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JEE Main 2013 questions

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

Mathematics

  1. If z is a complex number of unit modulus and argument θ, then arg (dfrac1+z1+z ) is equal to

    Complex Numbers and Quadratic Equations · with solution

  2. If the equations x^2 + 2x + 3 = 0 and ax^2 + bx + c = 0, a, b, c ∈ R have a common root, then a : b : c is

    Complex Numbers and Quadratic Equations · with solution

  3. The intercepts on X-axis made by tangents to the curve, y = int_0^x |t| dt, x ∈ R, which are parallel to the line y = 2x, are equal to

    Definite Integrals and Areas

  4. The real number k for which the equation, 2x^3 + 3x + k = 0 has two distinct real roots in [0, 1]

    Complex Numbers and Quadratic Equations

  5. A curve passes through the point (1, (π)/6 ). Let the slope of the curve at each point (x, y) be y/x + sec (y/x ), x > 0. Then, the equation of the curve is

    Differential Equations · with solution

  6. ABCD is a trapezium such that AB and CD are parallel and BC ⊥ CD, if ∠ ADB = θ, BC = p and CD = q, then AB is equal to

    Trigonometry

  7. At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P with respect to additional number of workers x is given by dP/dx = 100 - 12√(x). If the firm employees 25 more…

    Differential Equations · with solution

  8. The equation of the circle passing through the foci of the ellipse (x^2)/16 + (y^2)/9 = 1 and having centre at (0, 3) is

    Conic Sections · with solution

  9. The circle passing through (1, -2) and touching the axis of x at (3, 0) also passes through the point

    Circles · with solution

  10. If ∫ f(x) dx = ψ(x), then ∫ x^5 f(x^3) dx is equal to

    Indefinite Integration · with solution

  11. The sum of first 20 terms of the sequence 0.7, 0.77, 0.777, ... is

    Sequences and Series

  12. The value of cot \sum_n=1^23 cot^-1 (1 + sum_k=1^n 2k ) \ is

    Inverse Trigonometric Functions · with solution

  13. The expression (tan A)/(1 - cot A) + (cot A)/(1 - tan A) can be written as

    Trigonometry · with solution

  14. If x, y and z are in AP and tan^-1 x, tan^-1 y and tan^-1 z are also in AP, then

    Inverse Trigonometric Functions · with solution

  15. Four persons independently solve a certain problem correctly with probabilities 1/2, 3/4, 1/4, 1/8. Then, the probability that the problem is solved correctly by atleast one of them, is

    Probability · with solution

  16. If P = beginbmatrix 1 & α & 3 \ 1 & 3 & 3 \ 2 & 4 & 4 endbmatrix is the adjoint of a 3 × 3 matrix A and |A| = 4, then α is equal to

    Matrices and Determinants · with solution

  17. A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is

    Probability · with solution

  18. lim_x → 0 ((1 - cos 2x)(3 + cos x))/(x tan 4x) is equal to

    Limits Continuity and Differentiability · with solution

  19. Let T_n be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If T_n+1 - T_n = 10, then the value of n is

    Permutations and Combinations

  20. If y = sec(tan^-1 x), then dy/dx at x = 1 is equal to

    Limits Continuity and Differentiability · with solution

  21. The number of value of k, for which the system of equation (k+1)x + 8y = 4y ⇒ kx + (k+3)y = 3k - 1 has no solution, is

    Matrices and Determinants

  22. Let f : [1/2, 1] → R (the set of all real numbers) be a positive, non-constant and differentiable function such that f'(x) < 2f(x) and f(1/2) = 1. Then, the value of int_1/2^1 f(x) dx lies in the interval

    Definite Integrals and Areas · with solution

  23. The number of points in (-∞, ∞) for which x^2 - xsin x - cos x = 0, is

    Application of Derivatives

  24. The area (in sq units) bounded by the curves y = √(x), 2y - x + 3 = 0, X-axis and lying in the first quadrant, is

    Definite Integrals and Areas · with solution

  25. The term independent of x in expansion of (dfracx+1x^2/3-x^1/3+1-dfracx-1x-x^1/2 )^10 is

    Binomial Theorem · with solution

  26. The x-coordinate of the incentre of the triangle that has the coordinates of mid-points of its sides as (0, 1), (1, 1) and (1, 0) is

    Straight Lines and Pair of Lines

  27. Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is

    Three Dimensional Geometry · with solution

Chemistry

  1. The correct set of four quantum numbers for the valence electrons of rubidium atom (Z = 37) is

    Atomic Structure · with solution

  2. Energy of an electron is given by E = -2.178 × 10^-18 J ((Z^2)/(n^2) ) Wavelength of light required to excite an electron in an hydrogen atom from level n = 1 to n = 2 will be (h = 6.62 × 10^-34 Js and c = 3.0 × 10^8…

    Atomic Structure

  3. The molarity of a solution obtained by mixing 750 mL of 0.5 M HCl with 250 mL of 2 M HCl will be

    Solutions · with solution

Physics

  1. Let [ε_0] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = Time and A = electric current, then

    Units and Measurements

  2. The diameter of a cylinder is measured using a vernier calipers with no zero error. It is found that the zero of the vernier scale lies between 5.10 cm and 5.15 cm of the main scale. The vernier scale has 50 division…

    Experimental Physics

  3. A projectile is given an initial velocity of (i + 2j) m/s, where, i is along the ground and j is along the vertical. If g = 10 m/s², then the equation of its trajectory is

    Kinematics · with solution

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