1
JEE Advanced 2020 Paper 1 Offline
Numerical
+4
-0
Let f : [0, 2] $$ \to $$ R be the function defined by
$$f(x) = (3 - \sin (2\pi x))\sin \left( {\pi x - {\pi \over 4}} \right) - \sin \left( {3\pi x + {\pi \over 4}} \right)$$
If $$\alpha ,\,\beta \in [0,2]$$ are such that $$\{ x \in [0,2]:f(x) \ge 0\} = [\alpha ,\beta ]$$, then the value of $$\beta - \alpha $$ is ..........
$$f(x) = (3 - \sin (2\pi x))\sin \left( {\pi x - {\pi \over 4}} \right) - \sin \left( {3\pi x + {\pi \over 4}} \right)$$
If $$\alpha ,\,\beta \in [0,2]$$ are such that $$\{ x \in [0,2]:f(x) \ge 0\} = [\alpha ,\beta ]$$, then the value of $$\beta - \alpha $$ is ..........
Your input ____
2
JEE Advanced 2020 Paper 1 Offline
Numerical
+4
-0
For a polynomial g(x) with real coefficients, let mg denote the number of distinct real roots of g(x). Suppose S is the set of polynomials with real coefficients defined by
$$S = \{ {({x^2} - 1)^2}({a_0} + {a_1}x + {a_2}{x^2} + {a_3}{x^3}):{a_0},{a_1},{a_2},{a_3} \in R\} $$;
For a polynomial f, let f' and f'' denote its first and second order derivatives, respectively. Then the minimum possible value of (mf' + mf''), where f $$ \in $$ S, is ..............
$$S = \{ {({x^2} - 1)^2}({a_0} + {a_1}x + {a_2}{x^2} + {a_3}{x^3}):{a_0},{a_1},{a_2},{a_3} \in R\} $$;
For a polynomial f, let f' and f'' denote its first and second order derivatives, respectively. Then the minimum possible value of (mf' + mf''), where f $$ \in $$ S, is ..............
Your input ____
3
JEE Advanced 2018 Paper 2 Offline
Numerical
+3
-0
Let X be a set with exactly 5 elements and Y be a set with exactly 7 elements. If $$\alpha $$ is the number of one-one functions from X to Y and $$\beta $$ is the number of onto functions from Y to X, then the value of $${1 \over {5!}}(\beta - \alpha )$$ is ..................
Your input ____
4
IIT-JEE 2009 Paper 2 Offline
Numerical
+3
-1
If the function $$f(x) = {x^3} + {e^{x/2}}$$ and $$g(x) = {f^{ - 1}}(x)$$, then the value of $$g'(1)$$ is _________.
Your input ____
Questions Asked from Functions (Numerical)
Number in Brackets after Paper Indicates No. of Questions
JEE Advanced Subjects
Physics
Mechanics
Units & MeasurementsMotionLaws of MotionWork Power & EnergyImpulse & MomentumRotational MotionProperties of MatterHeat and ThermodynamicsSimple Harmonic MotionWavesGravitation
Electricity
ElectrostaticsCurrent ElectricityCapacitorMagnetismElectromagnetic InductionAlternating CurrentElectromagnetic Waves
Optics
Modern Physics
Chemistry
Physical Chemistry
Some Basic Concepts of ChemistryStructure of AtomRedox ReactionsGaseous StateChemical EquilibriumIonic EquilibriumSolutionsThermodynamicsChemical Kinetics and Nuclear ChemistryElectrochemistrySolid StateSurface Chemistry
Inorganic Chemistry
Periodic Table & PeriodicityChemical Bonding & Molecular StructureIsolation of ElementsHydrogens-Block Elementsp-Block Elementsd and f Block ElementsCoordination CompoundsSalt Analysis
Organic Chemistry
Mathematics
Algebra
Quadratic Equation and InequalitiesSequences and SeriesMathematical Induction and Binomial TheoremMatrices and DeterminantsPermutations and CombinationsProbabilityVector Algebra3D GeometryStatisticsComplex Numbers
Trigonometry
Coordinate Geometry
Calculus