# Question Bank - Number of Integral/Positive/Non-Negative Solutions - Set 1

• Q 8 ) Number of solutions for the inequality a + b + c ≤ 10 where, a, b and c are non-negative integers.

[OA: 286]

• Q 9) How many positive integral solutions are possible for the equations 2x + 2y + z = 1000 & x + 2y + 3z = 1000

OA : 99

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

OA : 0

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

OA : 3

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

OA : 7

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

OA : 12

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

OA : 4

• Q 15) Number of integral solution of x^2 + y^2 ≤ 36

OA : 113

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

OA : 109

• 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

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

OA : 90

• 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

• Q 20) How many pair of integers are possible for x^2 - y^2 = 287?

OA : 8

• Q 21) How many pair of positive integers are possible for a^2 = 9555^2 + b^2

OA: 67

• Q 22) No of integral solution for (x-3)^3 (x-6)^4 (x-9)^9 < 0 ?

OA : 4

• Q 23) How many integral solutions does the equation mn – 2m = 3n + 105 have?

OA : 8

• Q 24) Find the number of positive integral solutions of the equation 2x + 3y = 763?

OA : 127

• Q 25) How many positive integral solutions are possible for 1/x - 1/y = 1/12?

OA : 7

• Q 26) How many positive integral solutions does equation a + b + c + d = a × b × c × d has

OA : 12

• Q 27) Find the sum of integral roots of the following equation: 12x^4 − 91x^3 + 194x^2 − 91x + 12 = 0

OA : 7

65

45

127

61

48

63

89