Which of the following are true:(i) (2 + 3)! = 2! + 3!(ii) (2 × 3)! =

1.	Which of the following are true:(i) (2 + 3)! = 2! + 3!(ii) (2 × 3)! = 2! × 3!
Answer» (i) (2 + 3)! = 2! + 3! Now, let us consider LHS: (2 + 3)! (2 + 3)! = 5! Then RHS, 2! + 3! = (2 × 1) + (3 × 2 × 1) = 2 + 6 = 8 LHS ≠ RHS Thus, the given expression is false. (ii) (2 × 3)! = 2! × 3! Let us consider as LHS: (2 × 3)! (2 × 3)! = 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720 Then RHS, 2! × 3! = (2 × 1) × (3 × 2 × 1) = 12 LHS ≠ RHS Hence, the given expression is false.

Which of the following are true:(i) (2 + 3)! = 2! + 3!(ii) (2 × 3)! = 2! × 3!

Answer»

(i) (2 + 3)! = 2! + 3!

Now, let us consider LHS: (2 + 3)!

(2 + 3)! = 5!

Then RHS,

2! + 3! = (2 × 1) + (3 × 2 × 1)

= 2 + 6

= 8

LHS ≠ RHS

Thus, the given expression is false.

(ii) (2 × 3)! = 2! × 3!

Let us consider as LHS: (2 × 3)!

(2 × 3)! = 6!

= 6 × 5 × 4 × 3 × 2 × 1

= 720

Then RHS,

2! × 3! = (2 × 1) × (3 × 2 × 1)

= 12

LHS ≠ RHS

Hence, the given expression is false.