MATHEMATICS-17-09- 11th (PQRS) Space

REVIEW TEST-4 Class : XI Time : 100 min Max. Marks : 75 General Remarks: INSTRUCTIONS 1. The question paper contain 15 questions and 20 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 two pages are Extra pages. You may use it for any unfinished question with a specific remark: "continued on Page-19 or Page-20". 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 n n  ·2r ·5s if r  s  Q.1 Evaluate   rs where rs =  1 . if r  s r1 s1 Will the sum hold if n  ? [4] Q.2 Find the general solution of the equation, 2 + tan x · cot x + cot x · tan 2 x = 0. [4] 2 Q.3 Given that 3 sin x + 4 cos x = 5 where x  0,  2. Find the value of 2 sin x + cos x + 4 tan x. [4] Q.4 Find the integral solution of the inequality  0. [4]  Q.5 In  ABC, suppose AB = 5 cm, AC = 7 cm,  ABC = 3 (a) Find the length of the side BC. (b) Find the area of ABC. [4] Q.6 The sides of a triangle are n – 1, n and n + 1 and the area is n . Determine n. [4] Q.7 With usual notions, prove that in a triangle ABC, r + r1 + r2 – r3 = 4R cos C. [5] Q.8 Find the general solution of the equation, sin x + cos x = 0. Also find the sum of all solutions in [0, 100]. [5] Q.9 Find all negative values of 'a' which makes the quadratic inequality sin2x + a cos x + a2  1 + cos x true for every x  R. [5] Q.10 Solve for x, log x 2 2 log x 2 2  5log 2 x2 1 . [5] Q.11 In a triangle ABC if a2 + b2 = 101c2 then find the value of cot C cot A  cot B . [5] 1 1  log (sin x) 1  log (cosx) Q.12 Solve the equation for x, 52  52 5 =152 15 [5]  2 Q.13 Evaluate the sum  n . [5] n1 6 Q.14 Suppose that P(x) is a quadratic polynomial such that P(0) = cos340°, P(1) = (cos 40°)(sin240°) and P(2) = 0. Find the value of P(3). [8] Q.15 If l, m, n are 3 numbers in G.P. prove that the first term of an A.P. whose lth, mth, nth terms are in H.P. is to the common difference as (m + 1) to 1. [8] EXTRA PAGE EXTRA PAGE

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