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2004 (AIEEE / IIT-JEE, in the JEE Main bank) questions

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

Mathematics

  1. Area of triangle formed by the lines x + y = 3 and angle bisectors of the pair of straight lines x^2 - y^2 + 2y = 1 is

    Straight Lines and Pair of Lines · with solution

  2. If f(x) = sin x + cos x, g(x) = x^2 - 1, then g\f(x)\ is invertible in the domain

    Sets Relations and Functions · with solution

  3. The sides of a triangle are in the ratio 1 : √(3) : 2, then the angles of the triangle are in the ratio

    Trigonometry · with solution

  4. For all 'x', x^2 + 2ax + (10 - 3a) > 0, then the interval in which 'a' lies is

    Complex Numbers and Quadratic Equations · with solution

  5. The unit vector which is orthogonal to the vector 3i + 2j + 6k and is coplanar with the vectors 2i + j + k and i - j + k is

    Vector Algebra · with solution

  6. If f(x) is differentiable and int_0^t^2 x f(x) dx = 2/5t^5, then f (4/25 ) equals

    Definite Integrals and Areas · with solution

  7. If ω (≠ 1) be a cube root of unity and (1 + ω^2)^n = (1 + ω^4)^n, then the least positive value of n is

    Complex Numbers and Quadratic Equations · with solution

  8. If the lines (x-1)/2 = (y+1)/3 = (z-1)/4 and (x-3)/1 = (y-k)/2 = z/1 intersect, then the value of k is

    Three Dimensional Geometry · with solution

  9. If ^n-1C_r = (k^2 - 3) ^nC_r+1, then k belongs to

    Binomial Theorem

  10. An infinite GP has first term x and sum 5, then x belongs to

    Sequences and Series · with solution

  11. If one of the diameters of the circle x^2 + y^2 - 2x - 6y + 6 = 0 is a chord to the circle with centre (2, 1), then the radius of the circle is

    Circles

  12. If y = y(x) and (2 + sin x)/(y + 1) (dy/dx ) = -cos x, y(0) = 1, then y ((π)/2 ) equals

    Differential Equations · with solution

  13. If the line 2x + √(6)y = 2 touches the hyperbola x^2 - 2y^2 = 4, then the point of contact is

    Conic Sections · with solution

  14. If f(x) = x^3 + bx^2 + cx + d and 0 < b^2 < c, then in (-∞, ∞)

    Application of Derivatives · with solution

  15. The angle between the tangents drawn from the point (1,4) to the parabola y^2 = 4x is

    Conic Sections · with solution

  16. Given both θ and φ are acute angles and sinθ = 1/2, cosφ = 1/3, then the value of θ + φ belongs to

    Trigonometry

  17. If three distinct numbers are chosen randomly from the first 100 natural numbers, then the probability that all three of them are divisible by both 2 and 3, is

    Probability · with solution

  18. Tangents are drawn to the ellipse x^2 + 2y^2 = 2, then the locus of the mid-point of the intercept made by the tangents between the coordinate axes is

    Conic Sections · with solution

  19. If A = beginbmatrix α & 2 \ 2 & α endbmatrix and |A^3| = 125, then the value of α is

    Matrices and Determinants · with solution

  20. If y is a function of x and log(x + y) = 2xy, then the value of y'(0) is

    Limits Continuity and Differentiability · with solution

  21. Given, 2x - y + 2z = 2, x - 2y + z = -4, x + y + λ z = 4, then the value of λ such that the given system of equations has no solution, is

    Matrices and Determinants

  22. The value of the integral int_0^1 √((1-x)/(1+x)) dx is

    Definite Integrals and Areas · with solution

  23. The area enclosed between the curves y = ax^2 and x = ay^2 (a > 0) is 1 sq unit. Then, the value of a is

    Definite Integrals and Areas

  24. If one root is square of the other root of the equation x^2 + px + q = 0, then the relation between p and q is

    Complex Numbers and Quadratic Equations

Chemistry

  1. Which hydrogen like species will have same radius as that of Bohr orbit of hydrogen atom?

    Atomic Structure · with solution

Physics

  1. A particle starts from rest. Its acceleration (a) versus time (t) is as shown in the figure. The maximum speed of the particle will be (2004, 2M) [figure]

    Kinematics · with solution

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