Modulus — CAT Previous-Year Questions

If x and y satisfy the equations |x| + x + y = 15 and x + |y| - y = 20, then (x - y) equals

The number of distinct real values of x, satisfying the equation 

max{x, 2} - min{x, 2} = |x + 2| - |x - 2|, is

The number of distinct integer solutions (x, y) of the equation |x + y| + |x - y| = 2, is

The largest real value of a for which the equation |x + a| + |x - 1| = 2 has an infinite number of solutions for x is

Let 0 ≤ a ≤ x ≤ 100 and f(x) = |x - a| + |x - 100| + |x - a - 50|. Then the maximum value of f(x) becomes 100 when a is equal to

The number of integers n that satisfy the inequalities |n - 60| < |n - 100|  < |n - 20| is

For a real number x the condition |3x - 20| + |3x - 40| = 20 necessarily holds if

If 3x + 2|y| + y = 7 and x + |x| + 3y = 1, then x + 2y is

The number of distinct pairs of integers (m, n) satisfying |1 + mn| < |m + n| < 5 is

If |b| ≥ 1 and x = –|a|b, then which one of the following is necessarily true?

If x² + y² = 0.1 and |x – y| = 0.2, then |x| + |y| is equal to

If |r − 6| = 11 and |2q − 12| = 8,what is the minimum possible value of $\frac{q}{r}$?