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

• 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

• Q 20) Total no of Positive integral solutions of a + b + c + d < 14

OA: 715

• Q 21) How many integral solutions possible for below given equation 3/x - 2/y = 1/12

OA: 47

• Q 22) How many integral pairs (x, y) satisfy 2^x - 3^y = 55?

OA: 1

• Q 23) Number of integral solutions of 1/x + 1/y = 1/48

OA: 53

• Q 24) Find the total number of integral ordered pair solution of x^4 + y^4 = 256

OA: 4 pairs

• Q 25) Find the number of positive integral solutions of the equation a(a^2 – b) = (b^3 + 61).

OA: 1

• Q 26) Find the number of integral solutions of 1/√x +1/√y = 1/√20

OA: 1

• Q 27) How many natural solutions are possible for the equation: 2^n - 7 = x^2

OA: 10

• Q 28) Total number of integral solutions of 13x - 3y = 1000 for 100 < x < 200 ?

OA: 33

• Q 29) Number of integral solutions for (x + 1) (x - 3) (x + 5) ... (x - 99) < 0

OA: 75

• Q 30) Let a and b be the integral solutions 17a + 6b = 13. Find the smallest possible value of a - b

OA: 17

• a) Direct formula
|x| + |y| = n.
Total solution = 4n.
Total integral solution = 4 x 7 = 28.

b) |x| + |y| = 0, 1, 2, 3, 4, 5, 6.
|x| + |y| = 0 --> Solution :- 1.
|x| + |y| = 1 --> As per direct formula, total solution = 4 x 1 = 4.
Similarly find solutions for all the cases from 0 to 6.
Total solutions = 1 + 4 * (1 + 2 + 3 + 4 + 5 + 6)
Total solution = 85.

c) |x| + |y| = 0, 1, 2, 3, 4, 5, 6, 7
Total solutions = 1 + 4 * (1 + 2 + 3 + 4 + 5 + 6 + 7) = 113.

d) By direct formula, Total solutions = 4 x 7 = 28

e) By direct formula, Total solutions = 1 + 4 * (1 + 2 + 3 + 4 + 5 + 6 + 7) = 113.

f) By direct formula, Total solution = 4 x 7 = 28

g) By direct formula, Solutions = 1 + 4 * ( 1 + 2 + 3 + 4 + 5 + 6 + 7) = 113

58

62

102

92

33

61

60

61