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ProbabilityMCQ #1 on Basic ProbabilityMCQ #2: More Challenging Problems on ProbabilityMCQ #3- Conditional Probability and Bayes TheoremComplex NumbersMCQ #1MCQ #2: More on Complex NumbersQuadratic EquationsMCQ Quadratic EquationsQuadratic In-equationsMCQ Quadratic In-equationsComputer ScienceQuizzes on Basic Object Oriented Programming with C++ 1 MCQ #1: C++ and OOPS2 MCQ #2: Inheritance in C++Quizzes on C Programming- Arrays, Strings and Pointers1 C Programming MCQ #1: Strings- 12 C Programming MCQ #2: Strings (2)3 C Programming MCQ #3: Strings (3)4 C Programming MCQ #4: Arrays(1)5 C Programming MCQ #5: Arrays (2)6 C Programming MCQ #6: Arrays (3)7 C Programming MCQ #7: Pointers (1)8 C Programming MCQ #8: Pointers (2)Quizzes on Java Programming1 Java MCQ #1- Classes, Inheritances and Interfaces2 Java MCQ #2- Collections3 Java MCQ #3- ThreadingQuizzes on Data Structures, Algorithms and Complexity1 MCQ #1: The Basics of Sorting Algorithms- Quadratic Sorts2 MCQ #2: Efficient Sorting Algorithms- Quick sort, Merge Sort, Heap Sort3 MCQ #3- The Radix Sort4 MCQ #4: Divide and Conquer5 MCQ #5- Dynamic Programming6 MCQ #6- Complexity of Algorithms7 MCQ #7- Application of Master's Theorem8 MCQ #8: Binary Search Trees9 MCQ #9: B-Trees10 MCQ #9: AVL-Trees11 MCQ #10: Representing Graphs as Data Structures12 MCQ #11: Spanning Trees13 MCQ #12: Algorithms - Graphs: Spanning Trees - Kruskal and Prim Algorithms14 MCQ #13: Algorithms - Graphs: Depth and Breadth First SearchBasic English GrammarEnglish Online: Articles (Quiz #1)English Online: Articles (Quiz #2)English Online: Articles (Quiz #3)English Grammar- The Tenses: Quiz #1English Grammar- The Tenses: Quiz #2English Grammar- The Tenses: Quiz #3English Grammar- The Tenses: Quiz #4English Grammar- The Tenses: Quiz #5English Grammar: The Parts of Speech (Quiz #1)English Grammar: The Parts of Speech (Quiz #2)English Grammar: The Parts of Speech (Quiz #3)English Grammar: The Parts of Speech (Quiz #4)English Grammar: The Parts of Speech (Quiz #5)English Grammar: The Parts of Speech (Quiz #6)English Grammar: The Parts of Speech (Quiz #7)English Grammar: The Parts of Speech (Quiz #8)English Grammar: The Parts of Speech (Quiz #9)English Grammar: The Parts of Speech (Quiz #10)Examination Results 2016 Sign inRecent Site ActivityReport AbusePrint PagePowered By Google Sites . 3 MCQ #3 on Circles. Using factorization and visualization based methods.Series and ProgressionsArithmetic, Geometric, Harmonic and mixed progressions. Cubic and higher order equations - relationship between roots and coefficients for these. show that b+ c, c, c+ a, a + b are in H.P.Q: If the AM between a and b is twice as greater as the GM, show that a/b = 7+43Q: Sum to the n terms the series, 12-22+32-42+ n is even.The Complete Tutorial with Solved Problems (MCQ Quizzes/Worksheets after this)MCQ Quiz/Worksheet#1Arithmetic ProgressionMCQ Quiz: Arithmetic ProgressionGoogle Spreadsheet Form MCQ Quiz/Worksheet #2Geometric ProgressionMCQ Quiz: Geometric ProgressionGoogle Spreadsheet Form MCQ Quiz/Worksheet #3More on Geometric Progressions.Fill up the answers in the Answer Submission Form below this Question-Paper document. .. Graphs and plots of quadratic equations.Quadratic InequalitiesQuadratic inequalities.

Relationship between roots of a quadratic equation. Notes, formulas and solved problems related to these sub-topics.The Principle of Mathematical InductionIntroductory problems related to Mathematical Induction.Quadratic EquationsIntroducing various techniques by which quadratic equations can be solved - factorization, direct formula. Quizzes on ProgressionsMCQ #1: Arithmetic ProgressionMCQ #2: Geometric ProgressionMCQ #3 : More on Geometric Progressions.MCQ #4 : Harmonic Progressions.MCQ #5: More on Harmonic ProgressionMCQ #6: Mixed ProgressionsComplex NumbersMCQ #1MCQ #2: More on Complex NumbersQuadratic EquationsMCQ Quadratic EquationsQuadratic In-equationsMCQ Quadratic In-equationsCoordinate Geometry - Straight LinesMCQ #1: Cartesian Planes, Straight Line BasicsMCQ #2 on Straight LinesMCQ #3 on Straight LinesMCQ #4 on Straight LinesCircles1MCQ #1 on Circles.2MCQ #2 on Circles.3MCQ #3 on Circles.Conic Sections- Parabola, Hyperbola, Ellipse1MCQ- The Basics of Conic Sections2MCQ on Parabola.3MCQ on Hyperbola4MCQ on Ellipses.ProbabilityMCQ #1 on Basic ProbabilityMCQ #2: More Challenging Problems on ProbabilityMCQ #3- Conditional Probability and Bayes TheoremSeries and Progressions : AP, GP, HPAfter studying the chapter you might find it useful to attempt these Multiple Choice Question Quizzes to assess how well you understood the topic.MCQ Quiz#1MCQ Quiz/Worksheet #2MCQ Quiz/Worksheet #3MCQ Quiz/Worksheet #4MCQ Quiz/Worksheet #5MCQ Quiz/Worksheet #6A sequence refers to a list of numbers with some inherent pattern.General term of a sequence, generally written as an is an expression that for different values ofn gives different terms of the sequence.Arithmetic Progression, Terms and SummationA sequence of the typea,a+d,a+2d,a+3d,is said to form an AP.Each term differs from the previous one by a fixed value called as common difference.a and d are usually used to denote first term and common difference respectively.nth term of an AP is given byan=a1+(n-1)dThe tutorial will show you how to compute the sum of the first n terms of an APSelecting terms in AP:3 terms in an AP are a-d,a,a+d4 terms in an AP are a-3d,a-d,a+d,a+3dAnd so on.mth term from the end of an AP :It is the (n-m+1)th term from the beginning.Alternately, we can reverse the AP, and consider the first term and common difference of thenew AP as last term and negative of common difference of the old AP.If a constant is added, or subtracted, or multiplied or divided from every term on an AP, theresulting sequence is still an AP.Arithmetic Mean:if a,b,c are in AP, then b is said to be arithmetic mean of a and c.Equivalently, if 2b=a+c, then a,b,c are in AP.If between a and b we are to insert n numbers A1,A2,A3,.,An such that a, A1,A2,A3,.,An form anAP, then A1,A2,A3,.,An are called n Arithmetic Means.Geometric Progression, Terms and SummationA sequence of the type:a,ar,ar2,ar3,is called a GP.In a GP, thenth term of a GP is given by:an=arm-1The tutorial will show you how to compute the sum of first n terms of a GP.When r=1, the GP can be treated as an AP, and clearly the sum of first n terms then is nXa.Similar to an AP, mth term from the end is (n-m+1)th term from the starting.Selecting terms in a GP:A GP of 3 terms : a/r,a,arA GP of 4 terms:a/r3,a/r,ar,ar3And so on.If all terms in a GP are multiplied or divided by the same number, or are raised to the samepower, then the resulting sequence is still a GP.Geometric Mean:If a,b,c are in GP then b2=ac and b is called the GM of a and c.Conversely, if b2=ac, then a,b,c are in GP.Sum of infinite terms of a GP:If -1 GM>HMHere are some of the problems solved in the tutorial :Q: What is the common difference of an AP whose nth term is xn+y?Q: If the sum of n terms of an AP is 2n2+3n, what is the kth term?Q:If am=n and an=m, what is ap?Q:If the sums of n terms of two arithmetic progressions are in the ratio 2n+5:3n+4, then what is theratio of their nth terms?Q: If sum of n terms of an AP is 3n2+5n then which of its terms is 164?Q: If sum of first p terms is q and sum of first q terms is p then what is the sum of first p+q terms ?Q: If four numbers are in AP such that their sum is 50, and the greatest number is four times the least,then what are the numbers?Q: If n arithmetic means are inserted between 1 and 31 such that ratio of first and nth mean is 3:29,then what is the value of n?Q: If S1 is the sum of an AP of n odd number of terms and S2 the sum of terms of the series in oddplaces, then what is S1/S2?Q: What is the sum of 2 digit multiples of 4?Q: Find the sum of 2+6+18++4374.Q: Find the sum of 5+55+555+n termsQ: Find the sum of n terms of the sequence whose nth term is 2n+3nQ: Find a GP for which the sum of first two terms is -4 and the fifth term is 4 times the third term.Q: Find the least value of n for which the sum of 1+3+9+27+ to n terms is greater than 7000.Q: If a,b,c are in GP, prove that log a, log b, log c are in AP and vice versa.Q: If a,b,c are in GP and x,y are AMs between a,b and b,c respectively, then prove that x,b,y are inHP.Q: Find the sum to n terms of series1.2.3+2.3.4+3.4.5+4.5.6+Q:If a, b, c are in H.P., show that a/b+c, b/c+a, c/a+b are also in H.P.Q:Evaluate: 62 + 72 + 82 + 92 + 102Q: Prove that (a + b + c) (ab + bc + ca) > 9abc.Q: If a2, b2, c2 are in A.P. Your score will be emailed to you.Questions: Harmonic ProgressionGoogle DocumentAnswer Submission Form for MCQ Quiz #4Answer Submission Form: Harmonic ProgressionGoogle Spreadsheet Form MCQ Quiz/Worksheet #5More on Harmonic ProgressionMCQ Quiz: Harmonic ProgressionGoogle Spreadsheet Form MCQ Quiz/Worksheet #6Mixed ProgressionsMCQ Quiz: Harmonic ProgressionGoogle Spreadsheet Form You might like to take a look at our other algebra tutorials:Introduction to Complex NumbersIntroduction to Complex Numbers and iota. Cookies are required to use this site. Some suggestions: Go back to the last page Go to the home page .. N-th roots of a complex number.

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