IIT-JEE-Mathematics-Screening-2003

SCREENING
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7. The value of k such that (x-4)/1=(y-2)/1=(z-k)/2 lies in the plane 2x – 4y + z = 7, is:
(a) 7
(b) –7
(c) no real value
(d) 4

8. If the angles of a triangle are in the ratio 4 : 1 : 1, then the ratio of the longest side to the perimeter is:
(a) √3:(2+√3)
(b) 1 : 6
(c) 1 : 2 + √3
(d) 2 : 3

9. If lim_(x→0) (((a-n)nx - tan x)sin nx)/x² = 0, where n is non zero real number, then a is equal to:
(a) 0
(b) (n+1)/n
(c) n
(d) n+1/n

10. Two numbers are selected randomly from the set S = {1, 2, 3, 4, 5, 6} without replacement one by one. The probability that minimum of the two numbers is less than 4 is :
(a) [1/15]
(b) [14/15]
(c) [1/5]
(d) [4/5]

11. For hyperbola x²/(cos² α)-y²/(sin² α)=1 which of the following remains constant with change in ‘a’ :
(a) abscissae of vertices
(b) abscissa of foci
(c) eccentricity
(d) directrix

12. Range of the function f(x)=(x²+x+2)/(x²+x+1); x Î R is:
(a) (1, ¥)
(b) (1, 11/7)
(c) (1, 7/3)
(d) (1, 7/5)

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