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Sample Question Archives - CAT, XAT, TANCET, PGSEM Test

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1. Number System and Number Theory

   Number systesms and Number Theory are oft repeated topics in most top B Schools entrance tests. Includes word problems on LCM, HCF, framing equations, remainders, factorials, tests of divisibility.
   

2. Percentages, Fractions

   Percentages and fractions are the building blocks for questions that appear in many topics that follow this. Percentage change, conversions from percentages to fractions and typical questions on the topic.
   

3. Profit, Loss & Discounts

   Profit, loss, percentage profit, percentage loss. Discounts, percentage discounts. Concept of marked price, markup.
   

4. Simple and Compound Interest

   Questions on simple interest, compound interest, time taken for a sum of money to double in simple interest and in compound interest.
   

5. Speed, Time & Distance

   Questions, shortcuts on Speed, Time Distance. Relation between these quantities. Conversion from one unit to another. Average speed. Relative speeds.
   

6. Pipes & Cisterns And Work & Time

   Pipes, cisterns, work time questions. Questions on time taken to complete a task, work efficiency change etc. A topic from which a couple of questions do appear in most entrance tests.
   

7. Races

   Straight line race, start or lead given by one to the other. Circular race. Time taken to meet for the first time, time taken to meet for the first time at the starting point.
   

8. Averages, Arithmetic Mean

   Arithmetic mean, weighted arithmetic mean. Questions on elements joining or leaving a group resulting in change in the arithmetic mean.
   

9. Ratio, Proportion & Variation

   Elementary ratio proportion question. Direct proportion, inverse proportion, continued proportion. Questions on partnerships.
   

10. Mixtures & Rule of Alligation

    Problems on simple mixtures, compound mixtures. Rule of alligation and its application in finding weights used while computing weighted average.
    

11. 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.
    

12. Probability

    Elementary probability, sample space, events. Probability of a complementary event. Probability questions as a ratio of two permutation combination questions.
    

13. Inequalities - Linear Inequations

    Questions on linear inequations. Inequalities on quadratic equations, exponents, modulus. Results of adding and multiplying a constant term on either side of an inequality.
    

14. Progressions - AP, GP, HP

    Arithmetic Progression, Geometric Progression, Harmonic Progression. Relation between Arithmetic, Geometric and Harmomic Means. Sum up to n terms of each of these series.
    

15. Set Language and Theory

    Problems on finding union, intersection of two sets, three sets and four sets. Complement of a set, superset, subsets, powerset.
    

16. Geometry

    Lines, Angles between lines, polygons, triangles, quadrilaterals, parallelograms, rhombus, kites, trapezium, rectangles, squares, regular hexagon, regular pentagon, circles, tangents.
    

17. Mensuration - Solid Geometry

    Area, perimeter of two dimension objects. Curved Surface Area, Total Surface Area, Volume of three dimension solids such as cube, cuboid, cylinder, cone, sphere, hemisphere, prisms, pyramids.
    

18. Trigonometry

    Questions on trigonometric identities, trigonometric ratios including sin, cos, tan, cot, cosec, sec. Also questions on heights and distances.
    

19. Data Sufficiency

    Data sufficiency in quantitative reasoning. DS questions on concepts in arithmetic, algebra and geometry. A question is followed by two statements and you are expected to determine if the given information is sufficient to answer the question.
    

20. Clocks and Calendars

    Questions on finding the time at which the minute hand and hour hand of a clock are at a particular angle to each other. Finding the day of the week given a date.
    

21. Algebra

    Linear, quadratic equations. Word problems in Linear, Quadratic equations involving framing equations. Conditions for roots of quadratic equation being equal and real, being real, being complex.
    

22. Function

    Questions on functions are a big hit with XAT. CAT also features function questions at times as in CAT 1999 and CAT 2000.
    

23. English Grammar

    Sentence correction questions on common errors including Subject Verb agreement, Pronoun errors, Comparison errors, Tense errors, Parallel Construct error, error in incorrect use of prepositions.
    

24. Miscellaneous

    

25. General Knowledge and Awareness

    General Knowledge, Business Affairs, Current affairs questions that appear in some of the top B school entrance tests.