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JEE Main 2014 questions

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

Mathematics

  1. For x ∈ (0, π), the equation sin x + 2sin 2x - sin 3x = 3 has

    Trigonometry · with solution

  2. The angle between the lines whose direction cosines satisfy the equations l + m + n = 0 and l^2 = m^2 + n^2, is

    Three Dimensional Geometry

  3. Let f:[0,2] → R be a function which is continuous on [0,2] and is differentiable on (0,2) with f(0)=1. Let F(x) = int_0^x^2 f(√(t)) dt, for x ∈ [0,2]. If F'(x) = f'(x), forall x ∈ (0,2), then F(2) equals

    Definite Integrals and Areas

  4. The common tangents to the circle x^2 + y^2 = 2 and the parabola y^2 = 8x touch the circle at the points P, Q and the parabola at the points R, S. Then, the area (in sq units) of the quadrilateral PQRS is

    Definite Integrals and Areas

  5. Let the population of rabbits surviving at a time t be governed by the differential equation (dp(t))/dt = 1/2p(t) - 200. If p(0) = 100, then p(t) is equal to

    Differential Equations · with solution

  6. In a triangle, the sum of two sides is x and the product of the same two sides is y. If x^2 - c^2 = y, where c is the third side of the triangle, then the ratio of the inradius to the circumradius of the triangle is

    Trigonometry · with solution

  7. Three positive numbers form an increasing GP. If the middle term in this GP is doubled, then new numbers are in AP. Then, the common ratio of the GP is

    Sequences and Series · with solution

  8. If a ∈ R and the equation -3(x - [x])^2 + 2(x - [x]) + a^2 = 0 (where, [x] denotes the greatest integer ≤ x) has no integral solution, then all possible values of a lie in the interval

    Complex Numbers and Quadratic Equations · with solution

  9. If (10)^9 + 2(11)^1(10)^8 + 3(11)^2(10)^7 + … + 10(11)^9 = k(10)^9, then k is equal to

    Sequences and Series

  10. If z is a complex number such that |z| ≥ 2, then the minimum value of |z + 1/2 |

    Complex Numbers and Quadratic Equations

  11. Let A and B be two events such that P(A ∪ B) = 1/6, P(A ∩ B) = 1/4 and P(A) = 1/4, where A stands for the complement of the event A. Then, the events A and B are

    Probability · with solution

  12. If A is a 3 × 3 non-singular matrix such that AA^T = A^T A and B = A^-1A^T, then BB^T is equal to

    Matrices and Determinants · with solution

  13. The slope of the line touching both the parabolas y^2 = 4x and x^2 = -32y is

    Conic Sections · with solution

  14. Three boys and two girls stand in a queue. The probability that the number of boys ahead of every girl is atleast one more that the number of girls ahead of her, is

    Probability · with solution

  15. Let C be the circle with centre at (1, 1) and radius 1. If T is the circle centred at (0, y) passing through origin and touching the circle C externally, then the radius of T is equal to

    Circles · with solution

  16. lim_x → 0 (sin(π cos^2 x))/(x^2) is equal to

    Limits Continuity and Differentiability · with solution

  17. The locus of the foot of perpendicular drawn from the centre of the ellipse x^2 + 3y^2 = 6 on any tangent to it is

    Conic Sections · with solution

  18. If f and g are differentiable functions in (0, 1) satisfying f(0) = 2 = g(1), g(0) = 0 and f(1) = 6, then for some c ∈ [0, 1]

    Limits Continuity and Differentiability · with solution

  19. If α, β ≠ 0 and f(n) = α^n + β^n and beginvmatrix 3 & 1+f(1) & 1+f(2) \ 1+f(1) & 1+f(2) & 1+f(3) \ 1+f(2) & 1+f(3) & 1+f(4) endvmatrix = K(1-α)^2(1-β)^2(α-β)^2, then K is equal to

    Matrices and Determinants · with solution

  20. If x = -1 and x = 2 are extreme points of f(x) = α log|x| + β x^2 + x, then

    Application of Derivatives · with solution

  21. The function y = f(x) is the solution of the differential equation dy/dx + xy/(x^2-1) = fracx^4+2x√(1-x^2) in (-1,1) satisfying f(0) = 0. Then int_-frac√(3)2^frac√(3)2 f(x) dx is

    Differential Equations · with solution

  22. The area (in sq units) of the region described by A = \(x, y) : x^2 + y^2 ≤ 1 and y^2 ≤ 1 - x\ is

    Definite Integrals and Areas

  23. The area enclosed by the curves y = sin x + cos x and y = |cos x - sin x| over the interval [0, (π)/2 ] is

    Definite Integrals and Areas · with solution

  24. In the quadratic equation p(x) = 0 with real coefficients has purely imaginary roots. Then, the equation p[p(x)] = 0 has

    Complex Numbers and Quadratic Equations

  25. The coefficient of x^11 in the expansion of (1+x^2)^4(1+x^3)^7(1+x^4)^12 is

    Binomial Theorem

  26. The integral int_π/4^π/2 (2cosec x)^17 dx is equal to

    Definite Integrals and Areas · with solution

  27. Let α and β be the roots of equation px^2 + qx + r = 0, p ≠ 0. If p, q and r are in AP and 1/(α) + 1/(β) = 4, then the value of |α - β| is

    Complex Numbers and Quadratic Equations

  28. Let a, b, c and d be non-zero numbers. If the point of intersection of the lines 4ax + 2ay + c = 0 and 5bx + 2by + d = 0 lies in the fourth quadrant and is equidistant from the two axes, then

    Straight Lines and Pair of Lines

  29. The integral ∫limits_0^(π)/2 √(1 + 4sin^2x/2 - 4sinx/2) dx is equal to

    Definite Integrals and Areas

  30. If PS is the median of the triangle with vertices P(2,2), Q(6,-1) and R(7,3), then equation of the line passing through (1,-1) and parallel to PS is

    Straight Lines and Pair of Lines

  31. The image of the line (x-1)/3 = (y-3)/1 = (z-4)/(-5) in the plane 2x - y + z + 3 = 0 is the line

    Three Dimensional Geometry

Chemistry

  1. The ratio mass of oxygen and nitrogen of a particular gaseous mixture is 1 : 4. The ratio of number of their molecules is

    Some Basic Concepts of Chemistry · with solution

Physics

  1. From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle to hit the ground, is n times that taken by it to reach the highest point of its path. The relation…

    Kinematics

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