Modulus — CAT Previous-Year Questions
12 previous-year questions on Modulus from CAT, with full solutions. Practise free — check answers as you go; sign in to save your progress.
Modulus · CAT PYQs
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?
Answer the following question based on the information given below.
Sixteen teams have been invited to participate in the ABC Gold Cup cricket tournament. The tournament is conducted in two stages. In the first stage, the teams are divided into two groups. Each group consists of eight teams, with each team playing every other team in its group exactly once. At the end of the first stage, the top four teams from each group advance to the second stage while the rest are eliminated. The second stage comprises of several rounds. A round involves one match for each team. The winner of a match in a round advances to the next round, while the loser is eliminated. The team that remains undefeated in the second stage is declared the winner and claims the Gold Cup.
The tournament rules are such that each match results in a winner and a loser with no possibility of a tie. In the first stage, a team earns one point for each win and no points for a loss. At the end of the first stage teams in each group are ranked on the basis of total points to determine the qualifiers advancing to the next stage. Ties are resolved by a series of complex tie-breaking rules so that exactly four teams from each group advance to the next stage.
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 ?