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

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