CHINMAYA VIDYALAYA / B S CITY (CBSE NEW GENERATION SCHOOL) ANNUAL MODEL QUESTION PAPER -2014-2015 CLASS : XI F.M. - 100 SUBJECT : MATHEMATICS TIME : 3Hrs General Instructions a) Section ‘A’ contains 6 questions carry 1 mark each. b) Section ‘B’ contain 13 question carry 4 marks each. c) Section ‘C’ contain 7 question carry 6 marks each. SECTION-A 1. If y (1 TanA)(1 TanB), Where AB 4 , Find (1 y)1 y 2. If (a ib)5 i , then (b ai)8 x it (1 x) tan 3. Find x 1 2 4. If two coins are tossed once, find the probability of getting at most two heads. 5. By using counter-example, show that the following statement is not true. P: : The equation x2 – 1 = 0 does not have a root lying between 0 and 2. 6. . Write the negation of the statement “All politician are corrupt. SECTION-B 7. A relation R is defined on the set z of integers as ( x, y) R x2 y 2 25 . Find 8. (i) R (ii) R-1 (iii) domain of R (iv) Range of R-1 Find the domain of the function t ( x) 1 x2 log10 (1 x) OR, Draw the graph of the functions x2 , x0 f ( x ) x, 0 x 1 1 , 1 x x a b a cos tan 0 2, then prove that cos ab a b cos 10. Solve : tan tan 2 tan 3 0 OR Solve: tan tan( 3 ) tan( 2 3 ) 3. i 1 11. Write the complex number in polor form. cos 3 Sin 3 9. If tan 0 2 12. Solve : (2 i) x2 (5 i) x 2(1 i) 0 13. Prove by principle of mathematical induction : 11n2 122n1 is divisible by 133. 14. Let S be the sum, P the product and R the sum of reciprocals of n terms of a GP. Prove that S P 2 OR P2RN=Sn R OR If a,b,c be the pth,qth and rth terms of both AP and also of GP, prove that abc bca cab 1 15. Find the number of arrantgments of the letters of the word ‘INDEPENDENCE’. In how many of these arrangements. i) Do the words start with P ii) Do the vowels never occur together. iii) Do the words being with I and end with P ? 16. Prove that the first order equation in x and y always represents a straight line. 17. Find the equation of a circle which passes through the point (2,0) and whose centre is the limit point of intersection of the lines 3x 5 y 1 and (2 c) x 5i 2 y 1 c 1 . Find the difference co-efficient of y x tan x by first principle. 18. OR Find the d.c. of y tan x by first principle. 19. Two cards are drawn at random from a well-shutled pack of 52 cards. What is the probability that either both are red or both are Jacks ? PART-C 20. (i) For any three sets A, B and C, prove that A ( B C ) ( A B) ( A C ) (ii) Draw appropriate venn-diagrams for (a) A ' ( B C ) (b) A ( B C ) 21. If A+B+C = 0, prove that cos2 A Cos 2 B Cos 2C H 2 cos A cos BCosC 22. Solve the following an equation by graphical method : 3x y 6 0,4 x 9 y 36 0,4 x 3 y 12, x 3 y 6, x 0, y 0. 23. Find the sum of the first n terms of the series 3+7+13+21+31 + - - - - - 24. Find the centre, lengths of major and minor areas, co-ordinaters of vertices, eccentricity, co-ordinates of foci and length of latus rectuem of the ellipse 25x2 9 y 2 150 x 90 y 225 0 OR Find the standard equation of the hyperbola. 25. If a,b,c and d, in nay binomial expansion be the four consecutive terms then prove b 2 ac 4a that 2 c bd 3c OR, th th th If r , (r + 1) and (r + 2) terms in the expansion of (1+x)n are in AP, show that n2 n(ur 1) ur 2 2 0 26. Calculate the mean deviation about median age for the age distribution of 100 persons given below Age Numbers 16-20 5 21-25 6 26-30 12 31-35 14 ---xxx---- 36-40 26 41-45 12 46-50 16 51-55 9

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