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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.
√4 = ±2, which is not an irrational number.
Correct option is (c) Assertion (A) is true but reason (R) is false.
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.
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).
DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : 7^{8} ፥ 7^{4} = 7^{4}
Reason : If a > 0 be a real number and p and q be rational numbers. Then a^{p} x a^{q} = a^{p + q}.
So, Reason is correct.
Now, 7^{8} ፥ 7^{4} = 7^{8} ^{– 4} = 7^{4} (∵ 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).
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.
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).
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.
Now, (3 + 2√5) x (3 – 2√5) = 3^{2} – (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).
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.
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.
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.
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.
DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : 11^{3} x 11^{4} = 11^{12}
Reason : If a > 0 be a real number and p and q be rational numbers.
Then a^{p} x a^{q} = a^{p} + ^{q}.
So, Reason is true.
Now, 11^{3} x 11^{4} = 11^{3+4} = 11^{7}
Here assertion is incorrect but reason is correct.
Correct option is (d) Assertion (A) is false but reason (R) is true.
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).
So, Reason is not correct.
Now,
So, Assertion is correct
Correct option is (c) Assertion (A) is true but reason (R) is false.
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.
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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