Question

Assertion (A): (7 x 13 x 11) + 11 and (7 X 6 X 5 X 4 x 3 x 2 x 1) + 3 have exactly composite numbers
Reason (R): (3 x 12 x 101) + 4 is not a composite number.​

Answer 1

Step-by-step explanation:

Given 7×11×13+13

=13×(7×11+1)=3×78

This number is multiple of two integers.Hence it has more than two factors.Hence it is a composite number.

similarly in

7×6×5×4×3 ×2×1+5

=5(7×6×4×3 ×2×1+1)=5×1009

This number is multiple of two integers.Hence it has more than two factors.Hence

Answer 2

The assertion and the reason are true and the reason is not the correct explanation for the assertion.

To prove the assertion,

7 x 13 x 11 + 11 = (7 x 13 + 1) x 11

                        = (91 + 1) x 11

                        = 92 x 11  

                        = (2 x 2 x 23) x 11

                        = 2 x 2 x 11 x 23

It is a composite number because 7 x 13 x 11 + 11 may be written as a product of primes.

(7 x 6 x 5 x 4 x 3 x 2 x 1) + 3 = (7 x 6 x 5 x 4 x 2 x 1 + 1) x 3

                                                = (1680 + 1) x 3  

                                                = 1681 x 3

                                                = (41 x 41) x 3

                                                = 3 x 41 x 41

It is a composite number because (7 x 6 x 5 x 4 x 3 x 2 x 1) + 3 may be stated as a product of primes.

As a result, the assertion is correct.

Now,

To prove the reason,

(3 x 12 x 101) + 4 = (3636)+ 4

                             = 3640

Since 3630 cannot be written as the product of primes, it is not a composite number.

Thus, the reason is also correct.

As a result, both the reason and the assertion are valid, and the reason is the proper explanation for the reason.