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# IIT-JEE-2008-Paper1

PAPER - I
SECTION - I
Straight Objective Type
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This section contains 6 multiple choice questions. Each question has 4 choices (1), (2), (3) and (4), out of which ONLY ONE is correct.

1.  If 0 < x < 1 then √1+x2 [{x cos (cot-1 x) + sin (cot-1 x)}2 - 1]1/2
(1) x/√1+x2
(2) x
(3)  x√1+x2
(4) √1+x2

2. Consider the two curves
C1 : y2 = 4x
C2 : x2 + y2 - 6x + 1 = 0
Then,
(1) C1 and C2 touch each other only at one point
(2) Cand C2 touch each other exactly at two points
(3) C1 and C2 intersect (but do not touch) at exactly two points
(4) C1 and Cneither intersect nor touch each other

3. The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors a, b, c such that a.b = b.c = c.a = 1/2
Then, the volume of the parallelopiped is
(1) 1/√2
(2) 1/2√2
(3) √3 / 2
(4) 1/√3

4. Let a and b be non-zero real numbers. Then, the equation (ax2 + by2 + c) (x2 - 5xy + 6y2) = 0 represents
(1) four straight lines, when c = 0 and a, b are of the same sign
(2) two straight lines and a circle, when a = b, and c is of sign opposite to that of a
(3) two straight lines and a hyperbola, when a and b are of the same sign and c is of sign opposite to that of a
(4) a circle and an ellipse, when a and b are of the same sign and c is of sign opposite to that of a.

5. The total number of local maxima and minima of the function

(1) 0
(2) 1
(3) 2
(4) 3