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Theory Of Equations - Finding Number Of Integral Solutions ( 60 Questions )

Recommended read on this topic :

Number of Integral, Non Negative & Positive Solutions - Vikas Saini

Finding number of solutions for equations involving difference of perfect squares - Hemant Malhotra

Number of ways in which a natural number can be expressed as Sum of two perfect squares - Hemant Malhotra

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 out no of Integral solutions for 7|x|+3|y|<=28

OA : 8

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

OA : 6

Q 8) Number of integral solutions of x^2 - y^2 = 287

OA : 8

Q 9) Total number of integral solution ofa^3 + b^3 + c^3 = 43655

OA : 0

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 integral solutions of equation 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

Q 20) How many pair of integers are possible for x^2 - y^2 = 287?

OA : 8

Q 21) How many pair of positive integers are possible for a^2 = 9555^2 + b^2

OA: 67

Q 22) No of integral solution for (x-3)^3 (x-6)^4 (x-9)^9 < 0 ?

OA : 4

Q 23) How many integral solutions does the equation mn – 2m = 3n +105 have?

OA : 8

Q 24) Find the number of integral solutions of the equation 2x + 3y = 763?

OA : 127

Q 25) How many positive integral solutions are possible for 1/x-1/y= 1/12?

OA : 7

Q 26) How many positive integral solutions does equation a + b + c + d = a × b × c × d has

OA : 12

Q 27) Find the sum of integral roots of the following equation: 12x^4 − 91x^3 + 194x^2 − 91x + 12 = 0

OA : 7

Q 28) If m^3 - n^3 = 9^k + 123. Find the number of non-negative integral triplet(s) (m, n, k) satisfying the given equation.

OA : 1

Q 29) Find the total number of positive integral solution of 1/x + 1/y + 1/z = 1

OA : 10

Q 30) Number of non-negative integral solutions of x^(2/3) + x^(1/3 ) – 42 =< 0

OA : 217

Q 31) Find number of positive integral values satisfying (x^2 + 5x + 6)^(x-1) = 36

OA : 0

Q 32) Find number of positive integral values satisfying (x+y)^(y-1)=100

OA: 2

Q 33) Determine the number of positive integral solutions (x, y) to x^y = y^90

OA: 15

Q 34) Determine the number of positive integral solutions (x, y) to x^y = y^100

OA: 13

Q 35) Determine the number of positive integral solutions (x, y) to x^y = y^72

OA: 16

Q 36) How many pairs of integer (a, b) are possible such that a^2 – b^2 = 288?

OA: 24

Q 37) Find unordered number of integral solutions of a*b*c=110

OA: 19

Q 38) Find the number of integral solutions for (x,y) possible for 55x^2 + 2xy + y^2= 2007

OA: 2

Q 39) Find many integral solutions of |x| + |y| = 7

OA: 28

Q 40) Find many integral solutions of |x| + |y| < 7

OA: 85

Q 41) Find many integral solutions of |x| + |y| <= 7

OA: 113

Q 42) Find many integral solutions of |x+2| + |y| =7

OA: 28

Q 43) Find many integral solutions of |x+2| + |y| <= 7

OA: 113

Q 44) Find many integral solutions of |x+2| + |y+4| = 7

OA: 28

Q 45) Find many integral solutions of |x+2| + |y+4| <= 7

OA: 113

Q 46) Find number of positive integral solutions for x^2+y^2=30000

OA: 0

Q 47) Find number of integral solutions of |x| + 2|y| + 3|z| = 24

OA: 386

Q 48) Find number of integral solution of x^2+y^2=70

OA: 0

Q 49) Number of integral solutions of xy = 2x – y

OA: 4

Q 50) Total no of Positive integral solutions of a + b + c + d < 14

OA: 715

Q 51) How many integral solutions possible for below given equation 3/x - 2/y = 1/12

OA: 16

Q 52) How many integral pairs (x, y) satisfy 2^x - 3^y = 55?

OA: 1

Q 53) Number of integral solutions of 1/x+1/y=1/48

OA: 53

Q 54) Number of positive integral pairs (x, y) such that x ≤ y, that satisfies the equation √x + √y = √2009

OA: 3 pairs

Q 55) Find the number of positive integral solutions of the equation a(a^2 – b) = (b^3 + 61).

OA: 1

Q 56) Find the number of integral solutions of 1/√x +1/√y = 1/√20

OA: 1

Q 57) How many natural solutions are possible for the equation: 2^n - 7 = x^2

OA: 10

Q 58) Total number of integral solutions of 13x- 3y = 1000 for 100< x < 200 ?

OA: 33

Q 59) Number of integral solutions for (x + 1) (x - 3) (x + 5) ... (x - 99) < 0

OA: 75

Q 60) Let a and b be the integral solutions 17a + 6b = 13. Find the smallest possible value of a - b

OA: 17

 

Comments

Sunder Bora's picture

Could anyone post answers for these questions, I was not able to solve some of them even after going through the suggested material.

PS: wonderful set of questions.