Question Bank  Number of Integral/Positive/NonNegative Solutions  Set 1

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  2x 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 nonnegative 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 (x3)^3 (x6)^4 (x9)^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

Q 28 ) If m^3  n^3 = 9^k + 123. Find the number of nonnegative integral triplet(s) (m, n, k) satisfying the given equation.
OA : 1