Assertion (A): Number 1848 is divisible by 22.
Reason (R): (8 + 8) - (4 + 1) is divisible by 11.
A is true, R is false.
A is false, R is true.
Both A and R are true.
Both A and R are false.
Answer
A number is divisible by 22 if it is divisible by both 2 and 11.
1848 has 8 (an even number) at its unit place, so it is divisible by 2.
For 1848, the sum of digits in odd places = 8 + 8 = 16 and the sum of digits in even places = 4 + 1 = 5.
The difference = (8 + 8) - (4 + 1) = 16 - 5 = 11, which is divisible by 11.
So, 1848 is divisible by 11, and hence by 22.
So, assertion (A) is true.
Also, (8 + 8) - (4 + 1) = 11, which is divisible by 11.
So, reason (R) is true.
Hence, option 3 is the correct option.
Assertion (A): 10 and 11 are co-prime numbers.
Reason (R): Two numbers are co-prime if their greatest common divisor is 1.
A is true, R is false.
A is false, R is true.
Both A and R are true.
Both A and R are false.
Answer
10 = 2 × 5 and 11 = 11.
Since 10 and 11 have no common factor other than 1, their greatest common divisor (H.C.F.) is 1.
So, 10 and 11 are co-prime numbers.
So, assertion (A) is true.
Two numbers are co-prime if their greatest common divisor is 1.
So, reason (R) is true.
Hence, option 3 is the correct option.