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1983 (AIEEE / IIT-JEE, in the JEE Main bank) questions

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

Mathematics

  1. The straight lines x + y = 0, 3x + y - 4 = 0, x + 3y - 4 = 0 form a triangle which is

    Straight Lines and Pair of Lines · with solution

  2. The function f(x) = (log(1 + ax) - log(1 - bx))/x is not defined at x = 0. The value which should be assigned to f at x = 0, so that it is continuous at x = 0, is

    Limits Continuity and Differentiability · with solution

  3. Which of the following functions is periodic? (a) f(x) = x - [x] where [x] denotes the greatest integer less than or equal to the real number x (b) f(x) = sin(1/x) for x ≠ 0, f(0) = 0 (c) f(x) = xcos x (d) None of the…

    Sets Relations and Functions · with solution

  4. The value of tan [cos^-1 (4/5 ) + tan^-1 (2/3 ) ] is

    Inverse Trigonometric Functions · with solution

  5. The domain of definition of the function y = dfrac1log_10(1-x) + √(x+2) is

    Sets Relations and Functions

  6. AB is a diameter of a circle and C is any point on the circumference of the circle. Then,

    Circles · with solution

  7. The equation of the circle passing through (1, 1) and the points of intersection of x^2 + y^2 + 13x - 3y = 0 and 2x^2 + 2y^2 + 4x - 7y - 25 = 0 is

    Circles

  8. If f(x) = cos(log x), then f(x) · f(y) - 1/2 [f (x/y ) + f(xy) ] has the value

    Sets Relations and Functions

  9. The centre of the circle passing through the point (0, 1) and touching the curve y = x^2 at (2, 4) is

    Circles

  10. Let f(x) = |x - 1|. Then,

    Sets Relations and Functions · with solution

  11. The normal to the curve x = a(cosθ + θsinθ), y = a(sinθ - θcosθ) at any point 'θ' is such that

    Application of Derivatives

  12. The volume of the parallelopiped whose sides are given by OA = 2i - 3j, OB = i + j - k, OC = 3i - k, is

    Vector Algebra · with solution

  13. The points with position vectors 60i + 3j, 40i - 8j, ai - 52j are collinear, if

    Vector Algebra · with solution

  14. The points z_1, z_2, z_3 and z_4 in the complex plane are the vertices of a parallelogram taken in order, if and only if

    Complex Numbers and Quadratic Equations · with solution

  15. If z = x + iy and w = (1 - iz)/(z - i), then |w| = 1 implies that, in the complex plane

    Complex Numbers and Quadratic Equations · with solution

  16. If f(a) = 2, f'(a) = 1, g(a) = -1, g'(a) = 2, then the value of lim_x → a (g(x)f(a) - g(a)f(x))/(x - a) is

    Limits Continuity and Differentiability

  17. If G(x) = -√(25 - x^2), then lim_x → 1 (G(x) - G(1))/(x - 1) has the value

    Limits Continuity and Differentiability · with solution

  18. The coefficient of x^4 in (x/2 - 3/x )^10 is

    Binomial Theorem

  19. If y = a log x + bx^2 + x has its extremum values at x = -1 and x = 2, then

    Application of Derivatives · with solution

  20. The value of the integral int_0^π/2 dfrac√(cot x)√(cot x) + √(tan x) dx is

    Definite Integrals and Areas · with solution

Chemistry

  1. Rutherford's scattering experiment is related to the size of the

    Atomic Structure

  2. The principal quantum number of an atom is related to the

    Atomic Structure

  3. Any p-orbital can accommodate upto

    Atomic Structure

Physics

  1. A river is flowing from West to East at a speed of 5 m/min. A man on the South bank of the river, capable of swimming at 10 m/min in still water, wants to swim across the river in the shortest time. He should swim in a…

    Kinematics · with solution

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