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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)]

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