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2000 (AIEEE / IIT-JEE, in the JEE Main bank) questions

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

Mathematics

  1. If x + y = k is normal to y^2 = 12x, then k is

    Conic Sections · with solution

  2. If arg(z) < 0, then arg(-z) - arg(z) equals

    Complex Numbers and Quadratic Equations · with solution

  3. In a triangle ABC, let ∠ C = π/2. If r is the inradius and R is the circumradius of the triangle, then 2(r + R) is equal to

    Trigonometry · with solution

  4. How many different nine-digit numbers can be formed from the number 22 33 55 888 by rearranging its digits so that the odd digits occupy even positions?

    Permutations and Combinations

  5. If b > a, then the equation (x - a)(x - b) - 1 = 0 has

    Complex Numbers and Quadratic Equations

  6. Let the vectors a, b, c and d be such that (a × b) × (c × d) = 0. If P_1 and P_2 are planes determined by the pairs of vectors a, b and c, d respectively, then the angle between P_1 and P_2 is

    Vector Algebra · with solution

  7. The domain of definition of the function y(x) is given by the equation 2^x + 2^y = 2, is

    Sets Relations and Functions · with solution

  8. Consider an infinite geometric series with first term a and common ratio r. If its sum is 4 and the second term is 3/4, then

    Sequences and Series · with solution

  9. For 2 ≤ r ≤ n, binomnr + 2binomnr-1 + binomnr-2 is equal to

    Binomial Theorem · with solution

  10. Let f(θ) = sinθ(sinθ + sin 3θ). Then, f(θ)

    Trigonometry · with solution

  11. If a, b and c are unit coplanar vectors, then the scalar triple product [2a - b 2b - c 2c - a] is

    Vector Algebra · with solution

  12. If the circle x^2 + y^2 + 2x + 2ky + 6 = 0 and x^2 + y^2 + 2ky + k = 0 intersect orthogonally, then k is

    Circles · with solution

  13. If the line x - 1 = 0 is the directrix of the parabola y^2 - kx + 8 = 0, then one of the values of k is

    Conic Sections · with solution

  14. If the vectors a, b and c from the sides BC, CA and AB respectively of a triangle ABC, then

    Vector Algebra · with solution

  15. For all x ∈ (0, 1)

    Application of Derivatives

  16. The triangle PQR is inscribed in the circle x^2 + y^2 = 25. If Q and R have coordinates (3, 4) and (-4, 3) respectively, then ∠ QPR is equal to

    Circles · with solution

  17. Let f(x) = ∫ e^x(x-1)(x-2) dx. Then, f decreases in the interval

    Application of Derivatives

  18. If z_1, z_2 and z_3 are complex numbers such that |z_1| = |z_2| = |z_3| = |1/z_1 + 1/z_2 + 1/z_3 | = 1, then |z_1 + z_2 + z_3| is

    Complex Numbers and Quadratic Equations

  19. If x^2 + y^2 = 1, then

    Limits Continuity and Differentiability · with solution

  20. If f(x) = begincases |1-x|, & 0 < |x| ≤ 2 \ 1, & x = 0 endcases. Then, at x = 0, f has

    Application of Derivatives

  21. If the system of equations x - ky - z = 0, kx - y - z = 0, x + y - z = 0 has a non-zero solution, then possible values of k are

    Matrices and Determinants

  22. For the equation 3x^2 + px + 3 = 0, p > 0, if one of the root is square of the other, then p is equal to

    Complex Numbers and Quadratic Equations · with solution

  23. If f(x) = begincases e^cos x sin x & , for |x| ≤ 2 \ 2 & , otherwise endcases then int_-2^3 f(x) dx is equal to

    Definite Integrals and Areas · with solution

  24. A straight line through the origin O meets the parallel lines 4x + 2y = 9 and 2x + y + 6 = 0 at points P and Q respectively. Then, the point O divides the segment PQ in the ratio

    Straight Lines and Pair of Lines · with solution

  25. The value of the integral int_e^-1^e^2 | (log_e x)/x | dx is

    Definite Integrals and Areas · with solution

  26. If α and β (α < β) are the roots of the equation x^2 + bx + c = 0, where c < 0 < b, then

    Complex Numbers and Quadratic Equations

  27. The incentre of the triangle with vertices (1, √(3)), (0, 0) and (2, 0) is

    Straight Lines and Pair of Lines · with solution

Chemistry

  1. Among the following, the species in which the oxidation number of an element is +6

    Redox and Electrochemistry · with solution

  2. The electronic configuration of an element is 1s^2, 2s^2 2p^6, 3s^2 3p^6 3d^5, 4s^1. This represents its

    Atomic Structure · with solution

Physics

  1. A ball is dropped vertically from a height d above the ground. It hits the ground and bounces up vertically to a height d/2. Neglecting subsequent motion and air resistance, its velocity v varies with height h above the…

    Kinematics · with solution

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