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 – MATHEMATICS SECTION-A 1. Let f : R – { 0 } f : R – { 0 }, given by ()fxx5 . Find the inverse of ‘ f ’ . 2. Evaluate sinSin1132 3. If A is a square matrix, such that A2=A, then find AA213. 4. Find ‘x’, such that the points (,),(,),(,)x32288lie on a line 5. Let * be a binary operation on N given by *(,),abHCFab ,.abN Find 18*24 6. Evaluate tanxexdxx1211 7. Evaluate SinxCosxdx2220 8. If abab , show thata and b are perpendicular vectors 9. If ,ab34and .ab9 find |ab| 10. Write the equation of a line parallel to the vector ijk23 and passing through the point ( 5, -2, 4 ). SECTION – B 11. Show that :[,],()xfRgivenbyfxx112 is one-one. Find the inverse of the function:[,]frangeoff11. 12. Show that sinsincos111388451785 OR Solve of x: ()SinxSinx11122 13. Show that ()()()()yzxyzxxyxzyzxyzxyzxzyzxy22222 http://www.cbseguess.com/-------------------------------------------------------------------------------------------------------www.cbseguess.com Other Educational Portals www.icseguess.com | www.ignouguess.com | www.dulife.com | www.magicsense.com 14. Find the constants a and b so that the function ‘f’ defined below ,(),,xfxaxbxx133575 is continuous. 15. If sinyx1, show that ()dydyxxdxdx22210 OR If coscos(),cos,yxaywitha1 prove that cos()sindyaydxa2 16 A circular disc of radius 3 cm is being heated. Due to expansion, its radius increases at the rate of 0.05 cm/s. Find the rate at which its area is increasing when radius is 3.2 cm. OR Show that the xyandxyk244 cut at right angles if k2512 17. Evaluate xdxxx24211 OR Evaluate tandxx361 18. Solve the differential equation : (loglog)dyxyyxdx1 19. Solve the differential equation: cotcot,()dyyxxxxgivenydx2200 20. If the sum of two unit vectors is a unit vector, show that the magnitude of their difference is 3 21. Find the equation of the line passing through(,,)347and perpendicular to the two lines xyzxyzand123214 22. An urn contains 5 red and 3 blue balls. Find the probability distribution of the number of blue balls in a random draw of 3 balls with replacement. OR Suppose that 80% of the people are right-handed. What is the probability that at most 6 of a random sample of 10 people are right-handed? SECTION – C 23. If A3211 find the values of a and b such that .AAabI20 Hence find A-1. http://www.cbseguess.com/-------------------------------------------------------------------------------------------------------www.cbseguess.com Other Educational Portals www.icseguess.com | www.ignouguess.com | www.dulife.com | www.magicsense.com OR Using elementary row transformation, find the inverse of 235324111 24. Prove that the line xyab1 is a tangent to the curve xaybe at the point where the curve cuts y-axis. OR If the length of three sides of a trapezium, other than the base is equal to 10cm each, then find the area of trapezium when it is maximum. 25. Find the area of the region bounded by the curve yx21, line y=x and the positive x-axis. OR Find the area bounded by y=4x+5, y=5-x and 4y= x+5 26. Find the equation of the plane passing through the line of intersection of the planes x-2y+z=1 and 2x+y+z=8 and parallel to the line with the direction ratios 1,2,1. Also find the perpendicular distance of the point P(3,1,2) from this plane. 27. A housewife wishes to mix two kinds of foods X and Y in such a way that the mixture contains at least 10 units of Vitamin A, 12 units of Vitamin B and 8 units of Vitamin C. The vitamin contents of one kg of each food are given below: Vitamin A 10 Vitamin B 12 Vitamin C 8 Food X 1 2 3 Food Y 2 2 1 One kg of Food X and Food Y respectively cost Rs. 6 and Rs. 10. Find the least cost of the mixture graphically, making it a linear programming problem. 28. In a factory, which manufactures nuts, machines A,B and C manufacture respectively 25%, 35% and 40% of nuts. Of their outputs 5,4 and 2 percent respectively are defective nuts. A nut is drawn at random from the product and is found to be defective. Find the probability that it is manufactured by machine B. 29. Evaluate tandx or Evaluate (),fxdx05where ()||||||fxxxx25 -----------------------------------------------------0----------------------------------------------------Paper Submitted By : Name: M.S.RAMBABU Email ram_ind2006@yahoo.co.in Phone No. 213117