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JEE Main 2017 questions

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

Mathematics

  1. If f: R → R is a twice differentiable function such that f''(x) > 0 for all x ∈ R, and f (1/2 ) = 1/2, f(1) = 1, then

    Application of Derivatives · with solution

  2. For three events A, B and C, if P(exactly one of A or B occurs) = P(exactly one of B or C occurs) = P(exactly one of C or A occurs) = 1/4 and P(all the three events occur simultaneously) = 1/16, then the probability…

    Probability · with solution

  3. Let I_n = ∫ tan^n x dx (n > 1). If I_4 + I_6 = a tan^5 x + bx^5 + C, where C is a constant of integration, then the ordered pair (a, b) is equal to

    Indefinite Integration · with solution

  4. How many 3 × 3 matrices M with entries from \0, 1, 2\ are there, for which the sum of the diagonal entries of M^T M is 5?

    Permutations and Combinations · with solution

  5. For any three positive real numbers a, b and c, if 9(25a^2 + b^2) + 25(c^2 - 3ac) = 15b(3a + c), then

    Sequences and Series

  6. If (2 + sin x)dy/dx + (y+1)cos x = 0 and y(0) = 1, then y ((π)/2 ) is equal to

    Differential Equations · with solution

  7. If y = y(x) satisfies the differential equation 8√(x) (√(9+√(x)) )dy = (√(4+√(9+√(x))) )^-1dx, x > 0 and y(0) = √(7), then y(256) =

    Differential Equations · with solution

  8. If two different numbers are taken from the set {0, 1, 2, 3, ..., 10}, then the probability that their sum as well as absolute difference are both multiple of 4, is

    Probability · with solution

  9. If A = beginbmatrix 2 & -3 \ -4 & 1 endbmatrix, then adj(3A^2 + 12A) is equal to

    Matrices and Determinants · with solution

  10. If a hyperbola passes through the point P(√(2), √(3)) and has foci at (± 2, 0), then the tangent to this hyperbola at P also passes through the point

    Conic Sections · with solution

  11. Let O be the origin and let PQR be an arbitrary triangle. The point S is such that OP · OQ + OR · OS = OR · OP + OQ · OS = OQ · OR + OP · OS Then the triangle PQR has S as its

    Vector Algebra · with solution

  12. Three randomly chosen non-negative integers x, y and z are found to satisfy the equation x + y + z = 10. Then the probability that z is even, is

    Probability · with solution

  13. Let a, b, c ∈ R. If f(x) = ax^2 + bx + c be such that a + b + c = 3 and f(x+y) = f(x) + f(y) + xy, forall x, y ∈ R, and sum_n=1^10 f(n) is equal to

    Sets Relations and Functions · with solution

  14. The radius of a circle having minimum area, which touches the curve y = 4 - x^2 and the lines y = |x|, is

    Circles

  15. Let a = 2i + j - 2k, b = i + j and c be a vector such that |c - a| = 3, |(a × b) × c| = 3 and the angle between c and a × b is 30°. Then, a · c is equal to

    Vector Algebra · with solution

  16. The function f: R → [-1/2, 1/2 ] defined as f(x) = x/(1+x^2) is

    Sets Relations and Functions · with solution

  17. The eccentricity of an ellipse whose centre is at the origin is 1/2. If one of its directrices is x = -4, then the equation of the normal to it at (1, 3/2 ) is

    Conic Sections · with solution

  18. A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then, the total number of ways in which X and Y…

    Permutations and Combinations

  19. A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn one-by-one with replacement, then the variance of the number of green balls drawn is

    Probability · with solution

  20. lim_x → π/2 (cot x - cos x)/((π - 2x)^3) equals

    Limits Continuity and Differentiability · with solution

  21. The normal to the curve y(x-2)(x-3) = x + 6 at the point, where the curve intersects the Y-axis passes through the point

    Application of Derivatives

  22. The eccentricity of the hyperbola whose length of the latusrectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci, is

    Conic Sections · with solution

  23. Let S = \1, 2, 3, …, 9\. For k = 1, 2, …, 5, let N_k be the number of subsets of S, each containing five elements out of which exactly k are odd. Then N_1 + N_2 + N_3 + N_4 + N_5 =

    Permutations and Combinations

  24. Let a vertical tower AB have its end A on the level ground. Let C be the mid-point of AB and P be a point on the ground such that AP = 2AB. If ∠ BPC = β, then tanβ is equal to

    Trigonometry · with solution

  25. If 5(tan^2 x - cos^2 x) = 2cos 2x + 9, then the value of cos 4x is

    Trigonometry · with solution

  26. For x ∈ (0, 1/4 ), if the derivative of tan^-1 (frac6x√(x)1-9x^3 ) is √(x) · g(x), then g(x) equals

    Limits Continuity and Differentiability · with solution

  27. Let ω be a complex number such that 2ω + 1 = z, where z = √(-3). If beginvmatrix 1 & 1 & 1 \ 1 & -ω^2 - 1 & ω^2 \ 1 & ω^2 & ω^7 endvmatrix = 3k, then k is equal to

    Matrices and Determinants

  28. The area (in sq units) of the region \(x, y) : x ≥ 0, x + y ≤ 3, x^2 ≤ 4y and y ≤ 1 + √(x)\ is

    Definite Integrals and Areas

  29. The value of binom21C_1 - binom10C_1 + binom21C_2 - binom10C_2 + binom21C_3 - binom10C_3 + binom21C_4 - binom10C_4 + … + binom21C_10 - binom10C_10 is

    Binomial Theorem

  30. int_π/4^3π/4 dx/(1 + cos x) is equal to

    Definite Integrals and Areas · with solution

  31. Let k be an integer such that the triangle with vertices (k, -3k), (5, k) and (-k, 2) has area 28 sq units. Then, the orthocentre of this triangle is at the point

    Straight Lines and Pair of Lines · with solution

  32. If the image of the point P(1, -2, 3) in the plane 2x + 3y - 4z + 22 = 0 measured parallel to the line x/1 = y/4 = z/5 is Q, then PQ is equal to

    Three Dimensional Geometry · with solution

  33. The distance of the point (1, 3, -7) from the plane passing through the point (1, -1, -1) having normal perpendicular to both the lines (x-1)/1 = (y+2)/(-2) = (z-4)/3 and (x-2)/2 = (y+1)/(-1) = (z+7)/(-1), is

    Three Dimensional Geometry

  34. The equation of the plane passing through the point (1, 1, 1) and perpendicular to the planes 2x + y - 2z = 5 and 3x - 6y - 2z = 7 is

    Three Dimensional Geometry · with solution

Chemistry

  1. The radius of the second Bohr orbit for hydrogen atom is (Planck's constant (h) = 6.6262 × 10^-34 Js; mass of electron = 9.1091 × 10^-31 kg; charge of electron (e) = 1.60210 × 10^-19 C; permittivity of vacuum (ε_0) =…

    Atomic Structure

  2. The most abundant elements by mass in the body of a healthy human adult are oxygen (61.4%), carbon (22.9%), hydrogen (10.0 %), and nitrogen (2.6%). The weight which a 75 kg person would gain if all ^1H atoms are…

    Some Basic Concepts of Chemistry

  3. 1 g of a carbonate (M_2CO_3) on treatment with excess HCl produces 0.01186 mole of CO_2. The molar mass of M_2CO_3 in g mol^-1 is

    Some Basic Concepts of Chemistry · with solution

Physics

  1. A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time?

    Kinematics · with solution

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