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JEE Main 2015 questions

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

Mathematics

  1. The number of integers greater than 6000 that can be formed using the digits 3, 5, 6, 7 and 8 without repetition is

    Permutations and Combinations · with solution

  2. Let O be the vertex and Q be any point on the parabola x^2 = 8y. If the point P divides the line segment OQ internally in the ratio 1:3, then the locus of P is

    Conic Sections · with solution

  3. A complex number z is said to be unimodular, if |z| ≠ 1. If z_1 and z_2 are complex numbers such that dfracz_1 - 2z_22 - z_1z_2 is unimodular and z_0 is not unimodular. Then, the point z_1 lies on a

    Complex Numbers and Quadratic Equations

  4. If 12 identical balls are to be placed in 3 different boxes, then the probability that one of the boxes contains exactly 3 balls, is

    Probability

  5. If A = beginbmatrix 1 & 2 & 2 \ 2 & 1 & -2 \ c & 2 & b endbmatrix is a matrix satisfying the equation AA^T = 9I, where I is 3 × 3 identity matrix, then the ordered pair (a, b) is equal to

    Matrices and Determinants

  6. The number of common tangents to the circles x^2 + y^2 - 4x - 6y - 12 = 0 and x^2 + y^2 + 6x + 18y + 26 = 0 is

    Circles · with solution

  7. The area (in sq units) of the quadrilateral formed by the tangents at the end points of the latusrectum to the ellipse (x^2)/9 + (y^2)/5 = 1 is

    Conic Sections · with solution

  8. The normal to the curve x^2 + 2xy - 3y^2 = 0 at (1,1)

    Application of Derivatives · with solution

  9. If m is the AM of two distinct real numbers l and n (l, n > 1) and G_1, G_2 and G_3 are three geometric means between l and n, then G_1^4 + 2G_2^4 + G_3^4 equals

    Sequences and Series

  10. If g is the inverse of a function f and f'(x) = 1/(1+x^5), then g'(x) is equal to

    Limits Continuity and Differentiability

  11. The sum of first 9 terms of the series (1^3)/1 + (1^3 + 2^3)/(1+3) + (1^3 + 2^3 + 3^3)/(1+3+5) + … is

    Sequences and Series · with solution

  12. The value of ∫ dfracdxx^2(x^4+1)^3/4 is

    Indefinite Integration · with solution

  13. Let y(x) be the solution of the differential equation (x log x) dy/dx + y = 2x log x, (x ≥ 1). Then, y(e) is equal to

    Differential Equations

  14. The set of all values of λ for which the system of linear equations 2x_1 - 2x_2 + x_3 = λ x_1, 2x_1 - 3x_2 + 2x_3 = λ x_2, -x_1 + 2x_2 = λ x_3 has a non-trivial solution

    Matrices and Determinants

  15. The area (in sq units) of region described by \(x, y) y^2 ≤ 2x and y ≥ 4x - 1\ is

    Definite Integrals and Areas · with solution

  16. Let α and β be the roots of equation x^2 - 6x - 2 = 0. If a_n = α^n - β^n, for n ≥ 1, then the value of dfraca_10 - 2a_82a_9 is

    Complex Numbers and Quadratic Equations · with solution

  17. The sum of coefficients of integral powers of x in the binomial expansion (1 - 2√(x))^50 is

    Binomial Theorem

  18. The integral int_2^4 (log x^2)/(log x^2 + log(36 - 12x + x^2)) dx is equal to

    Definite Integrals and Areas · with solution

  19. The equation of the plane containing the lines 2x - 5y + z = 3, x + y + 4z = 5 and parallel to the plane x + 3y + 6z = 1 is

    Three Dimensional Geometry · with solution

  20. The distance of the point (1, 0, 2) from the point of intersection of the line (x-2)/3 = (y+1)/4 = (z-2)/12 and the plane x - y + z = 16 is

    Three Dimensional Geometry · with solution

Chemistry

  1. From the following statements regarding H_2O_2 choose the incorrect statement.

    Hydrogen and s-Block Elements

  2. Which of the following is the energy of a possible excited state of hydrogen?

    Atomic Structure

  3. The molecular formula of a commercial resin used for exchanging ions in water softening is C_8H_7SO_3Na (molecular weight = 206). What would be the maximum uptake of Ca^2+ ions by the resin when expressed in mole per…

    Some Basic Concepts of Chemistry

  4. 3 g of activated charcoal was added to 50 mL of acetic acid solution (0.06N) in a flask. After an hour it was filtered and the strength of the filtrate was found to be 0.042 N. The amount of acetic acid adsorbed (per…

    Surface Chemistry

Physics

  1. Two stones are thrown up simultaneously from the edge of a cliff 240 m high with initial speed of 10 m/s and 40 m/s, respectively. Which of the following graph best represents the time variation of relative position of…

    Kinematics

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