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Test: Number System- Assertion & Reason Type Questions


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10 Questions MCQ Test Mathematics (Maths) Class 9 | Test: Number System- Assertion & Reason Type Questions

Test: Number System- Assertion & Reason Type Questions for Class 9 2022 is part of Mathematics (Maths) Class 9 preparation. The Test: Number System- Assertion & Reason Type Questions questions and answers have been prepared according to the Class 9 exam syllabus.The Test: Number System- Assertion & Reason Type Questions MCQs are made for Class 9 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Number System- Assertion & Reason Type Questions below.
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Test: Number System- Assertion & Reason Type Questions - Question 1

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion : 5 is a rational number.

Reason : The square roots of all positive integers are irrationals.

Detailed Solution for Test: Number System- Assertion & Reason Type Questions - Question 1 Here reason is not true.

√4 = ±2, which is not an irrational number.

Correct option is (c) Assertion (A) is true but reason (R) is false.

Test: Number System- Assertion & Reason Type Questions - Question 2

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion : Sum of two irrational numbers 2 + √3 is an irrational number.

Reason : Sum of a rational number and an irrational numbers is always an irrational number.

Detailed Solution for Test: Number System- Assertion & Reason Type Questions - Question 2 We know that the sum of a rational number and an irrational numbers is always an irrational number. So, Reason is correct.

Now, 2 + √3 is an irrational numbers So, Assertion is also correct.

Correct option is (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

Test: Number System- Assertion & Reason Type Questions - Question 3

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion : 78 ፥ 74 = 74

Reason : If a > 0 be a real number and p and q be rational numbers. Then ap x aq = ap + q.

Detailed Solution for Test: Number System- Assertion & Reason Type Questions - Question 3 We know that If a > 0 be a real number and p and q be rational numbers then ap x aq = ap+q.

So, Reason is correct.

Now, 78 ፥ 74 = 78 – 4 = 74 (∵ ap ፥ aq = ap – q) So, Assertion is also correct.

But reason (R) is not the correct explanation of assertion (A)

Correct option is (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

Test: Number System- Assertion & Reason Type Questions - Question 4

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion : √5 is an irrational number.

Reason : A number is called irrational, if it cannot be written in the form p/q, where p and q are integers and q ≠ 0.

Detailed Solution for Test: Number System- Assertion & Reason Type Questions - Question 4 We know that “A number is called irrational, if it cannot be written in the form p/q, where p and q are integers and q ≠ 0.” So, Reason is correct.

Since, √5 cannot be written in the form of p/q, therefore it is an irrational number. Hence assertion is correct follows from reason.

Correct option is (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

Test: Number System- Assertion & Reason Type Questions - Question 5

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion : The rationalizing factor of 3 + 2√5 is 3 – 2√5.

Reason : If the product of two irrational numbers is rational then each one is called the rationalising factor of the other.

Detailed Solution for Test: Number System- Assertion & Reason Type Questions - Question 5 We know that If the product of two irrational numbers is rational then each one is called the rationalising factor of the other. So, Reason is correct.

Now, (3 + 2√5) x (3 – 2√5) = 32 – (2√5)2

= 9 – 20 = – 11

So, both Assertion and Reason are correct and Reason explains Assertion.

Correct option is (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

Test: Number System- Assertion & Reason Type Questions - Question 6

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion : Rational number lying between two rational numbers x and y is

½ (x + y).

Reason : There is one rational number lying between any two rational numbers.

Detailed Solution for Test: Number System- Assertion & Reason Type Questions - Question 6 We know that there are infinitely many rational numbers between any two given rational numbers.

So, Reason is not correct.

One of the rational number lying between two rational numbers x and y is ½ (x + y).

So, Assertion is correct

Correct option is (c) Assertion (A) is true but reason (R) is false.

Test: Number System- Assertion & Reason Type Questions - Question 7

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion : Sum of two irrational numbers 2 + √3 and 4 + √3 is irrational number.

Reason : Sum of two irrational numbers is always an irrational number.

Detailed Solution for Test: Number System- Assertion & Reason Type Questions - Question 7 Here, 2 + √3 + 4 + √3 = 6 + 2√3 which is an irrational number.

So, Assertion is correct.

Now, 2 + √3 and 4 – √3 are two irrational numbers Sum = 2 + √3 + 4 – √3 = 6 which is a rational number.

So, Reason is not correct.

Correct option is (c) Assertion (A) is true but reason (R) is false.

Test: Number System- Assertion & Reason Type Questions - Question 8

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion : 113 x 114 = 1112

Reason : If a > 0 be a real number and p and q be rational numbers.

Then ap x aq = ap + q.

Detailed Solution for Test: Number System- Assertion & Reason Type Questions - Question 8 We know that If a > 0 be a real number and p and q be rational numbers then ap x aq = ap+q.

So, Reason is true.

Now, 113 x 114 = 113+4 = 117

Here assertion is incorrect but reason is correct.

Correct option is (d) Assertion (A) is false but reason (R) is true.

Test: Number System- Assertion & Reason Type Questions - Question 9

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Q. Assertion : Rational number lying between

Reason : Rational number lying between two rational numbers x and y is ½(x y).

Detailed Solution for Test: Number System- Assertion & Reason Type Questions - Question 9 We know that Rational number lying between two rational numbers x and y is ½ (x + y).

So, Reason is not correct.

Now,

So, Assertion is correct

Correct option is (c) Assertion (A) is true but reason (R) is false.

Test: Number System- Assertion & Reason Type Questions - Question 10

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion : 0.329 is a terminating decimal.

Reason : A decimal in which a digit or a set of digits is repeated periodically, is called a repeating, or a recurring, decimal.

Detailed Solution for Test: Number System- Assertion & Reason Type Questions - Question 10 We know that a decimal in which a digit or a set of digits is repeated periodically, is called a repeating, or a recurring, decimal.

So, Reason is correct.

Also, we know that a decimal that ends after a finite number of digits is called a terminating decimal.

Hence Assertion is correct but reason is not the correct explanation of Assertion Correct option is (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

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