# 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 x|x| - 3|x| - 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.

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