Question Bank - Equations - Set 1


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    Number of Questions : 30
    Topic : Equations (Finding number of Integral solutions)
    Answer key available ? : Yes
    Source : CAT preparation forums.


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    Q 1) How many integral values of x satisfy the equation x = |2x -|120-3x|| ?

    OA : 3


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    Q 2) How many integral values of (x, y) satisfy the equation x^2 - y^2 = 627?

    OA : 16


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    Q 3) Find the number of positive integral solutions for a + b + c = 20

    OA : 171


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    Q 4) Find the number of positive integral solutions of x1 + x2 + x3 + x4 = 20, where x1 > x2 ?

    OA : 444


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    Q 5) Find the number of positive integral solution for a, b, c and d such that their sum is not more than 15

    OA : 1365


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    Q 6) Find out no of Integral solutions for 7|x|+3|y| < = 28

    OA : 8


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    Q 7) How many integral values of x will satisfy |x-3| + |2x+4| +|x| < = 11

    OA : 6


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    Q 8 ) Number of integral solutions of x^2 - y^2 = 287

    OA : 8


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    Q 9) Total number of integral solution of a^3 + b^3 + c^3 = 43655

    OA : 0


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    Q 10) Find the total no. of integral solutions of w^4 + x^4 + y^4 + z^4 = 1797

    OA : 0


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    Q 11) What is the number of positive integral solutions for the equation x^2 – xy + y^2 = x + y?

    OA : 3


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    Q 12) How many integral values of x will not satisfy x^2 - 2|x| -8 > = 0

    OA : 7


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    Q 13) Find the number of total integral solutions of x^2 + y^2 = 100.

    OA : 12


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    Q 14) Number of integral solution of x^2 + y^2 =36

    OA : 4


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    Q 15) Number of integral solution of x^2+y^2 < = 36

    OA : 113


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    Q 16) Number of integral solution of x^2+y^2 < 36

    OA : 109


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    Q 17) Number of integral solutions of equation a + b + c + d = 30 where a >= 2, b >= 0, c >= - 5, d >= 8

    OA : 3276


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    Q 18 ) Find number of Positive integral solutions of a * b * c = 120?

    OA : 90


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    Q 19) If E = |x| + |x - 1| + |x - 2| + |x - 3| + |x - 4|, for how many integral values of x is E less than or equal to 54?

    OA : 21


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