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IIT-JEE-Mathematics-Screening-2003
SCREENING
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1. If f:[0,
¥) --> [0, ¥),
and f(x)=x/(1+x) then f is:
(a) one-one and onto
(b) one-one but not onto
(c) onto but not one-one
(d) neither one-one nor onto
2. If P(B) = 3/4, P(AÇBÇC-)
= 1/3 and P(A-ÇBÇC-)
= 1/3, then P(BÇC) is:
(a) 1/12
(b) 1/6
(c) 1/15
(d) 1/9
3. In [0, 1] Lagranges Mean Value theorem is NOT applicable to
(c) f(x)=x|x|
(d) f(x)=|x|
4. The area of the quadrilateral formed by the tangents at the end points of latus rectum to the ellipse x2/9+(y2=1)/5, is :
(a) 27/4 sq. units
(b) 9 sq. units
(c) 27/2 sq. units
(d) 27 sq. units
5. The number of integral points (integral point means both the coordinates should be integer) exactly in the interior of the triangle with vertices (0, 0), (0, 21) and (21, 0), is:
(a) 133
(b) 190
(c) 233
(d) 105
6. If
then value of α for which A2 = B, is:
(a) 1
(b) –1
(c) 4
(d) no real values
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