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2011 (AIEEE / IIT-JEE, in the JEE Main bank) questions

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

Mathematics

  1. A value of b for which the equations x^2 + bx - 1 = 0, x^2 + x + b = 0 have one root in common is

    Complex Numbers and Quadratic Equations

  2. The circle passing through the point (-1, 0) and touching the Y-axis at (0, 2) also passes through the point

    Circles · with solution

  3. Let (x, y) be any point on the parabola y^2 = 4x. Let P be the point that divides the line segment from (0, 0) to (x, y) in the ratio 1:3. Then, the locus of P is

    Conic Sections · with solution

  4. Let P(6, 3) be a point on the hyperbola (x^2)/(a^2) - (y^2)/(b^2) = 1. If the normal at the point P intersects the X-axis at (9, 0), then the eccentricity of the hyperbola is

    Conic Sections · with solution

  5. Let a = i + j + k, b = i - j + k and c = i - j - k be three vectors. A vector v in the plane of a and b, whose projection on c is frac1√(3), is given by

    Vector Algebra · with solution

  6. Let f(x) = x^2 and g(x) = sin x for all x ∈ R. Then, the set of all x satisfying (fogogof)(x) = (gogof)(x), where (fog)(x) = f(g(x)), is

    Sets Relations and Functions · with solution

  7. If lim_x → 0 [1 + x log(1 + b^2)]^1/x = 2bsin^2θ, b > 0 and θ ∈ (-π, π], then the value of θ is

    Limits Continuity and Differentiability · with solution

  8. Let M and N be two 3 × 3 non-singular skew-symmetric matrices such that MN = NM. If P^T denotes the transpose of P, then M^2N^2(M^TN)^-1(MN^-1)^T is equal to

    Matrices and Determinants · with solution

  9. If P = \θ : sinθ - cosθ = √(2)cosθ\ and Q = \θ : sinθ + cosθ = √(2)sinθ\ be two sets. Then,

    Trigonometry · with solution

  10. Let f: [-1, 2] → [0, ∞) be a continuous function such that f(x) = f(1-x), forall x ∈ [-1, 2]. If R_1 = int_-1^2 x f(x) dx and R_2 are the area of the region bounded by y = f(x), x = -1, x = 2 and the x-axis. Then,

    Definite Integrals and Areas

  11. If the straight line x = b divide the area enclosed by y = (1-x)^2, y = 0 and x = 0 into two parts R_1(0 ≤ x ≤ b) and R_2(b ≤ x ≤ 1) such that R_1 - R_2 = 1/4. Then, b equals

    Definite Integrals and Areas

  12. The value of int_√(log 2)^√(log 3) (x sin x^2)/(sin x^2 + sin(log 6 - x^2)) dx is \hspace{1em}

    Definite Integrals and Areas · with solution

  13. A straight line L through the point (3, -2) is inclined at an angle 60° to the line √(3)x + y = 1. If L also intersects the X-axis, then the equation of L is

    Straight Lines and Pair of Lines · with solution

Chemistry

  1. Dissolving 120 g of urea (mol. wt. 60) in 1000 g of water gave a solution of density 1.15 g/mL. The molarity of the solution is

    Solutions

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