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Class X Subject MATHEMATICS [Time 3 Hrs] [Full Marks 100] Answer question 1 (compulsory)and five other questions from section A and answer any two questions from either section B or section C. Section A Question 1. (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) (ix) (x) Construct a 2 X 3 matrix whose elements aij are given by : aij = 2i j. [3] 1 Evaluate : sin[2 cos ( 3/5)] [3] The foci of a hyperbola coincide with the foci of the ellipse 9 x2 + 25 y2 = 225. Find the equation of the hyperbola if its eccentricity is 2. [3] Evaluate : Ltx 0 (e ax e bx)/x. [3] Evaluate : [(1 tan x)/(1 + tan x)]dx [3] Differentiate w. r. t. x : x tan x log 5 x. [3] A card is drawn at random from a pack of 52 playing cards. Find the probability of getting a king or a heart or a red card. [3] Find the coefficient of correlation from the regression lines given by : x 2 y + 3 = 0, 4 x 5 y + 1 = 0. [3] Solve the equation : 2 z = |z| + 2i. [3] Solve the differential equation : (x2 y x2) dy + (y2 + x y2) dx = 0 [3] Question 2. (a) Find the integers k for which the system of equations : x+2y 3z=1 2x ky 3z=2 x+2y+kz=3 has a unique solution. Find the solution for k = 0. (b) Solve the system of equation using matrix method : x y+z=4 1 [5]
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