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JEE Main 2018 questions

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

Mathematics

  1. A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at…

    Probability · with solution

  2. From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf, so that the dictionary is always in the middle. The number of such arrangements is

    Permutations and Combinations

  3. Tangents are drawn to the hyperbola 4x^2 - y^2 = 36 at the points P and Q. If these tangents intersect at the point T(0, 3), then the area (in sq units) of triangle PTQ is

    Conic Sections · with solution

  4. If the tangent at (1, 7) to the curve x^2 = y - 6 touches the circle x^2 + y^2 + 16x + 12y + c = 0, then the value of c is

    Circles · with solution

  5. Tangent and normal are drawn at P(16, 16) on the parabola y^2 = 16x, which intersect the axis of the parabola at A and B, respectively. If C is the centre of the circle through the points P, A and B and ∠ CPB = θ, then…

    Conic Sections · with solution

  6. For each t ∈ R, let [t] be the greatest integer less than or equal to t. Then, lim_x → 0^+ x ( [1/x ] + [2/x ] + … + [15/x ] )

    Limits Continuity and Differentiability

  7. If the curves y^2 = 6x, 9x^2 + by^2 = 16 intersect each other at right angles, then the value of b is

    Application of Derivatives · with solution

  8. Let a_1, a_2, a_3, …, a_49 be in AP such that sum_k=0^12 a_4k+1 = 416 and a_9 + a_43 = 66. If a_1^2 + a_2^2 + … + a_17^2 = 140 m, then m is equal to

    Sequences and Series

  9. PQR is a triangular park with PQ = PR = 200 m. A TV tower stands at the mid-point of QR. If the angles of elevation of the top of the tower at P, Q and R are respectively 45°, 30° and 30°, then the height of the tower…

    Trigonometry · with solution

  10. If sum of all the solutions of the equation 8cos x · (cos ((π)/6 + x ) · cos ((π)/6 - x ) - 1/2 ) = 1 in [0, π] is kπ, then k is equal to

    Trigonometry · with solution

  11. Let A be the sum of the first 20 terms and B be the sum of the first 40 terms of the series 1^2 + 2 · 2^2 + 3^2 + 2 · 4^2 + 5^2 + 2 · 6^2 + … If B - 2A = 100λ, then λ is equal to

    Sequences and Series

  12. Let S = \t ∈ R : f(x) = |x - π| · (e^|x| - 1)sin|x|\ is not differentiable at t. Then, the set S is equal to

    Limits Continuity and Differentiability

  13. The integral ∫ (sin^2 x cos^2 x)/( (sin^5 x + cos^3 x sin^2 x + sin^3 x cos^2 x + cos^5 x )^2) dx is equal to

    Indefinite Integration

  14. If beginvmatrix x-4 & 2x & 2x \ 2x & x-4 & 2x \ 2x & 2x & x-4 endvmatrix = (A + Bx)(x - A)^2, then the ordered pair (A, B) is equal to

    Matrices and Determinants · with solution

  15. Let S = \x ∈ R : x ≥ 0 and 2|√(x) - 3| + √(x)(√(x) - 6) + 6 = 0\. Then, S

    Complex Numbers and Quadratic Equations · with solution

  16. If α, β ∈ C are the distinct roots of the equation x^2 - x + 1 = 0, then α^101 + β^107 is equal to

    Complex Numbers and Quadratic Equations

  17. Let g(x) = cos x^2, f(x) = √(x) and α, β (α < β) be the roots of the quadratic equation 18x^2 - 9π x + π^2 = 0. Then, the area (in sq units) bounded by the curve y = (gof)(x) and the lines x = α, x = β and y = 0, is

    Definite Integrals and Areas · with solution

  18. Let y = y(x) be the solution of the differential equation sin x dy/dx + ycos x = 4x, x ∈ (0, π). If y ((π)/2 ) = 0, then y ((π)/6 ) is equal to

    Differential Equations · with solution

  19. If the system of linear equations x + ky + 3z = 0, 3x + ky - 2z = 0 2x + 4y - 3z = 0 has a non-zero solution (x, y, z), then xz/(y^2) is equal to

    Matrices and Determinants

  20. The sum of the coefficients of all odd degree terms in the expansion of (x + √(x^3 - 1) )^5 + (x - √(x^3 - 1) )^5, (x > 1) is

    Binomial Theorem · with solution

  21. A straight line through a fixed point (2, 3) intersects the coordinate axes at distinct points P and Q. If O is the origin and the rectangle OPRQ is completed, then the locus of R is

    Straight Lines and Pair of Lines · with solution

  22. If L_1 is the line of intersection of the planes 2x - 2y + 3z - 2 = 0, x - y + z + 1 = 0 and L_2 is the line of intersection of the planes x + 2y - z - 3 = 0, 3x - y + 2z - 1 = 0, then the distance of the origin from…

    Three Dimensional Geometry

  23. The length of the projection of the line segment joining the points (5, -1, 4) and (4, -1, 3) on the plane, x + y + z = 7 is

    Three Dimensional Geometry · with solution

  24. Let u be a vector coplanar with the vectors a = 2i + 3j - k and b = j + k. If u is perpendicular to a and u · b = 24, then |u|^2 is equal to

    Vector Algebra · with solution

Chemistry

  1. The ratio of mass per cent of C and H of an organic compound (C_xH_yO_z) is 6 : 1. If one molecule of the above compound (C_xH_yO_z) contains half as much oxygen as required to burn one molecule of compound C_xH_y…

    Some Basic Concepts of Chemistry

  2. An alkali is titrated against an acid with methyl orange as indicator, which of the following is a correct combination? Base Acid End point (a) Weak Strong Colourless to pink (b) Strong Strong Pinkish red to yellow (c)…

    Practical Chemistry

Physics

  1. All the graphs below are intended to represent the same motion. One of them does it incorrectly . Pick it up.

    Kinematics

  2. The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error…

    Units and Measurements · with solution

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