Assertion and Reason for Ch 1 Number Systems Class 9 Math
Important QuestionsA
Directions : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Answer
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
1
Assertion (A): 0.271 is a terminating decimal and we can express this number as 271/1000 which is of the form p/q , where p and q are integers and q ≠ 0.
Reason (R): A terminating or non – terminating decimal expansion can be expressed as rational number.
Reason (R): A terminating or non – terminating decimal expansion can be expressed as rational number.
Answer
(c) Assertion is true but reason is false.2
Assertion (A): Every integer is a rational number.
Reason (R): Every integer ‘m’ can be expressed in the form m/1 .
Reason (R): Every integer ‘m’ can be expressed in the form m/1 .
Answer
(a) Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.3
Assertion (A): Rational number lying between two rational numbers a and b is a + b/2.
Reason (R): There is one rational number lying between any two rational numbers.
Reason (R): There is one rational number lying between any two rational numbers.
Answer
(c) Assertion is true but reason is false.
There are infinitely many rational numbers between any two given rational numbers.
4
Assertion (A): If √2 = 1.414, √3 = 1.732, then √5 = √2 + √3.
Reason (R): Square root of a positive real number always exists.
Reason (R): Square root of a positive real number always exists.
Answer
(d) Assertion is false but reason is true.
√2 + √3 ≠5
√3 + √2 =1.732 + 1.414 = 3.146 ≠ √5 as
√5 = 2.236
5
Assertion (A): 2 + √6 is an irrational number.
Reason (R): Sum of a rational number and an irrational number is always an irrational number.
Reason (R): Sum of a rational number and an irrational number is always an irrational number.
Answer
(a) Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.6
Assertion (A): √2 is an irrational number.
Reason (R): A number is called irrational, if it cannot be written in the form p/q, where p and q are integers and q ≠ 0.
Reason (R): A number is called irrational, if it cannot be written in the form p/q, where p and q are integers and q ≠ 0.
Answer
(a) Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.7
Assertion (A): √2, √3 are examples of irrational numbers.
Reason (R): An irrational number can be expressed in the form p/q.
Reason (R): An irrational number can be expressed in the form p/q.
Answer
(c) Assertion is true but reason is false.
Irrational number cannot be expressed in the form p/q, where p and q are integers, q ≠ 0.
8
Assertion (A): 172 . 172 = 173
Reason (A): If a > 0 be a real number and p and q be rational numbers. Then ap . aq = ap+q .
Reason (A): If a > 0 be a real number and p and q be rational numbers. Then ap . aq = ap+q .
Answer
(d) Assertion is incorrect but Reason is correct.
172.175 = 172+5 = 177
9
Assertion (A): 5 – √2 = 5 – 1.414 = 3.586 is an irrational number.
Reason (R) : The difference of a rational number and an irrational number is an irrational number.
Reason (R) : The difference of a rational number and an irrational number is an irrational number.
Answer
(a) Both assertion and reason are true and reason is the correct explanation of assertion.10
Assertion (A): A rational number between 1/3 and ½ is 5/12 .
Reason (R): Rational number between two numbers a and b is √ab.
Reason (R): Rational number between two numbers a and b is √ab.
Answer
(c) Assertion is correct but Reason is incorrect.
½(1/3+1/2) = 5/12