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1997 (AIEEE / IIT-JEE, in the JEE Main bank) questions

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

Mathematics

  1. Let p, q, r be three mutually perpendicular vectors of the same magnitude. If a vector x satisfies the equation p × [(x - q) × p ] + q × [(x - r) × q ] + r × [(x - p) × r ] = 0 then x is given by

    Vector Algebra · with solution

  2. If f(x) = x/(sin x) and g(x) = x/(tan x), where 0 < x ≤ 1, then in this interval

    Application of Derivatives

  3. The parameter on which the value of the determinant beginvmatrix 1 & a & a^2 \ cos(p-d)x & cos px & cos(p+d)x \ sin(p-d)x & sin px & sin(p+d)x endvmatrix does not depend upon, is

    Matrices and Determinants

  4. Let f(x) = beginvmatrix x^3 & sin x & cos x \ 6 & -1 & 0 \ p & p^2 & p^3 endvmatrix, where p is constant. Then (d^3)/(dx^3) f(x) at x = 0 is

    Limits Continuity and Differentiability

  5. The determinant beginvmatrix xp+y & x & y \ yp+z & y & z \ 0 & xp+y & yp+z endvmatrix = 0, if

    Matrices and Determinants · with solution

  6. The equation √(x+1) - √(x-1) = √(4x-1) has

    Complex Numbers and Quadratic Equations · with solution

  7. If g(x) = int_0^x cos^4 t dt, then g(x + π) equals

    Definite Integrals and Areas · with solution

  8. Let f be a positive function. If I_1 = int_1-k^k x f [x(1-x) ] dx and I_2 = int_1-k^k f [x(1-x) ] dx, where 2k - 1 > 0. Then, I_1/I_2 is

    Definite Integrals and Areas · with solution

  9. The graph of the function cos x cos(x+2) - cos^2(x+1) is

    Trigonometry · with solution

Chemistry

  1. The number of moles of KMnO_4 that will be needed to react completely with one mole of ferrous oxalate in acidic medium is

    Redox and Electrochemistry

  2. For a d-electron, the orbital angular momentum is

    Atomic Structure

  3. The first use of quantum theory to explain the structure of atom was made by

    Atomic Structure

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