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1986 (AIEEE / IIT-JEE, in the JEE Main bank) questions

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

Mathematics

  1. The points (0, 8/3 ), (1, 3) and (82, 30) are vertices of

    Straight Lines and Pair of Lines · with solution

  2. The expression 3 [sin^4 ((3π)/2-α )+sin^4(3π+α) ]-2 [sin^6 ((π)/2+α )+sin^6(5π-α) ] is equal to

    Trigonometry · with solution

  3. Let a = a_1i + a_2j + a_3k, b = b_1i + b_2j + b_3k and c = c_1i + c_2j + c_3k be three non-zero vectors such that c is a unit vector perpendicular to both the vectors a and b. If the angle between a and b is (π)/6, then…

    Vector Algebra

  4. A vector a has components 2p and 1 with respect to a rectangular cartesian system. This system is rotated through a certain angle about the origin in the counter clockwise sense. If, with respect to the new system, a…

    Vector Algebra

  5. A student appears for tests I, II and III. The student is successful if he passes either in tests I and II or tests I and III. The probabilities of the student passing in tests I, II and III are p, q and 1/2,…

    Probability · with solution

  6. If P(x) = a_0 + a_1x^2 + a_2x^4 + … + a_nx^2n is a polynomial in a real variable x with 0 < a_0 < a_1 < a_2 < … < a_n. Then, the function P(x) has

    Application of Derivatives

Chemistry

  1. Rutherford's alpha particle scattering experiment eventually led to the conclusion that

    Atomic Structure

  2. A molal solution is one that contains one mole of solute in

    Solutions · with solution

  3. The ratio of the energy of a photon of 200 Å wavelength radiation to that of 4000 Å radiation is

    Atomic Structure

  4. Which one of the following sets of quantum numbers represents an impossible arrangement? n l m s

    Atomic Structure · with solution

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