MATHEMATICS-04-06- 11th (PQRS) Space

REVIEW TEST-1 Class : XI Time : 90 min Max. Marks : 75 General Remarks: INSTRUCTIONS 1. The question paper contain two parts. Part-A contains short question and Part-B contains subjective questions. All questions are compulsory. Paper contains 10 questions in Part-A and 9 questions in Part-B. 2. You are advised NOT to spend more than 30 minutes in any case for part-A. 3. Each question should be done only in the space provided for it, otherwise the solution will not be checked. 4. Use of Calculator, Log table and Mobile is not permitted. 5. Legibility and clarity in answering the question will be appreciated. 6. Put a cross ( × ) on the rough work done by you. Name : Roll No. Batch Class : XI Invigilator's Full Name For Office Use ……………………………. Total Marks Obtained………………… Part-A Part-B Q.No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Marks PART-A Q.1 Find the number of real solution(s) of the equation logx9 – log3x2 = 3. [3] Q.2 Simplify: cos x · sin(y – z) + cos y · sin(z – x) + cos z · sin (x – y) where x, y, z  R. [3] Q.3 If logx–3(2x – 3) is a meaningful quantity then find the interval in which x must lie. [3] Q.4 If x = 1 and x = 2 are solutions of the equation x3 + ax2 + bx + c = 0 and a + b = 1, then find the value of b. [3] Q.5 tan  = 1 2 + 1 2 + 1 where   (0, 2), find the possible value of . [3] 2 +O  Q.6 Find the exact value of cos12  cos 72 sin 72 + sin12 . [3] Q.7 If the tangent of DAB is expressed as a ratio of positive integers a b in lowest term, then find the value of (a + b). [3] 12 A Q.8 If sin A = 13 . Find the value of tan 2 . [3] Q.9 Let x = (0.15)20. Find the characteristic and mantissa in the logarithm of x, to the base 10. Assume log102 = 0.301 and log103 = 0.477. [3] Q.10 The figure (not drawn to scale) shows a regular octagon ABCDEFGH with diagonal AF = 1. Find the numerical value of the side of the octagon. [3] PART-B cos3  + cot(3 + ) sec(  3) cosec 3   Q.11 Simplify     tan2 (  ) sin(  2)     . [4] Q.12 Find the sum of the solutions of the equation 2e2x – 5ex + 4 = 0. [4] Q.13 Prove the identity cot A + cosec A 1 = cot A . [4] cot A  cosec A +1 2 Q.14 If log (log ( log x)) = log (log ( log y)) = 0 then find the value of (x + y). [5]  1 2   1  Q.15 If log25 = a and log 225 = b, then find the value of log   + log  in terms of a and  9    2250  b (base of the log is 10 everywhere). [5] Q.16 Prove that the expression sin2 + sin2(120° + ) + sin2(120° – ) remains constant    R. Find also the value of the constant. [5] Q.17 Suppose that x and y are positive numbers for which log9x = log12y = log16(x + y). If the value of y x = 2 cos , where   (0,  2) find . [6] tan  1 cot  Q.18 If tan   tan 3 = 3 , find the value of cot   cot 3 . [6]  2 3 4 Q.19 Let S = sec 0 + sec + sec + sec + sec and P = tan  · tan 2 · tan 4 then prove 5 5 5 5 9 9 9 S + P = 2 2 sin 7 [6] 12 EXTRA PAGE