# Assertion Reason Maths Class 10 Chapter 1 Real Numbers

Questions of Assertion Reason Chapter 1 Real Numbers maths CBSE Class 10 are very simple to understand as this chapter deals with Real Numbers. To solve assertion reason type questions of maths, deeper understanding of concept about Real numbers is required. In order to help the student in solving Assertion Reason type of questions, detailed process is explained.

How to solve Assertion Reason Type Questions?
In Assertion-Reason type of question, two statements are given, first is Assertion and second is called Reason. Student must have to think critically about both the statements in Assertion Reason Questions, since it combines multiple choice questions and true/false type of questions which requires a higher level of understanding.

How many types are there of Assertion Reason Type Questions?
Assertion-Reason type of questions can be asked either with four MCQ options or with five MCQ options. First four options are same in both the cases only one more options is being provided i.e. last one. One extra option increases the difficulty level of the questions.

In assertion reason type of questions, all 4 or 5 options are same for each question, which are as:

(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.
(e) Both Assertion and Reason are false.

Then a question haunts in every student’s mind, which option is correct and when?
This can be understood clearly with the following table:

Assertion (A)Reason (R)MCQ Options (Fixed for all questions)
If TrueTrue(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
If TrueTrue(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
If TrueFalse(c) Assertion (A) is true but reason (R) is false.
If FalseTrue(d) Assertion (A) is false but reason (R) is true.
If FalseFalse(e) Both Assertion and Reason are false.

Now, lets practice some Assertion Reason Questions of Biology : Chapter 10 Biotechnology and its Applications.

For question given below, two statements are given- one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given below:

(a) Both A and R are true and R is correct explanation of the assertion.
(b) Both A and R are true but R is not the correct explanation of the assertion.
(c) A is true but R is false.
(d) A is false but R is true.

Question.1.
Assertion : \frac{13}{3125} is a terminating decimal fraction.
Reason : If q = 2^{n}5^{m} where n, m are non-negative integers, then \frac{p}{q} is a terminating decimal fraction.

Ans.1. (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
Explanation: Since the factors of the denominator 3125 is of the form 2^{0}\times 5^{5}.
\frac{13}{3125} is a terminating decimal. Since, assertion follows from reason.

Question.2.
Assertion : A number N when divided by 15 gives the reminder 2. Then the remainder is same when N is divided by 5.
Reason : \sqrt{3} is an irrational number.

Ans.2. (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
Explanation: Clearly, both A and R are correct but R does not explain A.

Question.3.
Assertion : Denominator of 34.12345. When expressed in the form \frac{p}{q}, q≠0, is of the form 2^{m}\times 5^{n}, where m, n are non-negative integers.
Reason : 34.12345 is a terminating decimal fraction.

Ans.3. (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
Explanation: Reason is clearly true.
Again 34.12345 =\frac{3412345}{100000}=\frac{682469}{20000}=\frac{682469}{2^{5}\times 5^{4}}
Its denominator is of the form 2^{m}\times 5^{n}.
[m=5, n=4 are non-negative integers]
Hence, assertion is true. Since reason gives assertion (a) holds.

Question.4.
Assertion : The H.C.F. of two numbers is 16 and their product is 3072. Then their L.C.M. = 162.
Reason : If a, b are two positive integers, then
HCF \times LCM = a \times b .

Ans.4. (d) Assertion (A) is false but reason (R) is true.
Explanation: Here reason is true [standard result]
Assertion is false.
\frac{3072}{16}=192≠162

Question.5.
Assertion : 6^{n} ends with the digit zero, where n is natural number.
Reason : Any number ends with digit zero, if its prime factor is of the form 2^{m}\times 5^{n}, where m, n are natural numbers.

Ans.5. (d) Assertion (A) is false but reason (R) is true.
Explanation: 6^{n}=(2\times 3)^{n}=2^{n}\times 3^{n}, Its prime factors do not contain 5^{n} i.e., of the form 2^{m}\times 5^{n}, where m, n are natural numbers. Here assertion is incorrect but reason is correct.

Question.6.
Assertion : 2 is a rational number.
Reason : The square roots of all positive integers are irrationals.

Ans.6. (c) Assertion (A) is true but reason (R) is false.
Explanation: Here reason is not true. \sqrt{4} = ± 2, which is not an irrational number.

Question.7.
Assertion : \sqrt{a} is an irrational number, where a is a prime number.
Reason : Square root of any prime number is an irrational number.

Ans.7. (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
Explanation: As we know that square root of every prime number is an irrational number. So, both A and R are correct and R explains A.

Question.8.
Assertion : If L.C.M. {p,q} = 30 and H.C.F. {p,q} = 5, then pq = 150.
Reason : L.C.M. of (a,b) \times H.C.F. of (a,b) = ab.

Ans.8. (a) Assertion (A) is true but reason (R) is false.

Question.9.
Assertion : For any two positive integers a and b,
HCF of (a,b) \times LCM of (a,b) = a \times b
Reason : The HCF of two numbers is 5 and their product is 150. Then their LCM is 40.

Ans.9. (c) Assertion (A) is true but reason (R) is false.
Explanation: We have,
LCM of (a,b) \times HCF of (a,b) = a \times b
LCM \times 5 = 150
LCM = \frac{150}{5} = 30
LCM = 30
i.e., reason is incorrect and assertion is correct.

Question.10.
Assertion : n^{2}-n is divisible by 2 for every positive integer.
Reason : \sqrt{2} is not a rational number.

Ans.10. (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

Question.11.
Assertion : n^{2}+n is divisible by 2 for every positive integer n.
Reason : If x and y are odd positive integers, from x^{2}+y^{2} is divisible by 4.

Ans.11. (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).