Sample Questions, Answers - AIEEE Preparation

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Math Questions

1. Sets, Relations & Functions

   Sets and their representation; Union, intersection and complement of sets and their algebraic properties; Power set; Relation, Types of relations, equivalence relations, functions; one-one, into and onto functions, composition of functions.
   
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2. Permutation, Combination

   nCr, nPr, factorials, sampling with replacement, sampling without replacement, sampling with ordering and sampling without ordering. Questions on numbers, tossing of coins, rolling of dice, picking a card from a pack of cards and questions on combinations and permutations.
   
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3. Sequences & Series

   Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers. Relation between A.M. and G.M. Sum upto n terms of special series: S_n, S_n², S_n³. Arithmetico - Geometric progression.
   
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4. Limits, Continuity And Differentiability

   Real - valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential functions, inverse functions. Graphs of simple functions. Limits, continuity and differentiability. Differentiation of the sum, difference, product and quotient of two functions. Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions; derivatives of order upto two. Rolle's and Lagrange's Mean Value Theorems. Applications of derivatives: Rate of change of quantities, monotonic - increasing and decreasing functions, Maxima and minima of functions of one variable, tangents and normals.
   
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5. Statistics & Probability

   Measures of Dispersion: Calculation of mean, median, mode of grouped and ungrouped data. Calculation of standard deviation, variance and mean deviation for grouped and ungrouped data.
   
   Probability: Probability of an event, addition and multiplication theorems of probability, Baye's theorem, probability distribution of a random variate, Bernoulli trials and Binomial distribution.
   
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6. Trigonometry

   Trigonometrical identities and equations. Trigonometrical functions. Inverse trigonometrical functions and their properties. Heights and Distances.
   
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7. Mathematical Reasoning

   Statements, logical operations and, or, implies, implied by, if and only if. Understanding of tautology, contradiction, converse and contrapositive.
   
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Physics Questions

Chemistry Questions