Q98.The solution of the differential equation dx dy = x+yx satisfying the condition y(1) = 1 is (1) y = ln x + x (2) y = x ln x + x2 (3) y = xe(x−1) (4) y = x ln x + x

Q99.The differential equation of the family of circles with fixed radius 5 units and centre on the line y = 2 is (1) (x −2)y′2 = 25 −(y −2)2 (2) (y −2)y′2 = 25 −(y −2)2 (3) (y −2)2y′2 = 25 −(y −2)2 (4) (x −2)2y′2 = 25 −(y −2)2 Q100.The non-zero verctors →a,→b and →c are related by →a = 8→b and →c = −7→b. Then the angle between →a and→cis (1) 0 (2) π/4 (3) π/2 (4) π Q101.The vector →a = α^i + 2^j + β^k lies in the plane of the vectors →b = ^i + ^j and →c = ^j + ^k and bisects the angle between →b and →c. Then which one of the following gives possible values of α and β ? (1) α = 2, β = 2 (2) α = 1, β = 2 (3) α = 2, β = 1 (4) α = 1, β = 1 Q102.The line passing through the points (5, 1, a) and (3, b, 1) crosses the yz− plane at the point (0, 172 , −132 ). Then JEE Main 2008 JEE Main Previous Year Paper (1) a = 2, b = 8 (2) a = 4, b = 6 (3) a = 6, b = 4 (4) a = 8, b = 2 Q103.If the straight lines x−1 k = y−22 = z−33 and x−23 = y−3k = z−12 intersect at a point, then the integer k is equal to (1) −5 (2) 5 (3) 2 (4) −2 Q104.It is given that the events A and B are such that P(A) = 41 , P ( BA ) = 12 and P ( BA ) = 32 . Then P(B) is (1) 1 (2) 1 6 3 (3) 2 (4) 1 3 2 Q105.A die is thrown. Let A be the event that the number obtained is greater than 3 . Let B be the event that the number obtained is less than 5 . Then P(A ∪B) is (1) 3 (2) 0 5 (3) 1 (4) 2 5 JEE Main 2008 JEE Main Previous Year Paper

Q86.If →u, →v, ¯w are non-coplanar vectors and p, q are real numbers, then the equality [ 3→u p→v p→w ] −[ p→v →w q→u ] −[ 2→w q→v q→u ] = 0 holds for (1) exactly one value of (p, q) (2) exactly two values of (p, q) (3) more than two but not all values of (p, q) (4) all values of (p, q)

Q84.Solution of the differential equation cos xdy = y(sin x −y)dx, 0 < x < π2 is (1) y sec x = tan x + c (2) y tan x = sec x + c (3) tan x = (sec x + c)y (4) sec x = (tan x + c)y