IIT-JEE-Mathematics-Paper1-2007

______________________________________________________________________ 

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, e^e) intersects the line joining the points (e - 1, e^e-1) and (e+1, e^e+1) 

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


5.      lim_x->π/4 ∫₂^sec2 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 45^oE) direction. From there, he walks a distance of 4 units towards the north-west (N 45^o W) direction to reach a point P. Then the position of P in the Argand plane is 

(A) 3e^iπ/4 + 4i 
(B) (3 - 4i)e^iπ/4 
(C) (4 + 3i)e^iπ/4 
(D) (3 + 4i)e^iπ/4 

|Next >>