Question Bank - Number of Integral/Positive/Non-Negative Solutions - Set 1
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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 non-negative integral solutions of 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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Q 20) How many pair of integers are possible for x^2 - y^2 = 287?
OA : 8
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Q 21) How many pair of positive integers are possible for a^2 = 9555^2 + b^2
OA: 67
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Q 22) No of integral solution for (x-3)^3 (x-6)^4 (x-9)^9 < 0 ?
OA : 4
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Q 23) How many integral solutions does the equation mn – 2m = 3n + 105 have?
OA : 8
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Q 24) Find the number of positive integral solutions of the equation 2x + 3y = 763?
OA : 127
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Q 25) How many positive integral solutions are possible for 1/x - 1/y = 1/12?
OA : 7
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Q 26) How many positive integral solutions does equation a + b + c + d = a × b × c × d has
OA : 12
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Q 27) Find the sum of integral roots of the following equation: 12x^4 − 91x^3 + 194x^2 − 91x + 12 = 0
OA : 7
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Q 28 ) If m^3 - n^3 = 9^k + 123. Find the number of non-negative integral triplet(s) (m, n, k) satisfying the given equation.
OA : 1
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Q 29) Find the total number of positive integral solution of 1/x + 1/y + 1/z = 1
OA : 10
