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ISC Class XI Board Specimen 2019 : Mathematics

6 pages, 48 questions, 19 questions with responses, 22 total responses,    0    0
ISC 11th
Indian School Certificate Examination (ISC), New Delhi
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MATHEMATICS (Maximum Marks: 100) (Time allowed: Three hours) (Candidates are allowed additional 15 minutes for only reading the paper. They must NOT start writing during this time.) --------------------------------------------------------------------------------------------------------------------The Question Paper consists of three sections A, B and C. Candidates are required to attempt all questions from Section A and all questions EITHER from Section B OR Section C Section A: Internal choice has been provided in three questions of four marks each and two questions of six marks each. Section B: Internal choice has been provided in two questions of four marks each. Section C: Internal choice has been provided in two questions of four marks each. All working, including rough work, should be done on the same sheet as, and adjacent to the rest of the answer. The intended marks for questions or parts of questions are given in brackets [ ]. Mathematical tables and graph papers are provided. --------------------------------------------------------------------------------------------------------------------SECTION A (80 Marks) Question 1 [10 2] (i) If A = {1, 2, 3, 4, 5, 6,} B = {2, 4, 5, 6, 8, 9, 10}, find A B. (ii) Let A = {2, 4, 6, 8} B = {1, 2, 3, 4) and R = {(a, b) : a A, b B, a is divisible by b}. Write Relation R in set builder form. (iii) Prove that: = (iv) In a ABC, prove that ( ) = (v) If (vi) If and are the roots of the equation Px2 + qx + 1 = 0, find = + , find the values of a and b. + . -----------------------------------------------------------------------------------------------------------------------1 SPECIMEN QUESTION PAPER CLASS XI - 2019 (vii) (viii) (ix) In how many ways can 12 books be arranged on a shelf if: (a) 4 particular books must always be together. (b) 2 particular books must occupy the first position and the last position. Find the derivative of : Evaluate: Lim ( ) (x) An urn contains 60 blue pens and 40 red pens. Half of the pens of each one is defective. If one pen is chosen at random, what is the probability that it is a defective or a red pen? Question 2 [4] Find the domain and range of : 2 | 4| Question 3 (a) [4] Solve: 7 + 4 + = 0 0 < < 2 OR (b) Prove that cos A cos 3 A cos 5 A cos 7 A cot 4 A sin A sin 3 A sin 5 A sin 7 A Question 4 [4] Using Mathematical induction, prove that 10n + 3 4n+2 + 5 is divisible by 9 for an n N. Question 5 [4] If z = x + iy and |2 1| = | + 2 |, find the locus of z and represent it in the argand diagram. -----------------------------------------------------------------------------------------------------------------------2 SPECIMEN QUESTION PAPER CLASS XI - 2019 Question 6 (a) [4] A Committee of 6 members has to be formed from 8 boys and 5 girls. In how many ways can this be done if the Committee consists of : (i) Exactly 3 girls (ii) At least 3 girls OR (b) How many different words GRANDMOTHER , so that: can be (i) The word starts with G and end with R. (ii) The letters A, N, D are always together. formed of the letter of word (iii) All vowels never come together. Question 7 [4] Find the term independent of x in the expression of : 3 + 3 2 Question 8 [4] Find the equation of acute angled bisector of lines: 3x 4y + 7 = 0 and 12x 5y 8 = 0 Question 9 (a) [4] Find the equation of the tangent to the circle + 2 2 23 = 0 2 + + 3 = 0 OR (b) Find the equation of the circle which passes through the points (2, 3), (4, 5) and the centre lies on the line y 4x + 3 = 0. Question 10 [4] Differentiate the function Sin (2x 3) by First Principle of differentiation. -----------------------------------------------------------------------------------------------------------------------3 SPECIMEN QUESTION PAPER CLASS XI - 2019 Question 11 [6] = In a ABC, ( ) ( ) , prove that it is either a right angled or isosecles . Question 12 (a) [6] If x be real, find the maximum and minimum value of: y = OR (b) If , be the roots x2 +lx + m = 0, then form an equation whose roots are: ( + ) and ( ) Question 13 (a) [6] The sum of three consecutive numbers of a G.P is 56. If we substract 1, 7 and 21 from these numbers in the order, the resulting numbers form an A.P., find the numbers. OR (b) Find the sum of the series to n terms: + + + .. n terms. Question 14 [6] Find the mean, standard derivation for the following data: Class 0 10 Frequency 2 10 20 20 30 30 40 40 50 50 60 60 70 3 5 10 3 5 2 SECTION B (20 Marks) Question 15 [3 2] (a) Find the co-ordinates of a point on the parabola y2=8x, whose focal dististance is 4. (b) Prove that: ~(P q) = P^(~q) (c) Write Converse and inverse of the given conditional statement: If a number n is even, then n2 is even. -----------------------------------------------------------------------------------------------------------------------4 SPECIMEN QUESTION PAPER CLASS XI - 2019 Question 16 (a) [4] Find the equation of ellipse whose focus (1, 2), directrix 3x + 4y 5 = 0 and eccentricity is OR (b) Find the centre, focus, eccentricity and latus rectrum of the hyperbola 16x2 9y2 = 144. Question 17 (a) [4] In what ratio the point P( 2, y, z) divides the line joining the points A(2, 4, 3) and B( 4, 5, 6). Also, find the coordinates of point P. OR (b) If the origin is the centroid of the triangle with vertices ( 4, 2, 6) (2a, 3b, 2c) and (8, 14, 10) find the values of a, b and c. Question 18 [6] Find the equation of Parabola whose directrix is 2x 3y + 4 = 0 and vertex at (5 4) SECTION C (20 Marks) Question 19 (a) The mean weight of 150 students in a certain class is 60 kg. The mean weight of boys is 70 kg and that of girls in the class is 55 kg. Find the number of boys and girls in the class. [2] (b) Compute D3 and D7 for the following distribution: [4] Marks No. of students 0 10 10 20 20 30 30 40 40 50 50 60 60 70 70 80 3 10 17 7 6 4 2 1 OR Calcuate the mode from the following data: Marks No. of students 0 10 5 10 20 15 20 30 30 30 40 8 40 50 2 -----------------------------------------------------------------------------------------------------------------------5 SPECIMEN QUESTION PAPER CLASS XI - 2019 Question 20 (a) In a sample of n observations given that = 55 and rank correlation r = , then find the value of n . [2] (b) Find the correlation coefficient r(x, y) if: [4] n = 10, = 60, = 60, = 400, = 580, = 305, OR Ten students got the following percentages of marks in Mathematics and Physics: Mathematics 56 Physics 89 64 90 75 85 86 85 74 78 87 91 95 97 98 56 74 86 90 66 Find the Spearman s rank correlation coefficient for the above data. Question 21 [4] Calculate the index number for the year 1990 with respect to 1980 as base from the following data using weighted average of price relatives: Commodity Weights Year 1990 Year 1980 A 22 320 200 B 48 120 100 C 17 20 28 D 13 60 40 Question 22 [4] The number of letters, in hundreds, posted in a certain city on each day for a week is given below: Mon. 35 Tue. 70 Wed. Thur. 36 59 Fri. 62 Sat. Sun 60 71 Calculate 3 day moving averages and represent these graphically. -----------------------------------------------------------------------------------------------------------------------6 SPECIMEN QUESTION PAPER CLASS XI - 2019

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