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# IIT-JEE-Mathematics-Paper1-2007

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1. Let α, β be the roots of the equation x2 - px + r = 0 and α/2, 2β be the roots of the equation x2 - qx + r = 0. Then the value of r is

(A) 2/9 (p - q)(2q - p)
(B) 2/9 (q – p)(2p – q)
(C) 2/9 (q – 2p)(2q – p)
(D) 2/9 (2p - q)(2q - p)

2. Let f(x) be differentiable on the interval (0, ∞) such that f(1) = 1, and

lim t->∞(t2 f(x)-x2 f(t))/(t-x) - 1

for each x > 0. Then f(x) is

(A) 1/3x + (2x2 )/3
(B) (-1)/3x + (4x2 )/3
(C) (-1)/x + 2/x2
(D) 1/x

3. One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to this wife is

(A) 1/2
(B) 1/3
(C) 2/5
(D) 1/5

4. The tangent to the curve y = ex drawn at the point (e, ee) intersects the line joining the points (e - 1, ee-1) and (e+1, ee+1

(A) on the left of x = e
(B) on the right of x = e
(C) at no points
(D) at all points

5.      limx->π/4 ∫2sec2 x f(t) dt / ( x2 - π2/16 ) equals

(A) 8/π f(2)
(B) 2/π f(2)
(C) 2/π f(1/2)
(D) 4f(2)

6. A hyperbola, having the transverse axis of length 2 sin, is confocal with the ellipse 3x2 + 4y2 = 12. Then its equation is

(A) x2 cosex2 θ - y2 sec2 θ = 1
(B) x2 sec2 θ - y2 cosec2 θ = 1
(C) x2 sin2 θ - y2 cos2 θ = 1
(D) x2 cos2 θ - y2 sin2 θ = 1

7. The number of distinct real values of λ, for which the vectors -λ2î + ĵ + k̂, î - λ2ĵ + k̂ and î + ĵ - λ2k̂ are coplanar, is

(A) zero
(B) one
(C) two
(D) three

8. A man walks a distance of 3 units from the origin towards the north-east (N 45oE) direction. From there, he walks a distance of 4 units towards the north-west (N 45o W) direction to reach a point P. Then the position of P in the Argand plane is

(A) 3eiπ/4 + 4i
(B) (3 - 4i)eiπ/4
(C) (4 + 3i)eiπ/4
(D) (3 + 4i)eiπ/4

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