Question Bank - Number of Integral/Positive/Non-Negative Solutions - Set 2


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    Q 12) What is total number of ordered positive integral solutions for (x,y, z) such that x * y * z = 24?

    OA : 30


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    Q 13) How many integral solutions does the equation √(x + 1) = y have, where x ∈ [5,100]?

    OA : 8


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    Q 14) Number of positive integral pairs (x, y) such that x ≤ y, that satisfies the equation √x + √y = √2009

    OA: 3


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    Q 15) Find the maximum value of x * y if 3x + 5y = 150; where x and y are natural numbers

    OA: 375


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    Q 16) Find number of integral solutions for

    a) |x + 10| + |x - 5| < 100
    b) |x - 7| + |x + 15| + 3|x - 10| < 100

    OA: 100, 40


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    Q 17) Find the number of integral solutions of |x| + 2|y| + 3|z| = 24

    OA: 386


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    Q 18) Find the number of positive integral pairs (x, y) that satisfy the relation x^2 + y^2 = 2325

    OA: 0


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    Q 19) Number of integral solutions of xy = 2x – y

    OA: 4


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    Q 20) Total no of Positive integral solutions of a + b + c + d < 14

    OA: 715


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    Q 21) How many integral solutions possible for below given equation 3/x - 2/y = 1/12

    OA: 47


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    Q 22) How many integral pairs (x, y) satisfy 2^x - 3^y = 55?

    OA: 1


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    Q 23) Number of integral solutions of 1/x + 1/y = 1/48

    OA: 53


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    Q 24) Find the total number of integral ordered pair solution of x^4 + y^4 = 256

    OA: 4 pairs


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    Q 25) Find the number of positive integral solutions of the equation a(a^2 – b) = (b^3 + 61).

    OA: 1


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    Q 26) Find the number of integral solutions of 1/√x +1/√y = 1/√20

    OA: 1


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    Q 27) How many natural solutions are possible for the equation: 2^n - 7 = x^2

    OA: 10


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    Q 28) Total number of integral solutions of 13x - 3y = 1000 for 100 < x < 200 ?

    OA: 33


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    Q 29) Number of integral solutions for (x + 1) (x - 3) (x + 5) ... (x - 99) < 0

    OA: 75


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    Q 30) Let a and b be the integral solutions 17a + 6b = 13. Find the smallest possible value of a - b

    OA: 17



  • a) Direct formula
    |x| + |y| = n.
    Total solution = 4n.
    Total integral solution = 4 x 7 = 28.

    b) |x| + |y| = 0, 1, 2, 3, 4, 5, 6.
    |x| + |y| = 0 --> Solution :- 1.
    |x| + |y| = 1 --> As per direct formula, total solution = 4 x 1 = 4.
    Similarly find solutions for all the cases from 0 to 6.
    Total solutions = 1 + 4 * (1 + 2 + 3 + 4 + 5 + 6)
    Total solution = 85.

    c) |x| + |y| = 0, 1, 2, 3, 4, 5, 6, 7
    Total solutions = 1 + 4 * (1 + 2 + 3 + 4 + 5 + 6 + 7) = 113.

    d) By direct formula, Total solutions = 4 x 7 = 28

    e) By direct formula, Total solutions = 1 + 4 * (1 + 2 + 3 + 4 + 5 + 6 + 7) = 113.

    f) By direct formula, Total solution = 4 x 7 = 28

    g) By direct formula, Solutions = 1 + 4 * ( 1 + 2 + 3 + 4 + 5 + 6 + 7) = 113


 

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