CBSE Mathematics Sample Paper30 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 – Mathematics Time:3hrs Maximum Marks: 100 General Instructions: (i) All questions are compulsory. (ii) The question paper consists of 29 questions divided into three sections – A, B & C Section A contains 10 questions of 1 marks each. Section B contains12 questions of 4 marks each. Section C contains 7 questions of 6 marks each. (iii) Use of calculators is not permitted. SECTION – A Q.1 Give an example to show that the relation R in the set of natural numbers, defined by 2,,,,yxNyxyxRis not transitive. Q.2 Write the value of 21sin3sin1 Q.3 If the following matrix is skew symmetric, find the values of a, b, c. A = 011230cba Q.4 If A is square matrix then write the value of A(AdjA) Q.5 If A is a square matrix of 3 x 3 order and │adj A│= 64 , find the value of │A’│ Q.6 If | a + b | = | a -b | then find the angle between a and b Q.7 If a is a unit vector and ( x -a ).( x + a ) = 8 , then find | x |. Q.8 Find the value of λ such that the line 63192zyx is perpendicular to the plane 3x – y – 2z = 7. Q.9 Find f(x) satisfying the following : cxfedxxxexx)(tansec2 Q.10 Evaluate: dxeeeexxxxlog2log3log4log5 http://www.cbseguess.com/-------------------------------------------------------------------------------------------------------www.cbseguess.com Other Educational Portals www.icseguess.com | www.ignouguess.com | www.dulife.com | www.magicsense.com SECTION – B Q.11 Prove that : 22123123tan21sec2tan21cos2ec OR If byax11coscos, prove that 22222sincos2byabxyax Q.12 Show that the relation R in the set 120,;xZxxA given by R = {(a,b) : │a -b│is divisible by 4} is an equivalence relation. Find the set of all elements related to 1. Q.13 If a, b, c are all positive and distinct, show that bacacbcba has a negative value. Q.14 If 222cbyax, for some c > 0, prove that 222321dxyddxdy is a constant independent of a and b. OR If bxaxxylog prove that 2223ydxdyxdxydx Q.15 Find the equation of planes through the intersection of planes 012ˆ6ˆ2.jir and 0ˆ4ˆˆ3.kjir which are at unit distance from origin. Q.16 Solve the differential equation: ydxxdyxyyxdyydxxyxsincos Q.17 Form the differential equation for the curve xbxaeyxsincos Q.18 Find the interval in which the function 20,cossinxxxxf is strictly increasing or strictly decreasing. OR Find the equation of tangent to the curve yxycos,-2π ≤ x ≤ 2π that are parallel to the line x + 2y = 0. http://www.cbseguess.com/-------------------------------------------------------------------------------------------------------www.cbseguess.com Other Educational Portals www.icseguess.com | www.ignouguess.com | www.dulife.com | www.magicsense.com Q.19 Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation of X. Q.20 Integrate dxxxxx42sincoscossin OR Integrate dxxxxx422log2)1log(1 Q.21 If a,bandcbe three vectors 3a,4b and 5c and each one of them being perpendicular to sum of the other two, find cba Q.22 Find the value of a and b such that the function defined by 10,21102,2,5)(ifxxifbaxifxxf is continuous function. SECTION – C Q.23 Using elementary transformation find the inverse of matrix if it exists 310015102 Q.24 Two godowns 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 godowns to the shops is given below: 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? http://www.cbseguess.com/-------------------------------------------------------------------------------------------------------www.cbseguess.com Other Educational Portals www.icseguess.com | www.ignouguess.com | www.dulife.com | www.magicsense.com Q.25 Find the area of the region enclosed between the two circles x2+y2=4 and (x – 2)2 + y2 = 1. Q.26 Find the coordinates of the foot of the perpendicular and the perpendicular distance of the point (1, 3, 4) from the plane 2x–y+z+3 = 0. Find also the image of the point in the plane. Q.27 Evaluate 231sindxxx OR 20sinlogxdx Q.28 A point on the hypotenuse of a triangle is at distance a and b from the sides of the triangle. Show that the minimum length of the hypotenuse is ( a2/3 + b2/3 )3/2. OR Show that semi-vertical angle of right circular cone of maximum volume and of given slant height is 2tan1 Q.29 A card from a pack of 52 cards is dropped. From the remaining cards two cards are drawn and are found to be club. Find the prob. That the dropped card is club. FROM : DEEPAK DUTTA {MRADAV Sr. Sec. P School SOLAN} 09816055445