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^-1x) + sin (cot^-1x)}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) C₁and C₂ touch each other exactly at two points
(3) C₁ and C₂ intersect (but do not touch) at exactly two points
(4) C₁ and C₂neither 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

    2008-IIT-Maths

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

IIT-JEE-2008-Paper1

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