# Question Bank - Number of Integral/Positive/Non-Negative 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 -|120-3x|| ?

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 non-negative integer solution to 7x + 3y = 2000 ?

OA : 95

• Q 7) How many integral values of x will satisfy |x-3| + |2x+4| + |x| < = 11

OA : 6

• 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

1

200

1

33

44

7

45

61