Two numbers are in the ratio 5 : 4. If the difference of their cubes is 61; the numbers are :

1. 5 and 4

2. 25 and 16

3. 10 and 18

4. none of these

Statement 1: Cubes of all odd natural numbers are odd.

Statement 2: Cubes of negative integers are positive or negative integers.

Which of the following options is correct?

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.

Assertion (A) : The smallest number by which 1323 may be multiplied so that the product is a perfect cube of 7.

Reason (R) : A given natural number is a perfect cube if in its prime factorization every prime occurs three times.

1. Both A and R are correct, and R is the correct explanation for A.

2. Both A and R are correct, and R is not the correct explanation for A.

3. A is true, but R is false.

4. A is false, but R is true.