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

Lagranges-Mean-Value-theorem

(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
matrix-question

then value of α for which A² = B, is:
(a) 1
(b) –1
(c) 4
(d) no real values

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