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CUSTOMER_CODE SMUDE DIVISION_CODE SMUDE EVENT_CODE Jan2017 ASSESSMENT_CODE BC0033_Jan2017 QUESTION_TYPE DESCRIPTIVE_QUESTION QUESTION_ID 2959 QUESTION_TEXT What is a matrix? Explain six different types of matrices. Matrix: A matrix is a rectangular array of numbers arranged in rows and columns enclosed by a pair of brackets and subject to certain rules of Presentation. Six different types of matrices: SCHEME OF EVALUATION i. Square matrix: A matrix is said to be a square matrix if number of rows is equal to number of columns. ii. Column matrix: A matrix in which we have only one column is said to be a column matrix. iii. Row matrix: A matrix in which we have only one row is said to be a row matrix. iv. Diagonal matrix: A square matrix in which only the elements on the main diagonal are nonzero is said to be diagonal matrix. v. Identity matrix: A diagonal matrix in which all the diagonal elements are all equal to one is called identity matrix. vi. Scalar matrix: A diagonal matrix whose diagonal elements are equal is called a scalar matrix. vii. Null matrix: A matrix in which all the elements are zeroes, is called a null matrix viii. Upper Triangular matrix : A square matrix all of whose elements below the leading diagonal are zero, is called an upper triangular matrix ix. Unit matrix : A unit matrix is a square matrix in which every element in the principal diagonal is 1 and all the other elements are zero QUESTION_TYPE DESCRIPTIVE_QUESTION QUESTION_ID 2962 QUESTION_TEXT Define sample space. Explain equally likely events and mutually exclusive events with an example. SCHEME OF EVALUATION The set of all possible outcomes of a random experiment is the sample space.(2 marks) Equally likely events:(4 marks) Two or more events are equally likely of they have equal chance of occurrence. That is equally likely events are such that none of them has greater chance of occurrence than the others. Ex: while throwing a fair die, A = {2, 4, 6}, B = {1, 3, 5} and C = {1, 2, 3} are equally likely. Mutually exclusive events:(4 marks) Two or more events are mutually exclusive if only one of them can occur at a time. That is the occurrence of any of these events totally excludes the occurrence of the other events. Mutually exclusive events cannot occur together. Ex: While tossing a coin, the outcomes ‘Head’ and ‘Tail’ are mutually exclusive because when the coin is tossed once the result cannot be Head as well as Tail. QUESTION_TYPE DESCRIPTIVE_QUESTION QUESTION_ID 2964 QUESTION_TEXT Define Statistics. What are the basic characteristics of statistics? SCHEME OF EVALUATION Statistics: When one refers to numerical descriptions of quantitative aspects of things, it is called statistics. (1.25 marks) Basic Characteristics of Statistics: (1.75 x 4 = 8.75 marks) 1. Statistics are aggregates of facts: statistics are a number of facts. A single fact cannot be called a statistics. e.g. Enrollment in 1994 is not astatistics but enrollment from 1985-1995 is a statistics. 2. Statistics are affected to a marked extent by a multiplicity of causes:For example number of pass outs in a exam. will depend upon a numberof factors viz., total enrollment, dropout quantity of level of exam. etc. 3. Statistics must be estimated with a reasonable accuracy: For example:number of trees in a orchad should not be in decimals or figures0.297743 should not be written as 0.3 when it represents lakhs. 4. Data in statistics is collected in a systematic manner with a predetermined purpose e.g. Blood pressure level of a patient before drug administration,after I week and alter 2week of drug administration. 5. Statistics should be placed in relation to each other in point of time. Space or condition putting all these characteristic together statistics could be defined as : Aggregate of facts, affected to a marked extent by multiplicity of causes, numerically expressed enumerated or estimated according to a reasonable standard of accuracy, collected in a systematic manner for a predetermined purpose and placed in relation to each other. QUESTION_T DESCRIPTIVE_QUESTION YPE QUESTION_ID 74105 a. There are two restaurants next to each other. One has a sign that says “Good food is not cheap” and the other has a sign that says “cheap food is not QUESTION_T good”. Show that both signs are saying the same thing. EXT b. In how many ways the letters of the word MISSISSIPPI be arranged such that 4S’s are not together? a. Let g: Food is Good c: Food is cheap The sign of first restaurant can be written as g→~c, and the sign of second be written as c→~g. SCHEME OF EVALUATION Hence the prove. (5 marks) b. 33810 ways (5 marks) QUESTION_TYPE DESCRIPTIVE_QUESTION QUESTION_ID 74107 QUESTION_TEXT a. A bag contains 3 red and 4 green and 3 yellow marbles. Three marbles are randomly drawn from the bag. What is the probability that they are of i. the same colour ii. different colours b. The probabilities of two students A and B solving a problem are 1/2 and 3/4 respectively. If both of them independently try , what is the probability that the problem is solved? SCHEME OF EVALUATION a. i. 1/20 ii. 3/10 (3+3 marks) b. 0.875 (4 marks) QUESTION_TYPE DESCRIPTIVE_QUESTION QUESTION_ID 104870 There are two book shelves. The first self has 8 Sanskrit books and 4 Kannada books. The Second self has 10 Sanskrit books and 15 Kannada books. Once of the two shelves is selected at random. Two books are then selected at random from the selected shelf. Find the probability that QUESTION_TEXT i. Both the selected books are Kannada books ii. Both the selected books are Sanskrit books iii. One of them is a Kannada book and other is a Sanskrit book The first shelf is selected B- Both the selected books are Kannada books C- Both the selected books are Sanskrit books D- One of them is Kannada book and other is a Sanskrit book (1 mark) A1 the second shelf is selected SCHEME OF EVALUATION (3 MARKS) i. P [both Kannada books] = ii. p [both Sanskrit books] = iii P [ one Kannada and one Sanskrit] = (2 M) = 0.2205 (2 M) = 0.2871 (2 M) = 0.9848