# Question Bank - Number of Integral/Positive/Non-Negative Solutions - Set 2

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

• Q 1) Total number of Integral solutions of x^2 + 4 * y^2 = 100
a. 6
b. 8
c. 10
d. 12
e. 14

OA : 12

• Q 2) Find number of positive integral values satisfying (x+y)^(y-1)=100

OA: 2

• Q 3) Determine the number of positive integral solutions (x, y) to x^y = y^90

OA: 15

• Q 4) Determine the number of positive integral solutions (x, y) to x^y = y^100

OA: 13

• Q 5) Determine the number of positive integral solutions (x, y) to x^y = y^72

OA: 16

• Q 6) How many pairs of integer (a, b) are possible such that a^2 – b^2 = 288?

OA: 24

• Q 7) Find unordered number of integral solutions of a * b * c = 110

OA: 19

• Q 8 ) Find the number of integral solutions for (x,y) possible for 55x^2 + 2xy + y^2= 2007

OA: 2

• Q 9) Find the integral solutions of

1. |x| + |y| = 7
2. |x| + |y| < 7
3. |x| + |y| ≤ 7
4. |x + 2| + |y| = 7
5. |x + 2| + |y| ≤ 7
6. |x + 2| + |y + 4| = 7
7. |x + 2| + |y + 4| ≤ 7

OA : 28, 85, 113, 28, 113, 28, 113

• Q 10) Find the number of integral solutions of |x| + |y| + |z| = 15

OA: 902

• Q 11) What is the number of positive integral solutions that exist for the equation 7x + 12y + 4z = 30?

OA: 1

• Q 12) What is total number of ordered positive integral solutions for (x,y, z) such that x * y * z = 24?

OA : 30

• Q 13) How many integral solutions does the equation √(x + 1) = y have, where x ∈ [5,100]?

OA : 8

• Q 14) Number of positive integral pairs (x, y) such that x ≤ y, that satisfies the equation √x + √y = √2009

OA: 3

• Q 15) Find the maximum value of x * y if 3x + 5y = 150; where x and y are natural numbers

OA: 375

• Q 16) Find number of integral solutions for

a) |x + 10| + |x - 5| < 100
b) |x - 7| + |x + 15| + 3|x - 10| < 100

OA: 100, 40

• Q 17) Find the number of integral solutions of |x| + 2|y| + 3|z| = 24

OA: 386

• Q 18) Find the number of positive integral pairs (x, y) that satisfy the relation x^2 + y^2 = 2325

OA: 0

• Q 19) Number of integral solutions of xy = 2x – y

OA: 4

62

7

102

58

92

1

3

1