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1998 (AIEEE / IIT-JEE, in the JEE Main bank) questions

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

Mathematics

  1. If E and F are events with P(E) ≤ P(F) and P(E ∩ F) > 0, then which one is not correct?

    Probability

  2. If x > 1, y > 1, z > 1 are in GP, then 1/(1 + ln x), 1/(1 + ln y), 1/(1 + ln z) are in

    Sequences and Series · with solution

  3. The number of values of x in the interval [0, 5π] satisfying the equation 3sin^2 x - 7sin x + 2 = 0 is

    Trigonometry · with solution

  4. An n-digit number is a positive number with exactly n digits. Nine hundred distinct n-digit numbers are to be formed using only the three digits 2, 5 and 7. The smallest value of n for which this is possible, is

    Permutations and Combinations

  5. If f(x) = 3x - 5, then f^-1(x)

    Sets Relations and Functions · with solution

  6. If P = (x, y), F_1 = (3, 0), F_2 = (-3, 0) and 16x^2 + 25y^2 = 400, then PF_1 + PF_2 equals

    Conic Sections · with solution

  7. In a collage of 300 students, every student reads 5 newspapers and every newspaper is read by 60 students. The number of newspapers is

    Permutations and Combinations

  8. If a_n = sum_r=0^n frac1^nC_r, then sum_r=0^n fracr^nC_r equals

    Permutations and Combinations

  9. If ω is an imaginary cube root of unity, then (1 + ω - ω^2)^7 is equal to

    Complex Numbers and Quadratic Equations · with solution

  10. The order of the differential equation whose general solution is given by y = (c_1 + c_2)cos(x + c_3) - c_4 e^x+c_5, where c_1, c_2, c_3, c_4, c_5 are arbitrary constants, is

    Differential Equations · with solution

  11. If in a triangle PQR, sin P, sin Q, sin R are in AP, then

    Trigonometry · with solution

  12. For three vectors u, v, w which of the following expressions is not equal to any of the remaining three?

    Vector Algebra

  13. If g\f(x)\ = |sin x| and f\g(x)\ = (sin √(x))^2, then

    Sets Relations and Functions · with solution

  14. If int_0^x f(t) dt = x + int_x^1 t f(t) dt, then the value of f(1) is

    Definite Integrals and Areas · with solution

  15. Which of the following numbers is rational?

    Trigonometry · with solution

  16. The value of sum_k=1^6 (sin(2π k)/7 - icos(2π k)/7 ) is

    Complex Numbers and Quadratic Equations · with solution

  17. The number of common tangents to the circles x^2 + y^2 = 4 and x^2 + y^2 - 6x - 8y = 24 is

    Circles

  18. Let n be an odd integer. If sin nθ = sum_r=0^n b_r sin^r θ, for every value of θ, then

    Trigonometry · with solution

  19. A fair coin is tossed repeatedly. If tail appears on first four tosses, then the probability of head appearing on fifth toss equals

    Probability · with solution

  20. Seven white balls and three black balls are randomly placed in a row. The probability that no two black balls are placed adjacently, equals

    Probability · with solution

  21. If from each of the three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, one ball is drawn at random, then the probability that 2 white and 1 black balls will be drawn, is

    Probability · with solution

  22. The number of values of c such that the straight line y = 4x + c touches the curve (x^2)/4 + y^2 = 1 is

    Conic Sections · with solution

  23. lim_x → 1 dfrac√(1 - cos 2(x-1))x-1

    Limits Continuity and Differentiability

  24. If f(x) = (x^2 - 1)/(x^2 + 1) for every real number x, then the minimum value of f

    Application of Derivatives · with solution

  25. The number of values of x, where the function f(x) = cos x + cos(√(2)x) attains its maximum, is

    Application of Derivatives · with solution

  26. If A_0, A_1, A_2, A_3, A_4 and A_5 be a regular hexagon inscribed in a circle of unit radius. Then, the product of the lengths of the line segments A_0A_1, A_0A_2 and A_0A_4 is

    Complex Numbers and Quadratic Equations · with solution

  27. If the vertices P, Q, R of a triangle PQR are rational points, which of the following points of the triangle PQR is/are always rational point(s)

    Straight Lines and Pair of Lines

  28. If P(1,2), Q(4,6), R(5,7) and S(a,b) are the vertices of a parallelogram PQRS, then

    Straight Lines and Pair of Lines · with solution

  29. The diagonals of a parallelogram PQRS are along the lines x + 3y = 4 and 6x - 2y = 7. Then, PQRS must be a

    Straight Lines and Pair of Lines · with solution

Chemistry

  1. The energy of an electron in the first Bohr orbit of H-atom is -13.6 eV. The possible energy value(s) of the excited state(s) for electrons in Bohr orbits of hydrogen is (are)

    Atomic Structure · with solution

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