CBSE Mathematics Sample Paper57 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 SECTION ‘ A’ (1) Prove that the function f : RR given by f(x) = 2x is one – one. (2) Write Sin -1 ( 2 x ) in the simplest form . (3) Find the value of x, y and z if = . (4) A matrix of order 3x3 has = 7, find. (5) If area of triangle is 35 sq. units with vertices (2, – 6), (5, 4) and (k, 4) then by using determinant, Find the value of k. (6) Evaluate: (7) Evaluate: (8) Find a vector in the direction of vector = i – 2j that has magnitude 7 units. (9) Find a vector in the direction of vector = i – 2j that has magnitude 7 units. (10) Find the area of triangle whose adjacent sides are determined by the vectors = i – j + 3k and . http://www.cbseguess.com/-------------------------------------------------------------------------------------------------------www.cbseguess.com Other Educational Portals www.icseguess.com | www.ignouguess.com | www.dulife.com | www.magicsense.com SECTION ‘B’ (11) If R1 and R2 are equivalence relations in a set A, Show that R1R2 is also an equivalence relation. (12) If Cos-1 ) + Cos-1 ) = , prove that (13) Prove that: = abc + bc +ca +ab (14) Find the value of a and b, if f(x) = is a continuous function (15) Differentiate with respect to x. OR Differentiate Tan-1 with respect to x. (16) Find the equations of the tangent and normal to the curve x = 1 – Cos y = at . (17) Evaluate: (18) Solve: (1+ e2x ) dy + ex (1+y2) dx = 0 , given y(0) = 1 (19) Solve: x dy = {y – x tan ()} dx (20) Find the projection and projection vector of 2i – j + k on . (21) Find the vector equation of the plane passing through the intersection of the planes .(i + j + k) = 6 and .(2i + 3j + 4k) +5 = 0 and the point (1, 1, 1) . http://www.cbseguess.com/-------------------------------------------------------------------------------------------------------www.cbseguess.com Other Educational Portals www.icseguess.com | www.ignouguess.com | www.dulife.com | www.magicsense.com (22) In a factory which manufactures bolts, machines A, B and C manufacture respectively 25%, 35% and 40% of the bolts .Of their outputs 5%, 4% and 2% are respectively defective bolts. A bolt is drawn at random from the output and is found to be defective .What is the probability that it is manufacture by machine B. SECTION ‘C’ (23) Two cards are drawn simultaneously (i) without replacement, (ii) with replacement from a well shuffled pack of 52 cards. Find the mean and standard deviation of the number of kings. (24) Find the equation of the line which intersects the lines and passes through the point (1, 1, 1). (25) Find the area of the region bounded by the parabola x2 = 4y and the line x = 4y – 2. (26) Evaluate:) dx as limit of sums. (27) A wire of length 28 m. is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the length of the two pieces so that the combined area of the square and the circle is minimum? (28) Using elementary transformation, find the inverse of a matrix A = . (29) A manufacturing company makes two models A and B of a product. Each piece of model A requires 9 labour hours for fabricating and 1 hour for finishing. Each piece of model B requires 12 labour hours for fabricating and 3 hour for finishing. For fabricating and finishing the maximum labour hours available are 180 and 30 respectively. The makes a profit of Rs. 8000 on each piece of model A and Rs. 12000 on each piece of model B. How many pieces of model A and B should be manufactured per week to realize a maximum profit? What is the maximum profit per week? Paper Submitted by: V.P. Tripathi Email : bhanutiwari.in@gmail.com Ph No. : 9451018950