MATHEMATICS-27-08- 11th (J-Batch) WA

REVIEW TEST-2 Class : XI (J-Batch) Time : 100 min Max. Marks : 75 General Remarks: INSTRUCTIONS 1. The question paper contain 17 questions and 23 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. Page No. 23 is Extra pages. You mayuse it for any unfinished question with a specific remark: "continued on page-23". 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 Find the set of values of 'a' for which the quadratic polynomial (a + 4)x2 – 2ax + 2a – 6 < 0  x  R. [3] Q.2 Solve the inequality by using method of interval, x +1  x + 5 . [3] x 1 x +1 Q.3 Find the minimum vertical distance between the graphs of y = 2 + sin x and y = cos x. [3] Q.4 Solve: d  3 cos x  cos3 x when x = 18°. [3]   dx  4  Q.5 If p, q are the roots of the quadratic equation x2 + 2bx + c = 0, prove that 2 log ( + y  q ) = log 2 + log  y + b + y2 + 2by + c  . [4] Q.6 Find the maximum and minimum value of y = x2 +14x + 9 x2 + 2x + 3  x  R. [4] 7 Q.7 Suppose that a and b are positive real numbers such that log27a + log9b = 2 and log27b + log9a = 3 . Find the value of the ab. [4] Q.8 Given sin2y = sin x · sin z where x, y, z are in an A.P. Find all possible values of the common difference of the A.P. and evaluate the sum of all the common differences which lie in the interval (0, 315). [4] Q.9 Prove that tan 8 tan  = (1 + sec2) (1 + sec4) (1 + sec8). [4] Q.10 Find the exact value of tan2  + tan2 3 + tan2 5 + tan2 7 . [4] 16 16 16 16 89 Q.11 Evaluate  1 . [5] n=11+ (tan n) Q.12 Find the value of k for which one root of the equation of x2 – (k + 1)x + k2 + k–8=0 exceed 2 and other is smaller than 2. [5] Q.13 Let an be the nth term of an arithmetic progression. Let Sn be the sum of the first n terms of the arithmetic progression with a1 = 1 and a3 = 3a8. Find the largest possible value of Sn. [5] A + C  C A B Q.14(a) If A+B+C =  & sin   2  = k sin 2 , then find the value of tan 2 ·tan 2 in terms of k.  (b) Solve the inequality, log0.5 log6 x2 + x  < 0. [2 + 4]  x + 4  Q.15 Let f (x) = sin6x + cos6x + k(sin4x + cos4x) for some real number k. Determine (a) all real numbers k for which f (x) is constant for all values of x. (b) all real numbers k for which there exists a real number 'c' such that f (c) = 0. [2 + 4] Q.16 Given the product p of sines of the angles of a triangle & product q of their cosines, find the cubic equation, whose coefficients are functions of p & q & whose roots are the tangents of the angles of the triangle. [6] Q.17 If each pair of the equations x2 + p1x + q1 = 0 x2 + p2 x + q2 = 0 x2 + p3x + q3 = 0 has exactly one root in common then show that (p1 + p2 + p3)2 = 4(p1p2 + p2p3 + p3p1 – q1 – q2 – q3). [6] EXTRA PAGE EXTRA PAGE