedium
- 34Even and odd functions from a composite definitionIIT JAM 2015 MSDifferential calculus of one variableMedium
- 49Number of real solutions of a cubic equationIIT JAM 2015 MSDifferential calculus of one variableMedium
- 50Second derivative of a function constant along a sequenceIIT JAM 2015 MSDifferential calculus of one variableHard
- 1Roots of a cubic equation in an interval via Rolle's theoremIIT JAM 2014 MSDifferential calculus of one variableHard
- 25Continuity and differentiability at zero of a piecewise oscillating functionIIT JAM 2014 MSDifferential calculus of one variableHard
- 26Limit of a ratio vanishing to third order at one halfIIT JAM 2014 MSDifferential calculus of one variableHard
- 17Condition for differentiability at a point of a split rational irrational functionIIT JAM 2013 MSDifferential calculus of one variableHard
Differential calculus of two variables
- 13Minimum of a quartic over a half planeIIT JAM 2018 MSDifferential calculus of two variablesHard
- 25Local minimum and maximum of a function of two variablesIIT JAM 2017 MSDifferential calculus of two variablesMedium
- 27Local minima of a cubic polynomial in two variablesIIT JAM 2016 MSDifferential calculus of two variablesHard
- 28Derivative of a double integral over a squareIIT JAM 2015 MSDifferential calculus of two variablesHard
- 16Type of the critical point of a cubic polynomial in two variablesIIT JAM 2014 MSDifferential calculus of two variablesHard
- 4Value making a function of two variables continuous at the originIIT JAM 2013 MSDifferential calculus of two variablesMedium
- 5Continuity and partial derivatives at a point for an oscillating function of two variablesIIT JAM 2012 MSDifferential calculus of two variablesHard