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2007 (AIEEE / IIT-JEE, in the JEE Main bank) questions

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

Mathematics

  1. The number of solutions of the pair of equations 2sin^2θ - cos 2θ = 0 and 2cos^2θ - 3sinθ = 0 in the interval [0, 2π] is

    Trigonometry · with solution

  2. A man walks a distance of 3 units from the origin towards the North-East (N 45° E) direction. From there, he walks a distance of 4 units towards the North-West (N 45° W) direction to reach a point P. Then, the position…

    Complex Numbers and Quadratic Equations

  3. The number of distinct real values of λ, for which the vectors -λ^2i + j + k, i - λ^2j + k and i + j - λ^2k are coplanar, is

    Vector Algebra · with solution

  4. The differential equation dy/dx = dfrac√(1-y^2)y determines a family of circles with

    Differential Equations · with solution

  5. Let ABCD be a quadrilateral with area 18, with side AB parallel to the side CD and AB = 2CD. Let AD be perpendicular to AB and CD. If a circle is drawn inside the quadrilateral ABCD touching all the sides, then its…

    Circles · with solution

  6. The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN, is

    Permutations and Combinations · with solution

  7. Let a, b, c be unit vectors such that a + b + c = 0. Which one of the following is correct?

    Vector Algebra · with solution

  8. Let E^c denotes the complement of an event E. If E, F, G are pairwise independent events with P(G) > 0 and P(E ∩ F ∩ G) = 0. Then, P(E^c ∩ F^c | G) equals

    Probability · with solution

  9. A hyperbola, having the transverse axis of length 2sinθ, is confocal with the ellipse 3x^2 + 4y^2 = 12. Then, its equation is

    Conic Sections

  10. If |z| = 1 and z ≠ ± 1, then all the values of z/(1-z^2) lie on

    Complex Numbers and Quadratic Equations · with solution

  11. (d^2x)/(dy^2) equals

    Limits Continuity and Differentiability · with solution

  12. If f(x) = dfracx(1+x^n)^1/n for n ≥ 2 and g(x) = underbrace(f o f o … o f)_f occurs n times(x). Then ∫ x^n-2 g(x) dx equals

    Indefinite Integration · with solution

  13. Let f(x) be differentiable on the interval (0, ∞) such that f(1) = 1, and lim_t → x (t^2 f(x) - x^2 f(t))/(t - x) = 1 for each x > 0. Then, f(x) is

    Limits Continuity and Differentiability

  14. Let α, β be the roots of the equation x^2 - px + r = 0 and (α)/2, 2β be the roots of the equation x^2 - qx + r = 0. Then, the value of r is

    Complex Numbers and Quadratic Equations

  15. Let O(0, 0), P(3, 4) and Q(6, 0) be the vertices of a triangle OPQ. The point R inside the triangle OPQ is such that the triangles OPR, PQR and OQR are of equal area. The coordinates of R are

    Straight Lines and Pair of Lines

Chemistry

  1. Consider a titration of potassium dichromate solution with acidified Mohr's salt solution using diphenylamine as indicator. The number of moles of Mohr's salt required per mole of dichromate is

    Redox and Electrochemistry

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