MATHEMATICS-13-08- 11th (PQRS) Space

REVIEW TEST-3 Class : XI (PQRS) Time : 100 min Max. Marks : 75 General Remarks: INSTRUCTIONS 1. The question paper contain 15 questions and 24 pages. All questions are compulsory. Please ensure that the Question Paper you have received contains all the QUESTIONS and Pages. If you found some mistake like missing questions or pages then contact immediately to the Invigilator. 2. Each question should be done only in the space provided for it, otherwise the solution will not be checked. 3. Use of Calculator, Log table and Mobile is not permitted. 4. Legibility and clarity in answering the question will be appreciated. 5. Put a cross ( × ) on the rough work done by you. 6. Last page is an Extra page. You may use it for any unfinished question with a specific remark: "continued on Extra page". Name Father's Name Class : Batch : B.C. Roll No. Invigilator's Full Name For Office Use ……………………………. Total Marks Obtained………………… Q.No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Marks Q.1 The sum of the first five terms of a geometric series is 189, the sum of the first six terms is 381, and the sum of the first seven terms is 765. What is the common ratio in this series. [4] Q.2 Form a quadratic equation with rational coefficients if one of its root is cot218°. [4] Q.3 Let  and  be the roots of the quadratic equation (x – 2)(x – 3)+(x – 3)(x + 1)+(x + 1)(x – 2)=0. Find the value of 1 ( +1)( +1) 1 + (  2)(  2) 1 + (  3)(  3) . [4] Q.4 If a sin2x + b lies in the interval [–2, 8] for every x  R then find the value of (a – b). [4] Q.5 For x  0, what is the smallest possible value of the expression log(x3 – 4x2 + x + 26) – log(x + 2)? [4] Q.6 The coefficients of the equation ax2 + bx + c = 0 where a  0, satisfy the inequality (a + b + c)(4a – 2b + c) < 0. Prove that this equation has 2 distinct real solutions. [4] Q.7 In an arithmetic progression, the third term is 15 and the eleventh term is 55. An infinite geometric progression can be formed beginning with the eighth term of this A.P. and followed by the fourth and second term. Find the sum of this geometric progression upto n terms. Also compute S if it exists. [5] Q.8 Find the solution set of this equation log|sin x|(x2 – 8x + 23) > log|sin x|(8) in x  [0, 2]. [5] Q.9 Find the positive integers p, q, r, s satisfying tan 24 = ( – q )( – s). [5] Q.10 Find the sum to n terms of the series. 1 + 2 + 3 + 4 + 5 + ........ 2 4 8 16 32 Also find the sum if it exist if n  . [5] Q.11 If sin x, sin22x and cos x · sin 4x form an increasing geometric sequence, find the numerial value of cos 2x. Also find the common ratio of geometric sequence. [5] Q.12 Find all possible parameters 'a' for which, f (x) = (a2 + a – 2)x2 – (a + 5)x – 2 is non positive for every x  [0, 1]. [5] Q.13 The 1st, 2nd and 3rd terms of an arithmetic series are a, b and a2 where 'a' is negative. The 1st, 2nd and 3rd terms of a geometric series are a, a2 and b find the (a) value of a and b (b) sum of infinite geometric series if it exists. If no then find the sum to n terms of the G.P. (c) sum of the 40 term of the arithmetic series. [5] Q.14 The nth term, an of a sequence of numbers is given by the formula an = an – 1 + 2n for n  2 and a1 = 1. Find an equation expressing an as a polynomial in n. Also find the sum to n terms of the sequence. [8]  Q.15 Let f (x) denote the sum of the infinite trigonometric series, f (x) = sin n1 2x sin x . 3n 3n Find f (x) (independent of n) also evaluate the sum of the solutions of the equation f (x) = 0 lying in the interval (0, 629). [8] EXTRA PAGE