# Question Bank - Equations - Set 1

• Number of Questions : 30
Topic : Theory of Equations
Answer key available ? : No
Source :

• Q1) How many integer value of x satisfy |x-2| + |x-5| - |7-2x| = 96 ?

• Q2) If x + 1/x = √3 then find x^10! + x^9! + x^8! + x^7!+ x^(5!+2) - x^2! ?

• Q3) If x = √(3+√2 ) then find √x + 1/√x ?

• Q4) Is (x - 1)^2000 - x^2000 + 2x - 1 divisible by 2x^3 - 3x^2 + x ?

• Q5) If a + b + c = 0, find a^2/bc + b^2/ca + c^2/ab ?

• Q6) How many triplets (x,y,z) of integers such that x^3 + y^4 = z^31 ?

• Q7) Find all integers a,b,c for a^2 = bc + 4 & b^2 = ca + 4

• Q8) Find all integers triplet for (a+1/b) (b+1/c) (c+1/a) = 2

• Q9) Find Maximum point (x,y) of curve x = e^x * y ?

• Q10) if a and b are roots of x^2 - x + 1 = 0 then find a^5 + b^5 ?

• Q11) Find non negative integer solutions for 7x + 2y + z = 56 ?

• Q12) Find Non negative integer solutions for x + 3y + z = 21 ?

• Q13) Find non negative integer solutions for 2x + 5y + z = 20 ?

• Q14) Find non negative integer solution of x + 2y + 3z = 100 ?

• Q15) Find all ordered pairs of real numbers (x,y) which satisfy 17 x^2 +2y^2 -10xy -6x = -2 ?

• Q16) If x^2 * y^3 = 8 , where x, y > 0. What is the minimum value of 4x + 3y ?

• Q17) If a^2 + ab + b^2 = 1. How many ordered pairs (a,b) satisfy, where a,b are integers ?

• Q18) If a^6 + b^6 is a prime number .If a and b are distinct integers ,then what is their sum ?

• Q19) If x + y = 1, then what is the value of x^3 + y^3 + 3xy ?

34

136

71

200

63

145