Question Bank  Number of Integral/Positive/NonNegative 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. 14OA : 12

Q 2) Find number of positive integral values satisfying (x+y)^(y1)=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
 x + y = 7
 x + y < 7
 x + y ≤ 7
 x + 2 + y = 7
 x + 2 + y ≤ 7
 x + 2 + y + 4 = 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 + 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