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CBSE Class 11 Pre Board 2020 : Mathematics (Delhi Public School (DPS), Jammu)

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DELHI PUBLIC SCHOOL, JAMMU Assignment(2019-20) Sub: Mathematics Q1. Class: XI From 50 students taking examinations in mathematics, physics and chemistry, 37 passed mathematics, 24 physics and 43 chemistry. At most 19 passed mathematics chemistry and at most 20 physics and chemistry. The largest possible number that could have passed all three exams is a. 10 Q2. Q3. b. 12 1+ b. 3 c. 1 d. None of these is The remainder when 2740 is divided by 12 b. 7 c. 9 d. 11 c. 20C10 d. none of these Maximum value of 20Cr, is equal to 20 C11 b. 20C12 The middle term in the expansion of (x + 4)4 is a. 96 x3 Q6. 1 2 a. 4 a. Q5. d. None The term independent of x in the expansion of a. 3 Q4. c. 9 b. 96x2 c. 96x2 d. none of these Equations of circles which pass through the points (1, -2) and (3, -4) and touch the x-. axis is a. 2 + 2 + 6 + 2 + 9 = 0b. 2 + 2 + 10 + 20 + 25 = 0 c. 2 + 2 6 + 4 + 9 = 0 Q7. d. none The equation of circles passing through (3, -6) touching both the axes is a. 2 + 2 6 + 6 + 9 = 0 b. 2 + 2 + 6 6 + 9 = 0 c. 2 + 2 + 30 30 + 225 = 0 d. 2 + 2 30 + 30 + 225 = 0 Q8. The sequences S = i + 2i2 + 3i3 + 4i4 + .upto 100 terms simplifies to, where i = 1 a. 50(1 i) Q9. Q10. Q14. is equal to c. 4(b2 a2) d. None of these 8 Chairs are numbered from 1 to 8. Two women & 3 men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4, then the men select the chairs from among the remaining. The number of possible arrangements is: b. P2.4P3 c. 4C34P3 d. 4P2.6P3 Number of words that can be made with the letters of the word GENIUS if each word neither begins with G nor ends in S, is: b. 240 c. 480 d. 504 5 boys & 3 girls are sitting in a row of 8 seats. Number of ways in which they can be seated so that not all the girls sit side by side, is: b. 9080 c. 3960 d. 11600 A line makes an angles 45o with X axis and at a distance of 2 from the origin. Its equation is a. x + y 2 = 1 b. 2 + = 1 c. y x = 2 d. y x = 2 A line passes through the point (1, 2) and makes 60o angle with X- axis. A point on this line at a distance 3 from the point (1, 2), is 5 a. c. Q15. b. 4(a2 b2) a. 36000 Q13. a. 4 (a2 + b2) a. 24 Q12. If (x + iy)1/3 = a + ib, then + a. 6C3, 4C4 Q11. c. 25(1 + i) d. 100(1 i) b. 25i 2 5 ,2 ,2 + 2 3 3 2 3 3 2 b. 3 2 ,2 + 3 2 d. None of these If a line passes through the point P (1, 2) makes an angles of 45o with the X axis and meets the line x + 2y 7 = 0 at Q, then PQ equals. 2 2 a. b. 3 3 2 c. 3 3 d. 2 Q16. The sum of n terms of 1.2.3 + 2.3.4 + 3.4.5 + . is 1 a. c. 4 1 2 1 + 1 ( + 2) b. + 1 + 2 ( + 3) + 1 + 2 ( + 3) d. none of these 4 Q17. If a1, a2, a3 .an .are in AP such that a4 a7 + a10 = m, then the sum of first 13 terms of this AP is a. 15 m Q18. b. 10m d. 13m The equation of the parabola whose focus is (-3, 0) and directrix is, x + 5 = 0 is: a. y2 = 4 (x 4) Q19. c. 12m b. y2 = 2(x + 4) c. y2 = 4(x 3) d. y2 = 4 (x + 4) If (2, 0) is the vertex & y axis the diretrix of a parabola, then its focus is: a. (2, 0) b. (-2, 0) 2 + 1, 3 = 5 1 , c. (4, 0) d. (-4, 0) Q20. If Q21. If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in (A B). Q22. A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second? 3 3 3 (i) 10 cm , find the values of x and y. (ii) 15 cm (iii) 21 cm Q23. The angle of a quadrilateral are in A.P. and the greatest angle is 120o. Express the angles in radians. Q24. Find the coefficient of 17 in the expansion of 4 3 Q25. Find the sixth term of the expansion 2 + 3 third term from the end is 45. Q26. Find the value of r, if the coefficients of (2r + 4)th and (r 2)th terms in the expansion of (1 + x)18 are equal. 1 15 1 1 1 , if the binomial coefficient of the Q27. Find the equation of the circle whose centre lies on the positive direction of y-axis at a distance 6 from the origin and whose radius is 4. Q28. If the equation of two diameters of a circle are 2x + y = 6 and 3x + 2y = 4 and the radius is 10, find the equation of the circle. Q29. 2 2 +9 5 5 +5 Q30. 2 4 +3 3 2 2 3 Q31. If P (2n 1, n) : P(2n + 1, n 1) = 22 : 7 find n Q32. If P(n , 5) : P(n, 3) = 2 : 1, find n. Q33. If P (15, r 1) : P(16, r 2) = 3 : 4, find r. Q34. Find the sum of all integers between 50 and 500 which are divisible by 7. Q35. Find the sum of all those integers between 100 and 800 each of which on division by 16 leaves the remainder 7 ? Q36. The sum of first 7 terms of an A.P. is 10 and that of next 7 terms is 17. Find the progression. Q37. If 5th, 8th and 11th terms of a G.P. are p.q and s respectively, prove that q2 = ps. Q38. Find three numbers in G.P. whose sum is 38 and their product is 1728. Q39. Find the image of the point (3, 8) with respect to the line x + 3y = 7 assuming the line to be a plane mirror. Q40. If the lines y = 3x + 1 and 2y = x + 3 are equally inclined to the line y = mx + 4, find the value of m. Q41. If sum of the perpendicular distances of a variable point P (x, y) from the lines x + y 5 = 0 and 3x 2y + 7 = 0 is always 10. Show that P must move on a line. Q42. Find equation of the line which is equidistant from parallel lines 9x + 6y 7 = 0 and 3x + 2y + 6 = 0. Find the mean deviation about the mean for the data .Q43. dncome per day 0-100 Number of 4 100-200 200-300 300-400 400-500 500-600 600-700 700-800 8 9 10 7 5 4 3 persons Q44. Height in cms 95-105 105-115 115-125 125-135 135-145 145-155 Number of boys 9 13 26 30 12 10 Q45. A rod of length 12 cm moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point P on the rod, which is 3 cm from the end in contact with the x-axis. Q46. Find the area of the triangle formed by the lines joining the vertex of the parabola x2 = 12y to the ends of its latus rectum. Q47. From the employees of a company, 5 persons are selected to represent them in the managing committee of the company. Particulars of five persons are as follows. S. No. Name Sex Age in years 1. Harish M 30 2. Rohan M 3. Sheetal F 46 4. Alis F 28 5. Salim M 41 33 A person is selected at random from this group to act as a spokesperson. What is the probability that the spokesperson will be either male or over 35 years? Q48. If 4-digit numbers greater than 5,000 are randomly formed from the digits 0, 1, 3, 5, and 7, what is the probability of forming a number divisible by 5 when, (i) the digits are repeated? (ii) the repetition of digits is not allowed? Q49. A manufacturer has 600 litres of a 12% solution of acid. How many litres of a 30% acid solution must be added to it so that acid content in resulting mixture will be more than 15% but less than 18%? Q50.Prove the following by using the principle of mathematical induction for all n : 1 + 3 + 32 + + 3n-1 = Q51. Find the value of tan . Find the general solution for each of the following equations: Q52. Cos 4x = cos 2 x Q53. cos 3x + cos x cos 2x = 0 Q54. If are different complex numbers with = , then find .

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