MATHEMATIC-24-09- 11th (J-Batch)

REVIEW TEST-3 Class : XI (J-Batch) Time : 100 min Max. Marks : 75 General Remarks: INSTRUCTIONS 1. The question paper contain 14 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 page is an Extra pages. 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 If tan , tan  are the roots of x2 – px + q = 0 and cot , cot  are the roots of x2 – rx + s = 0 then find the value of rs in terms of p and q. [4] Q.2 Let P(x) = ax2 + bx + 8 is a quadratic polynomial. If the minimum value of P(x) is 6 when x = 2, find the values of a and b. [4]   1  Q.3 Let P = 102n1  then find log (P). [4]   n1   0.01 Q.4 Prove the identity sec8A 1 sec 4A 1 = tan 8A tan 2A . [4] Q.5 Find the general solution set of the equation logtan x(2 + 4 cos2x) = 2. [4] Q.6 Find the value of sin  + sin 3 + sin 5 + + sin17 cos  + cos 3 + cos 5 + + cos17  when  = 24 . [4] Q.7(a) Sum the following series to infinity 1 1·4·7 1 + 4·7 ·10 1 + 7 ·10·13 + ........... [3] Q.7(b) Sum the following series upto n-terms. 1 · 2 · 3 · 4 + 2 · 3 · 4 · 5 + 3 · 4 · 5 · 6 + ............. [3] Q.8 The equation cos2x – sin x + a = 0 has roots when x  (0, /2) find 'a'. [6] Q.9 A, B and C are distinct positive integers, less than or equal to 10. The arithmetic mean of A and B is 9. The geometric mean of A and C is 6 . Find the harmonic mean of B and C. [6] Q.10 Express cos 5x in terms of cos x and hence find general solution of the equation cos 5x = 16 cos5x. [6] Q.11 If x is real and 4y2 + 4xy + x + 6 = 0, then find the complete set of values of x for which y is real. [6] Q.12 Find the sum of all the integral solutions of the inequality [6] 2 log3x – 4 logx27  5. 1 tan  1 tan   1 tan   Q.13 If  +  +  =   , show that         sin  + sin  + sin  1 = . 2 1+ tan   1+ tan   1+ tan   cos  + cos + cos              [7] Q.14(a) In any  ABC prove that c2 = (a – b)2cos2 C + (a + b)2sin2 C . [4] 2 2 Q.14(b) In any  ABC prove that a3cos(B – C) + b3cos(C – A) + c3cos(A – B) = 3 abc. [4] EXTRA PAGE