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2009 (AIEEE / IIT-JEE, in the JEE Main bank) questions

12 questions, by subject. Each opens with its options and answer.

Mathematics

  1. If a, b, c and d are the unit vectors such that (a × b) · (c × d) = 1 and a · c = 1/2, then

    Vector Algebra

  2. The number of seven-digit integers, with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only, is

    Permutations and Combinations · with solution

  3. Let z = cosθ + isinθ. Then, the value of sum_m=1^15 Im(z^2m-1) at θ = 2° is

    Complex Numbers and Quadratic Equations · with solution

  4. Tangents drawn from the point P(1, 8) to the circle x^2 + y^2 - 6x - 4y - 11 = 0 touch the circle at the points A and B. The equation of the circumcircle of triangle PAB is

    Circles

  5. If the sum of first n terms of an AP is cn^2, then the sum of squares of these n terms is

    Sequences and Series · with solution

  6. Let z = x + iy be a complex number where, x and y are integers. Then, the area of the rectangle whose vertices are the root of the equation zz^3 + zz^3 = 350, is

    Complex Numbers and Quadratic Equations

  7. The normal at a point P on the ellipse x^2 + 4y^2 = 16 meets the X-axis at Q. If M is the mid-point of the line segment PQ, then the locus of M intersects the latusrectum of the given ellipse at the points

    Conic Sections · with solution

  8. The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse x^2 + 9y^2 = 9 meets its auxiliary circle at the point M. Then, the area (insqunits) of the triangle with…

    Conic Sections

  9. The locus of the orthocentre of the triangle formed by the lines (1+p)x - py + p(1+p) = 0, (1+q)x - qy + q(1+q) = 0 and y = 0, where p ≠ q, is

    Straight Lines and Pair of Lines

  10. A line with positive direction cosines passes through the point P(2, -1, 2) and makes equal angles with the coordinate axes. The line meets the plane 2x + y + z = 9 at point Q. The length of the line segment PQ equals

    Three Dimensional Geometry

  11. If P is (3, 2, 6) is a point in space and Q be a point on the line r = (i - j + 2k) + μ(-3i + j + 5k). Then, the value of μ for which the vector overrightarrowPQ is parallel to the plane x - 4y + 3z = 1, is

    Three Dimensional Geometry · with solution

Chemistry

  1. Given that the abundances of isotopes _54Fe, _56Fe and _57Fe are 5%, 90% and 5%, respectively, the atomic mass of Fe is

    Atomic Structure · with solution

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