IIT-JEE-2008-Paper1

PAPER - I

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6.
logerithm

m and n are integers m ≠ 0, n > 0 and let p be the left hand derivative of
log-question

(1) n = 1, m = 1
(2) n = 1, m = -1
(3) n = 2, m = 2
(4) n > 2, m = n

SECTION II

Multiple Correct Answers Type

This section contains 4 multiple correct answer(s) type questions. Each question has 4 choices (1), (2), (3) and (4), out of which ONE OR MORE is/are correct.

7. Let P (x₁, y₁) and Q(x₂, y₂), y₁ < 0, y₂ < 0, be the end points of the latus rectum of the ellipse x² + 4y² = 4. The equations of parabolas with latus rectum PQ are
(1)    x² + 2√3 y = 3 + √3
(2)    x² - 2√3 y = 3 + √3
(3)    x² + 2√3 y = 3 - √3
(4)    x² - 2√3 y = 3 - √3

8. A straight line through the vertex P of a triangle PQR intersects the side QR at the point S and the circumcircle of the triangle PQR at the point T. If S is not the centre of the circumcircle, then
(1)    1/PS + 1/ST < 2/√(QS * SR)
(2)    1/PS + 1/ST > 2/√(QS * SR)
(3)    1/PS + 1/ST < 4/ QR
(4)    1/PS + 1/ST > 4/ QR

9. Let f(x) be a non-constant twice differentiable function defined
    question1