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2001 (AIEEE / IIT-JEE, in the JEE Main bank) questions

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

Mathematics

  1. If α + β = (π)/2 and β + γ = α, then tanα equals hspace2em

    Trigonometry · with solution

  2. If the positive numbers a, b, c, d are in AP. Then, abc, abd, acd, bcd are

    Sequences and Series

  3. Area of the parallelogram formed by the lines y = mx, y = mx + 1, y = nx and y = nx + 1 equals

    Straight Lines and Pair of Lines · with solution

  4. If f:[1,∞) → [2,∞) is given by f(x) = x + 1/x, then f^-1(x) equals

    Sets Relations and Functions · with solution

  5. Let f(x) = (1 + b^2)x^2 + 2bx + 1 and let m(b) be the minimum value of f(x). As b varies, the range of m(b) is

    Sets Relations and Functions · with solution

  6. The domain of definition of f(x) = (log_2(x+3))/(x^2+3x+2) is

    Sets Relations and Functions

  7. The complex numbers z_1, z_2 and z_3 satisfying (z_1 - z_3)/(z_2 - z_3) = frac1 - i√(3)2 are the vertices of a triangle which is

    Complex Numbers and Quadratic Equations · with solution

  8. The triangle formed by the tangent to the curve f(x) = x^2 + bx - b at the point (1,1) and the coordinate axes, lies in the first quadrant. If its area is 2 sq units, then the value of b is

    Definite Integrals and Areas

  9. Let f(x) = (α x)/(x+1), x ≠ -1. Then, for what value of α is f[f(x)] = x?

    Sets Relations and Functions · with solution

  10. Let z_1 and z_2 be nth roots of unity which subtend a right angled at the origin, then n must be of the form (where, k is an integer)

    Complex Numbers and Quadratic Equations

  11. Let AB be a chord of the circle x^2 + y^2 = r^2 subtending a right angle at the centre. Then, the locus of the centroid of the triangle PAB as P moves on the circle, is

    Circles

  12. If a = i - k, b = xi + j + (1-x)k and c = yi + xj + (1+x-y)k. Then, [a b c] depends on

    Vector Algebra · with solution

  13. Let PQ and RS be tangents at the extremities of the diameter PR of a circle of radius r. If PS and RQ intersect at a point X on the circumference of the circle, then 2r equals

    Circles · with solution

  14. The equation of the directrix of the parabola y^2 + 4y + 4x + 2 = 0 is

    Conic Sections · with solution

  15. If f(x) = xe^x(1-x), then f(x) is

    Application of Derivatives

  16. Let f:(0,∞) → R and F(x) = int_0^x f(t) dt. If F(x^2) = x^2(1+x), then f(4) equals

    Definite Integrals and Areas · with solution

  17. Let α, β be the roots of x^2 - x + p = 0 and γ, δ be the roots of x^2 + 4x + q = 0. If α, β, γ, δ are in GP, then the integer values of p and q respectively are

    Sequences and Series

  18. If the sum of the first 2n terms of the AP series 2, 5, 8, … is equal to the sum of the first n terms of the AP series 57, 59, 61, …, then n equals

    Sequences and Series · with solution

  19. Let E = \1, 2, 3, 4\ and F = \1, 2\. Then, the number of onto functions from E to F is

    Sets Relations and Functions · with solution

  20. If a, b and c are unit vectors, then |a - b|^2 + |b - c|^2 + |c - a|^2 does not exceed

    Vector Algebra

  21. The number of distinct real roots of beginvmatrix sin x & cos x & cos x \ cos x & sin x & cos x \ cos x & cos x & sin x endvmatrix = 0 in the interval -(π)/4 ≤ x ≤ (π)/4 is

    Matrices and Determinants · with solution

  22. Which of the following functions is differentiable at x = 0?

    Limits Continuity and Differentiability

  23. The left hand derivative of f(x) = [x] sin(π x) at x = k, k is an integer, is

    Limits Continuity and Differentiability · with solution

  24. Let f: R arrow R be a function defined by f(x) = max\x, x^3\. The set of all points, where f(x) is not differentiable, is

    Limits Continuity and Differentiability · with solution

  25. In the binomial expansion of (a - b)^n, n ≥ 5 the sum of the 5th and 6th terms is zero. Then, a/b equals

    Binomial Theorem · with solution

  26. The value of int_-π^π (cos^2 x)/(1 + a^x) dx, a > 0, is

    Definite Integrals and Areas

  27. The number of solutions of log_4(x-1) = log_2(x-3)

    Complex Numbers and Quadratic Equations · with solution

  28. The number of integer values of m, for which the x-coordinate of the point of intersection of the lines 3x + 4y = 9 and y = mx + 1 is also an integer, is

    Straight Lines and Pair of Lines · with solution

Chemistry

  1. In the standardisation of Na_2S_2O_3 using K_2Cr_2O_7 by iodometry, the equivalent weight of K_2Cr_2O_7 is

    Redox and Electrochemistry

  2. The reaction, 3ClO^-(aq) → ClO_3^-(aq) + 2Cl^-(aq) is an example of

    Redox and Electrochemistry · with solution

  3. An aqueous solution of 6.3 g oxalic acid dihydrate is made up to 250 mL. The volume of 0.1 N NaOH required to completely neutralise 10 mL of this solution is

    Some Basic Concepts of Chemistry · with solution

  4. The quantum numbers +1/2 and -1/2 for the electron spin represent

    Atomic Structure

  5. The wavelength associated with a golf ball weighing 200 g and moving at a speed of 5 m/h is of the order

    Atomic Structure · with solution

  6. The number of nodal planes in a p_x orbital is

    Atomic Structure · with solution

Physics

  1. A quantity X is given by ε_0 L (Δ V)/(Δ t) where ε_0 is the permittivity of free space, L is a length, Δ V is a potential difference and Δ t is a time interval. The dimensional formula for X is the same as that of

    Units and Measurements

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