Question Bank  Equations

Number of Questions : 30
Topic : Equations
Answer key available ? : Yes
Source :

Q 1) Given the equation (5/2)x  b = (8/5)x + 142, find the smallest positive integer b such that the solution x is a positive integer.

Q 2) Solve for x if (x  a  b)/c + (x  b  c)/a + (x  c  a)/b = 3 and ab + bc + ca ≠ 0.

Q 3) Find the condition for 'a' such that equation ax  2y  3 + 5x + 9 = 0 has the solution (x, y) where x, y have same sign.

Q 4) Find the number of positive integer solutions of the equation 123x + 57y = 531.

Q 5) Find all x which satisfy the equation x^4  12x^3 + 47x^2  60x = 0.

Q 6) Given x  2 < 3, solve the equation x + 1 + x  3 + x  5 = 8.

Q 7) Find real x such that xx  3x  4 = 0

Q 8 ) For how many integers (m, n) whose absolute value is less than 7, the system of equations 3x + my  5 = 0 and x + ny  4 = 0 has no solution?

Q 9) Assume the equation 2x² + x + a = 0 has the solution set A, and the equation 2x² + bx + 2 = 0 has the solution set B, and A ⋂ B = {1/2}, find A ⋃ B.

Q 10) Find real valued solutions (x, y, z) for the equation √(x) + √(y  1) + √(z  2) = (x + y + z)/2.

Q 11) Solve the equation (x + 1)/(x + 4)  (x + 4)/(x + 1) + (x + 1)/(x  2)  (x  2)/(x + 1) = 2/3.

Q 12) If the equation x²  2x  4y = 5 has real valued solutions, find the maximum value of x  2y.

Q 13) Find the sum of all solutions of 3x  1  2x = 2.

Q 14) For what value/s of k, the quadratic equation (k²  1)x²  6(3k  1)x + 72 = 0 with variable x has two distinct positive integer roots.

Q 15) Solve system of equations; logₓ8 + log₂y = 2 and logₓ2 + log₈y² = 1.

Q 16) Given f(x) = x  1/x, solve the equation f(f(x)) = x.

Q 17) Find sum of all real x such that x² + x  2x√(x  2)  6 = 0.

Q 18) How many triplets of prime numbers (x, y, z) satisfy x(x + y) = z + 120?

Q 19) Find pair of positive integers (m, n) such that the quadratic equation 4x²  2mx + n = 0 has two real roots both of which are between 0 and 1.