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2002 (AIEEE / IIT-JEE, in the JEE Main bank) questions

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

Mathematics

  1. Let T > 0 be a fixed real number. Suppose, f is a continuous function such that for all x ∈ R, f(x + T) = f(x). If I = int_0^T f(x) dx, then the value of int_3^3+3T f(2x) dx is

    Definite Integrals and Areas · with solution

  2. If P(B) = 3/4, P(A ∩ B ∩ C) = 1/3 and P(A ∩ B ∩ C) = 1/3, then P(B ∩ C) is equal to

    Probability · with solution

  3. The number of integral values of k for which the equation 7cos x + 5sin x = 2k + 1 has a solution, is

    Trigonometry · with solution

  4. Suppose f(x) = (x+1)^2 for x ≥ -1. If g(x) is the function whose graph is reflection of the graph of f(x) with respect to the line y = x, then g(x) equals

    Sets Relations and Functions

  5. Which of the following pieces of data does not uniquely determine an acute angled triangle ABC (R being the radius of the circumcircle)?

    Trigonometry · with solution

  6. If 0 < α < (π)/2 is a fixed angle. If P = (cosθ, sinθ) and Q = (cos(α - θ), sin(α - θ)), then Q is obtained from P by

    Complex Numbers and Quadratic Equations

  7. The number of arrangements of the letters of the word BANANA in which the two N's do not appear adjacently, is

    Permutations and Combinations · with solution

  8. The area (in sq units) bounded by the curves y = |x| - 1 and y = -|x| + 1 is

    Definite Integrals and Areas · with solution

  9. Let ω = -1/2 + idfrac√(3)2, then value of the determinant beginvmatrix 1 & 1 & 1 \ 1 & -1-ω^2 & ω^2 \ 1 & ω^2 & ω endvmatrix is

    Matrices and Determinants · with solution

  10. If V = 2i + j - k and W = i + 3k. If U is a unit vector, then the maximum value of the scalar triple product [U \ V \ W] is

    Vector Algebra · with solution

  11. The sum displaystylesum_i=0^m binom10ibinom20m-i, where binompq = 0 if p > q, is maximum when m is equal to

    Binomial Theorem · with solution

  12. If the tangent at the point P on the circle x^2 + y^2 + 6x + 6y = 2 meets the straight line 5x - 2y + 6 = 0 at a point Q on the Y-axis, then the length of PQ is

    Circles · with solution

  13. The length of a longest interval in which the function 3sin x - 4sin^3 x is increasing, is

    Application of Derivatives · with solution

  14. Let f(x) = int_1^x √(2 - t^2) dt. Then, the real roots of the equation x^2 - f'(x) = 0 are

    Definite Integrals and Areas · with solution

  15. Let a, b, c be in an AP and a^2, b^2, c^2 be in GP. If a < b < c and a + b + c = 3/2, then the value of a is

    Sequences and Series · with solution

  16. The point(s) on the curve y^3 + 3x^2 = 12y, where the tangent is vertical, is (are)

    Application of Derivatives · with solution

  17. Let function f: R → R be defined by f(x) = 2x + sin x for x ∈ R. Then, f is

    Sets Relations and Functions · with solution

  18. The equation of the common tangent to the curves y^2 = 8x and xy = -1 is

    Conic Sections · with solution

  19. Let f: R → R be such that f(1) = 3 and f'(1) = 6. Then, lim_x → 0 [(f(1+x))/(f(1)) ]^1/x equals

    Limits Continuity and Differentiability

  20. If a and b_1 are two unit vectors such that a + 2b and 5a - 4b, are perpendicular to each other, then the angle between a and b is

    Vector Algebra · with solution

  21. For all complex numbers z_1, z_2 satisfying |z_1| = 12 and |z_2 - 3 - 4i| = 5, the minimum value of |z_1 - z_2| is

    Complex Numbers and Quadratic Equations · with solution

  22. If a_1, a_2, …, a_n are positive real numbers whose product is a fixed number c, then the minimum value of a_1 + a_2 + … + a_n-1 + 2a_n is

    Sequences and Series · with solution

  23. The integer n for which lim_x → 0 ((cos x - 1)(cos x - e^x))/(x^n) is a finite non-zero number, is

    Limits Continuity and Differentiability · with solution

  24. If a > 2b > 0, then positive value of m for which y = mx - b√(1 + m^2) is a common tangent to x^2 + y^2 = b^2 and (x - a)^2 + y^2 = b^2 is

    Conic Sections · with solution

  25. The domain of the derivative of the functions f(x) = begincases tan^-1x, & if |x| ≤ 1 \ 1/2(|x|-1), & if |x| > 1 endcases is

    Limits Continuity and Differentiability

  26. The number of values of k for which the system of equations (k+1)x + 8y = 4k and kx + (k+3)y = 3k - 1 has infinitely many solutions, is/are

    Matrices and Determinants

  27. The integral int_-1/2^1/2 [ [x] + log ((1+x)/(1-x) ) ] dx equals

    Definite Integrals and Areas · with solution

  28. The set of all real numbers x for which x^2 - |x + 2| + x > 0 is

    Complex Numbers and Quadratic Equations · with solution

Chemistry

  1. Rutherford's experiment, which established the nuclear model of the atom, used a beam of

    Atomic Structure

  2. If the nitrogen atom had electronic configuration 1s^7, it would have energy lower than that of the normal ground state configuration 1s^2 2s^2 2p^3, because the electrons would be closer to the nucleus, yet 1s^7 is not…

    Atomic Structure

  3. How many moles of electron weighs 1 kg?

    Atomic Structure · with solution

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