Question Bank - Number of Integral/Positive/Non-Negative Solutions - 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 the number of non-negative integer solution to 7x + 3y = 2000 ?
OA : 95
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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 solutions for the inequality a + b + c ≤ 10 where, a, b and c are non-negative integers.
[OA: 286]
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Q 9) How many positive integral solutions are possible for the equations 2x + 2y + z = 1000 & x + 2y + 3z = 1000
OA : 99
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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
