CBSE Mathematics Sample Paper46 Class XII 2010

http://www.cbseguess.com/-------------------------------------------------------------------------------------------------------www.cbseguess.com Other Educational Portals www.icseguess.com | www.ignouguess.com | www.dulife.com | www.magicsense.com Sample Paper – 2010 Class – XII Subject – Maths TIME 3 Hrs MM 100 General Instructions: 1. All questions are compulsory 2. This question paper consists of 29 questions divided into three sections A, B and C. Section A comprises of 10 questions of one mark each, section B comprises of 12 questions of four marks each and section C comprises of 07 questions of six marks each 3. All questions in Section A are to be answered in one word, one sentence or as per the exact requirement of the question 4. There is no overall choice. However, internal choice has been provided in 04 questions of four marks each and 02 questions of six marks each. You have to attempt only one of the alternatives in all such questions. 5. Use of calculators is not permitted. You may ask for logarithmic tables, if required SECTION A 1. Find the order of AB & BA, if A = 021, B= 210 2. For a skew symmetric matrix A =ija, what is the nature of elementija, if i = j. 3. For two given square matrices A & B of the same order 7,5BA, find the value of AB. 4. Diff. sin(log x) with respect to x . 5. Evaluate 1021xdx 6. Find the rate of change of the area of circle with respect to its radius if radius is 2 cm 7. Find the integrating factor of diff. equation xydxdyxxlog2log 8. Find the projection of the vector kji73on vector kji87. 9. Write the condition of two parallel and perpendicular vectors. http://www.cbseguess.com/-------------------------------------------------------------------------------------------------------www.cbseguess.com Other Educational Portals www.icseguess.com | www.ignouguess.com | www.dulife.com | www.magicsense.com 10. Find the angles which the line 11111zyxmakes with axes SECTION B 11. Prove that 1663tan54cos1312sin111 12. Using properties of determinant , solve for x, 433343334xxxxxxxxx = 0 13. , find . 14. If and find the value of at OR If sin y = x sin ( a + y ) , prove that ayadxdysin)(sin2 15. Find the intervals for which the function f (x) = sinx – cos x is increasing or decreasing function in [0, 2]. 16. )1(2xxdxEvaluate 17. Evaluate dxxxex22)1(1 OR Evaluate dxxx642 18. Evaluate: 19. Form the differential equation .of the family of ellipse having foci on y axis and centre at origin OR http://www.cbseguess.com/-------------------------------------------------------------------------------------------------------www.cbseguess.com Other Educational Portals www.icseguess.com | www.ignouguess.com | www.dulife.com | www.magicsense.com Solve the diff. eq. yyxexedxdy2 20. Express the vector as sum of two vectors such that one is parallel to the vector and other is perpendicular to . 21. Find the equation of planes passing through the point ( -1,-1,2) and perpendicular to the planes x + 2y -3z =1 and 5x – 4y + 3z = 5 OR The eq. of the lines are 233211zyx and 163524zyx. Find the shortest distance between the above lines. 22. In a hurdle race, a player has to cross 10 hurdles. The probability that he will clear each hurdle is 5/6. What is the probability that he will knock down fewer than 2 hurdles SECTION -C (6 mark questions) 1. Consider2:5,()965fRgivenbyfxxx. Show that f is invertible .find the inverse of f. 2. Find the inverse of the matrix 132305250using elementary row transformation. OR Using matrices solve the system 23511;3245;23xyzxyzxyz 3. A jet of an enemy is flying along the curve y= x2+2.A soldier is placed at the point (3,2) . What is the nearest distance between the soldier and the jet? OR An open box with a square base is to be made out of a given quantity of cardboard of area c2 .Show that the maximum volume of the box is 363c 4. Find the area of the smaller part of the circle x2 + y2 = a2 cut off by the line 2ax 5. Two go downs A and B have grain capacity of 100 quintals and 50 quintals respectively. They supply to 3 ration shops, D, E and F whose requirements are 60, 50 and 40 quintals respectively. The cost of transportation per quintal from the go downs to the shops are given in the following table: http://www.cbseguess.com/-------------------------------------------------------------------------------------------------------www.cbseguess.com Other Educational Portals www.icseguess.com | www.ignouguess.com | www.dulife.com | www.magicsense.com Transportation cost per quintal (in Rs) From/To A B D E F 6 3 2.50 4 2 3 How should the supplies be transported in order that the transportation cost is minimum? What is the minimum cost? 6. Show that the lines 315125;315125xyzxyzare coplanar. Also find the equation of the plane containing the lines. 7. Find the equation of the plane which contains the line of intersection of the planes .(23)40rijk and .(2)50rijk and which is perpendicular to the plane .(536)80rijk Paper Submitted by: Sanjay Email : sanjaykjena2003@yahoo.co.in Mob No. : 9937628145