Exams › JEE Advanced › Maths

Which of the following statements is true?

1. The sum of a rational number and an irrational number is always irrational.
2. The product of two rational numbers is always rational.
3. The product of two irrational numbers is always irrational.
4. The sum of two rational numbers is always rational.

Correct answer: The sum of a rational number and an irrational number is always irrational.

Solution

Statement A is true: if p is rational and q is irrational, then p + q is irrational (proof by contradiction). Statement B is also true; Statement C is false (e.g., sqrt(2)*sqrt(2)=2); Statement D is also true. In a single-answer context, A is the most distinctive true statement that JEE tests.

Related JEE Advanced Maths questions

• Given that 4 / (2 + sqrt(3) + sqrt(7)) = sqrt(a) + sqrt(b) - sqrt(c), which of the following sets of values (a, b, c) can be true?
• Let a = 111...1 (n ones), b = 444...4 (n fours), c = 777...7 (n sevens), d = 999...9 (n nines). Find the value of 4d(d + 2) / b.
• In a chemistry class, there are 20 students, while a physics class has 30 students. If 10 students are enrolled in both classes, and the two classes are held at separate times, determine the value of k/8, where k represents the total number of students attending either class.
• Given that A represents the divisors of 15, B contains prime numbers less than 10, and C includes even numbers less than 9, how many elements are there in the intersection of (A ∪ C) and B?
• Identify the periodic function among the following:
• The function f(x) = √|x² - 5| x + 6 + √8 + 2|x| - |x|² is defined as a real number for values of x within which range?

⚔️ Practice JEE Advanced Maths free + battle 1v1 →