Most Important Selected Qs for JEE AdvancedMathematicsPermutation and Combination
If x y z=2^3 3^1 5^2 7^1 , then identify which of the following statement(s) is(are) correct?
Options
- AIf x, y, z N , then number of ordered triplets (x, y, z) is 540 .
- BIf x, y, z I , then number of ordered triplets (x, y, z) is 1620 .
- CIf P=x y z , then number of divisors of P which are divisible by 12 is 12 .
- DIf P=x y z , then product of divisors of P which are divisible by 12 is (12 P)^6 .
Correct answer
D. If P=x y z , then product of divisors of P which are divisible by 12 is (12 P)^6 .
Step-by-step solution
(1) ^5 C₂ ^3 C₂ ^4 C₂ ^3 C₂=540 (2) ^5 C₂ ^3 C₂ ^4 C₂ ^3 C₂ 4=2160 (3) P=2^3 3^1 5^2 7^1 Number of divisors of P which are divisible by 12=2 3 2=12 (4) P 12 =2^1 5^2 7^1 Product of divisors of P which are divisible by 12=(12)¹² ( P 12 )^6=(12 P)^6 .