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

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

Q 1) How many integral values of x satisfy the equation x = 2x 1203x ?
OA : 3

Q 2) How many integral values of (x, y) satisfy the equation x^2  y^2 = 627?
OA : 16

Q 3) Find the number of positive integral solutions for a + b + c = 20
OA : 171

Q 4) Find the number of positive integral solutions of x1 + x2 + x3 + x4 = 20, where x1 > x2 ?
OA : 444

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

Q 6) Find the number of nonnegative integer solution to 7x + 3y = 2000 ?
OA : 95

Q 7) How many integral values of x will satisfy x3 + 2x+4 + x < = 11
OA : 6

Q 8 ) Number of solutions for the inequality a + b + c ≤ 10 where, a, b and c are nonnegative 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  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