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

Comments

Post a Comment

Popular posts from this blog

PHYSICS-15-10- 11th (PQRS) SOLUTION

XI (PQRS) PHYSICS REVIEW TEST-5 Select the correct alternative. (Only one is correct) [15 × 3 = 45] There is NEGATIVE marking. 1 mark will be deducted for each wrong answer. Q.31 Two trains, which are moving along different tracks in opposite directions towards each other, are put on the same track due to a mistake. Their drivers, on noticing the mistake, start slowing down the trains when the trains are 300 m apart. Graphs given below show their velocities as function of time as the trains slow down. The separation between the trains when both have stopped, is: (A) 120 m (B) 280 m (C) 60 m (D*) 20 m 1 [Sol: x1 = 2 1 × 10 × 40 = 200 m; x2 = – 2 × 8 × 20 = –80 m  xreletive = x1 + x2 = 280  separation = 300 – 280 = 20 m (D) ] Q.32 One end of a thin uniform rod of length L and mass M is riveted to the centre of a uniform circular disc of radius r and mass 2 M so that the rod is normal to the disc. The centre of mass of the combination from the centre of the disc is at dist
Read more

8-Circular Motion

8.1 (D) The maximum angular speed of the hoop corresponds to the situation when the bead is just about to slide upwards. The free body diagram of the bead is For the bead not to slide upwards. m2 (r sin 45°) cos 45° – mg sin 45° < N (1) where N = mg cos 45° + m2 (r sin 45ยบ) sin 45° (2) From 1 and 2 we get.  = rad / s. 8.2 (C) Let v be the speed of particle at B, just when it is about to loose contact. From application of Newton's second law to the particle normal to the spherical surface. mv2 = mg sin  (1) r Applying conservation of energy as the block moves from A to B.. 1 mv2 = mg (r cos  – r sin ) (2) 2 Solving 1 and 2 we get 3 sin  = 2 cos  8.3 (A) As the mass is at the verge of slipping ∴ mg sin37 –  mg cos37 = m2r 6 – 8 = 4.5   = 3 16 8.4 (B) As when they collide vt  1  72v 2  2 2  25R   R = vt  t =   5R 6v Now angle covered by A =   vt R 11 Put t  angle covered by A = 6 8.5 (C) The acceleration vector s
Read more

4. THEORY-Current Electrictricity

CURRENT ELECTRICITY  1 . ELECTRIC CURRENT (a) Time rate of flow of charge through a cross sectional area is called Current. if q charge flows in time interval t then average current is given by q Iav = t and Instantaneous current i =. lim q  dq t0 t dt (b) Direction of current is along the direction of flow of positive charge or opposite to the direction of flow of negative charge. But the current is a scalar quantity. i i q+ velocity q– velocity SI unit of current is ampere and 1 Ampere = 1 coloumb/sec 1 coloumb/sec = 1A 2 . CONDUCTOR In some materials, the outer electrons of each atom or molecule are only weakly bound to it. These electrons are almost free to move throughout the body of the material and are called free electrons. They are also known as conduction electrons. When such a material is placed in an electric field, the free electrons drift in a direction opposite to the field. Such materials are called conductors. 3 . INSULATOR Another class o
Read more