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2003 (AIEEE / IIT-JEE, in the JEE Main bank) questions

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

Mathematics

  1. Domain of definition of the function f(x) = sqrtsin^-1(2x) + (π)/6 for real valued x, is

    Sets Relations and Functions · with solution

  2. The area of the quadrilateral formed by the tangents at the end points of latusrectum to the ellipse (x^2)/9 + (y^2)/5 = 1, is

    Definite Integrals and Areas · with solution

  3. If a = (i + j + k), a · b = 1 and a × b = j - k, then b is equal to

    Vector Algebra · with solution

  4. The value of a, so that the volume of parallelopiped formed by i + aj + k, j + ak and ai + k become minimum, is

    Vector Algebra · with solution

  5. If f(x) = int_x^2^x^2+1 e^-t^2 dt, then f(x) increases in

    Definite Integrals and Areas · with solution

  6. The centre of circle inscribed in square formed by the lines x^2 - 8x + 12 = 0 and y^2 - 14y + 45 = 0, is

    Circles · with solution

  7. If the angles of a triangle are in the ratio 4:1:1, then the ratio of the longest side to the perimeter is

    Trigonometry · with solution

  8. If I(m,n) = int_0^1 t^m(1+t)^n dt, then the expression for I(m,n) in terms of I(m+1, n-1) is

    Definite Integrals and Areas · with solution

  9. If A = beginbmatrix α & 0 \ 1 & 1 endbmatrix and B = beginbmatrix 1 & 0 \ 5 & 1 endbmatrix then value of α for which A^2 = B, is

    Matrices and Determinants · with solution

  10. If f:[0,∞) → [0,∞) and f(x) = x/(1+x), then f is \hfill

    Sets Relations and Functions · with solution

  11. Two numbers are selected randomly from the set S = \1, 2, 3, 4, 5, 6\ without replacement one by one. The probability that minimum of the two numbers is less than 4, is

    Probability · with solution

  12. lim_h → 0 (f(2h + 2 + h^2) - f(2))/(f(h - h^2 + 1) - f(1)), given that f'(2) = 6 and f'(1) = 4.

    Limits Continuity and Differentiability · with solution

  13. If |z| = 1 and w = (z-1)/(z+1) (where, z ≠ -1), then Re(w) is

    Complex Numbers and Quadratic Equations

  14. Tangent is drawn to ellipse (x^2)/27 + y^2 = 1 at (3√(3)cosθ, sinθ) (where, θ ∈ (0, π/2)). Then, the value of θ such that the sum of intercepts on axes made by this tangent is minimum, is

    Conic Sections · with solution

  15. If y(t) is a solution of (1+t)dy/dt - ty = 1 and y(0) = -1, then y(1) is equal to

    Differential Equations · with solution

  16. Coefficient of t^24 in (1 + t^2)^12 (1 + t^12) (1 + t^24)

    Binomial Theorem

  17. If f(x) = x^2 + 2bx + 2c^2 and g(x) = -x^2 - 2cx + b^2, such that min f(x) > max g(x), then the relation between b and c is

    Complex Numbers and Quadratic Equations · with solution

  18. Orthocentre of triangle with vertices (0, 0), (3, 4) and (4, 0) is

    Straight Lines and Pair of Lines · with solution

  19. The value of k such that (x-4)/1 = (y-2)/1 = (z-k)/2 lies in the plane 2x - 4y + z = 7, is

    Three Dimensional Geometry

Chemistry

  1. Mixture X = 0.02 mole of [Co(NH_3)_5SO_4]Br and 0.02 mole of [Co(NH_3)_5Br]SO_4 1 L of mixture X + excess of AgNO_3 solution → Y 1 L of mixture X + excess of BaCl_2 solution → Z Number of moles of Y and Z are

    Coordination Compounds

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