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 x2 + x5  72x = 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 ?