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CBSE Class 11 Pre Board 2019 : Mathematics (St Xavier's Sr. Sec. School, Delhi)

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Annual Examination in MATHEMATICS Std. 11 19-2-2019 Time : 3 hrs. Max. Marks : 100 GENERAL INSTRUCTIONS: i) SECION A contains 4 questions each of 1 mark. ii) SECTION B contains 8 questions each of 2 marks. iii) SECTION C contains 11 questions each of 4 marks. iv) SECTION D contains 6 questions each of 6 marks. SECTION A 1. Find the slope of the line which makes an angle of 30o with the positive direction of y-axis measured anti-clockwise. 2. Find the equation of hyperbola whose vertices are at ( 2, 0) and foci at ( 3, 0). 3. Name the octant in which point A( 4, 2, 5) lie. (OR) The centroid of ABC is the point (1, 1, 1). If the co-ordinates of A, B, C are (3, 5, 7), ( 1, 7, 6) and (1, k, 2) find k. 4. Let A and B be two sets such that n(A) = 3 and n(B) = 2, find number of relations from A to B. SECTION B 5. Find equation of parabola with vertex at (0, 0) and passing through ( 5, 2) and symmetric with respect to y-axis. 6. Find the ratio in which line segment joining the points (4, 8, 10) and (6, 10, 8) is divided by YZ plane. 7. Find the distance between the lines 2x + 3y 4 = 0 and 6x + 9y + 5 = 0. (OR) Reduce x 3 + 8 = 0 in normal form. 8. Find the equation of set of points P such that its distances from the points A (3, 4, 5) and B( 2, 1, 4) are equal. 9. In a survey of 400 students in a school, 100 were listed as taking apple juice, 150 as taking orange juice and 75 were listed as taking both apple as well as orange juice. Find how many were taking neither apple nor orange juice? 10. If A = {1, 2, 3, 4, 6}, B = {2, 4, 6, 8}, C = {3, 4, 5, 6} and D = {2, 3, 5, 6, 8} find (A B) - (C D) (OR) U = {1, 2, 3, .. 9}, A = {2, 4, 6, 8}, B = {2, 3, 5, 7} then prove (A B) = A B . 11. Find the derivative of (px + q) ( + s) with respect to x. r (OR) Find the derivative of 12. 3 x5 - cosx sinx x with respect to x. 3 Evaluate: cos ( 2 + x) cos(2 + x) [cot ( 2 - x)) +cot(2 + x)] Std. 11 -2- MATHEMATICS SECTION C 13. Find the equation of circle concentric with circle 2x2 + 2y2 8x 12y 9 = 0 and passing through the centre of x2 + y2 + 8x + 10y 7 = 0. (OR) Find the equation of circle passing through the points (9, 1), (7, 9) and (-2, 12). 14. If the term free from x in the expansion of ( x- x2 ) 15. Find the equation of line passing through the point of intersection of the lines x y + 1 = 0 and 2x 3y + 5 = 0 and whose distance from the point (3, 2) is 7/5. 16. Show that k 10 Prove is 405, find k. cos6x = 32cos6 x - 48cos4 x + 18cos2 x 1 (OR) sin5x - 2sin3x + sinx cos5x - cosx = tanx. 17. Find the domain and range of real function (x)= 25 - x2 . 18. Find the coordinates of foci, equation of major axis, length of minor axis, length of latus rectum of the given curve 36x2 + 4y2 = 144. 19. The relation R={(x ,x3) : x is a prime number less than 10} is given a) Write R in roster form. b) Write domain of R. c) Write range of R. d) Write co-domain of R. 20. Evaluate lt f ( x) ( ) = {| | x 0 0 21. If y = 22. Two students Anil and Aashima appeared in an examination. The probability that Anil will qualify the examination is 0.05 and that Aashima will qualify examination is 0.10. The probability that both will qualify the examination is 0.02. Find the probability that a) Both Anil and Aashima will not qualify the examination. b) Atleast one of them will notqualify the examination. (OR) An integer is chosen at random from the numbers varying from 1 to 60. What is the probability that the integer chosen is multiple of 2 or 5 or 10? 23. In a survey of 60 people, it was found that 25 people liked product H, 26 liked product T, 26 people liked product I, 9 liked both H and I, 11 people liked both H and T, 8 people liked both T and I, 3 like all the three products. Find a) The number of people who liked atleast two of the products. b) The number of people who liked only product T. sinx - xcosx xsinx + cosx , prove dy dx = , , 0 . =0 x2 (xsinx + cosx) 2 . Std. 11 -3- MATHEMATICS SECTION D 24. 3 1 If the seventh term from the beginning and the end in the expansion of ( 2 + 3 ) are 3 equal, find . (OR) If the coefficients of a , a and a in the expansion of (1 + a)n are in A.P., Prove n2 n(4r + 1) + 4r2 2 = 0. r 1 25. r r+1 Find the derivative of ( ) = using the 1st principle. (OR) Find the derivative of ( ) = 2 +3 2 using the 1st principle. 26. Find the probability that when a hand of 5 cards is drawn from a well-shuffled deck of 52 cards, it contains a) All Queens b) at least 3 Queens c) At most 3 Queens d) 3 Queens 27. If = + , prove 2 dx = 28. Prove that the product of the lengths of the perpendiculars drawn from the points ( 2 2 , 0) ( 2 2 , 0) to the line + = 1 is 2 . dy x a a - x. (OR) A line is such that its segment between the lines 5x y + 4 = 0 and 3x + 4y 4 = 0 is bisected at the point (1,5). Obtain its equation. 29. Solve the following system of inequalities graphically: 4x + 3y 60, y 2x, x 3, x, y 0. -x-x-x-x-x-x-x-

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