Palindromic polynomial

May 19th, 2015
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A polynomial is palindromic, if the sequence of its coefficients are a palindrome. Some examples of palindromic polynomials are: (x + 1)2 = x2 + 2x + 1 (x + 1)3 = x3 + 3x2 + 3x + 1. Generally, the expansion of (x + 1)n is palindromic for all n (can see this from binomial expansion)

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MATHEMATICSTime allowed : 3 hours Maximum marks : 100General Instructions :(i) All questions are compulsory.(ii) Question number 1 to 15 are of 2 marks each.Question number 16 to 25 are of 4 marks each.Question number 26 to 30 are of 6 marks each.(iii) If you wish to answer any question already answered for any reason, cancel the previousanswer.(iv) Use of calculator is not permitted, however you may ask for logarithmic tablesQuestion Paper Code 65/1/11. A coin is tossed 12 times. What is the probability of getting exactly 8 tails ?2. Three coins are tossed simultaneously. List the sample space for the event.3. Two cards are drawn without replacement from a well shuffled pack of 52 cards. What isthe probability that one is a red queen and the other is a king of black colour ?4. Find the unit vector perpendicular to both a +3 + j-2k and b= 2+3j-k5. Find if a =4-j+k and -2j+2k are perpendicular to each other.6. Find the regression co-efficient bxy and byx given thatn=7 x=24 y=12 x2=374 y2=97 and xy=1577. Solve: (1+x) (1+y2) dx+1 (x+y) (1+x2) dy=08. Evaluate:9. Evaluate:10.Evaluate:11.If y= tan-1x show that:12.Discuss the applicability of Rolles theorem for the function f(x) = x2/3 on [-1,1]13. Evaluate:14. Iffind the matrix C such thatA+B+C is a zero matrix15. Construct a 2 X 3 matrix whose element in the in the ith row and the jth column aregiven by aij = 3i-j/2.16. Show that the points with position vectors 6- 7, 6-19 -4k,3j

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