Test: Number System- Assertion & Reason Type Questions - Class 8 MCQ

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

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

The correct answer is:

1. Assertion (A) is true but reason (R) is false.

Explanation:

• Assertion (A): "Sum of two irrational numbers is an irrational number." This is not always true. For example, 2\sqrt{2}2​ and −2-\sqrt{2}−2​ are both irrational numbers, but their sum is 000, which is a rational number. Thus, the assertion is false.

• Reason (R): "Sum of a rational number and an irrational number is always an irrational number." This is true because adding any non-zero rational number to an irrational number will not cancel out the irrational part, so the result is irrational.

So, the assertion is false, but the reason is true.

So, Reason is correct.

Now, 7⁸ ፥ 7⁴ = 7^{8 – 4} = 7⁴ (∵ a^p ፥ a^q = a^{p – 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).

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).

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).

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.

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.

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.

So, Reason is not correct.

Now,

So, Assertion is correct

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

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).