CBSE Mathematics Sample Paper Class XII 2011

http://www.cbseguess.com/-------------------------------------------------------------------------------------------------------www.cbseguess.com Other Educational Portals www.icseguess.com | www.ignouguess.com | www.dulife.com | www.magicsense.com Sample Paper – 2011 Class – XII Subject – Mathematics SECTION-A 1. If A is a square matrix of order 3 such that =. 2. If A = show that A -is a skew symmetric matrix. 3. Write the value of . 4. Find if y=x . 5. At what point on the curve , the tangents are parallel to y-axis. 6. Evaluate dx (where). 7. Write I.F. for -= (1+x). 8. Find the projection of the vector i-j to the vector i+j 9. If P(A) = , P(B)=0, then find P. 10. If X has a Binomial distribution B= write P(X=1). SECTION-B 11. Show that the relation R onR defined as R = is reflexive and transitive but not symmetric. OR On R-a binary operation * defined by a*b =a+b-ab. Prove that * is commutative and associative. Find identity element for * on R-12. Prove that =2abc 13. For what value of K the following is continous at x=0. f (x)=. OR http://www.cbseguess.com/-------------------------------------------------------------------------------------------------------www.cbseguess.com Other Educational Portals www.icseguess.com | www.ignouguess.com | www.dulife.com | www.magicsense.com If y= (1-) . 14. Verify the applicability of LMV Theorem for the following in 15. Determine the interval, where f(x)=, 0, is strictly increasing or strictly decreasing. 16. Evaluate . 17. Evaluate . 18. Evaluate dx OR Find . 19. Solve hat y. 20. For any vectors = . OR If the vector bisects the angle between the vector and the vector 3i+4j, then find the unit vector in the direction of . 21. A speaks truth in 60% of cases and B in 90% of cases .In what percentage of cases are they likely to contradict to each other in stating the same fact ? . OR Two cards are drawn without replacement from a well-shuffled pack of 52 cards. find the probability that one is spade and other is a queen of red colour 22. Suppose X has a binomial distribution B Show that X=3 is the most likely outcome. SECTION-C 23. If A= and B= are two square matrices , find AB and hence solve the system of linear equation : x –y=3, 2x+ 3y +4z =17, y+2z =7. OR Obtain the inverse of the following matrix using elementary operation : A= 24. Show that the height of the cone of maximum volume that can be inscribed in a sphere of radius 12 cm is 16cm. 25. Find the area of the region OR http://www.cbseguess.com/-------------------------------------------------------------------------------------------------------www.cbseguess.com Other Educational Portals www.icseguess.com | www.ignouguess.com | www.dulife.com | www.magicsense.com Using the integration, find the area of ∆PQR where P is ,Q is and R is 26. Solve :y 27. Find the image of the point having position vector in the plane . 28. A producer has 30 and 17 units of labour and capital respectively which he can use to produce two types of goods Xand Y .to produce one unit of X ,2 units of labour and 3 units of capital is required. Similarly, 3 units of labour and 1 unit of capital is re produquired to produce one unit of Y. If X and Y are priced at Rs 100 and Rs 120 per unit respectively, how should the producer use his resources to maximize the total revenue? Solve the problem graphically. 29. Let X denote the number of hours you study during a randomly selected school days . the probability that X can take the values x ,has the following form ,where k is some unknown constant . PAPER SUBMITTED BY: Name : POONAM SINGH Email : yashmragendra@gmail.com Phone No. 07597453169