Question Bank  Number of Integral/Positive/NonNegative 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 + 3x  10 < 100OA: 100, 40

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