π-22/7 is
(A) a rational number
(B) an irrational number
(C) a prime number
(D) an even number
1 Answers
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Decide whether the real numbers are rational or not. If they are rational ,then write its p/q form.What can you say about the prime factors of q?
Solution: (i) 43.123456789 Since this number has a terminating decimal expansion, it is a rational number of the form / and q is of the form 2×5 i.e., the prime factors of q...
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If A = {x: x is a natural number}, B ={x: x is an even natural number} C = {x: x is an odd natural number} and D = {x: x is a prime number}, find
A = {x: x is a natural number} = {1, 2, 3, 4, 5 …} B ={x: x is an even natural number} = {2, 4, 6, 8 …} C = {x:...
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Is product of a rational number and an irrational number, a rational number?
Solution: The product of a rational number and an irrational number can be a rational number or an irrational number. Examples: i. rational number = 0 irrational number = √2 => 0 x √2 = 0, which...
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The product of a non zero rational and an irrational number is (A) always irrational (B) always rational (C) rational or irrational (D) one
The product of a non zero rational and an irrational number is always irrational
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The reciprocal of an irrational number is (A) an integer (B) a rational (C) a natural number (D) an irrational
The reciprocal of an irrational number is an irrational
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The product of two irrational numbers is (A) always a rational (B) always an irrational (C) one (D) always a non-zero number
Correct answer is (D) always a non-zero number
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A rational number in its decimal expansion is 327.7081. What can you say about the prime factors of q, when this number is expressed in the form p/q ?
Solution: 327.7081 = 3277081/10000 = 3277081 / 24 x 54 = p/q Here, q is of the form 2m × 5n, where m and n are natural numbers. The prime factors of p and q will...
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Write: (i) The rational s that does not have a reciprocal. (ii) The rational s that are equal to their reciprocals.
(i) 0 (ii) 1 and -1 (iii) 0
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A rational number in its decimal expansion is 1.7351. What can you say about the prime factors
As 1.7351 is a terminating decimal number, so q must be of the form 2m 5m where m ,n are natural numbers.
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f is defined in [–5, 5] as f(x) = { (x, if x is rational and), (-x, if x is rational).
(b) : f (x) is discontinuous at every x, except x = 0
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