Most Important Selected Qs for JEE AdvancedMathematicsPermutation and Combination
Let S= 14,15,16, , 22 . If N is the number of subsets of S containing two or more elements such that sum of the least and greatest elements has odd number of divisors, then:
Options
- Athe number of prime factors of N is 3
- Bthe number of divisors of N is 8
- Csum of the digits of N is 8
- Dthe number of divisors of N is 16
Correct answer
C. sum of the digits of N is 8
Step-by-step solution
S= 14,15,16, , 22 Sum of the least and greatest number must be a perfect square i.e., 36 ( number of divisors of their sum is odd.) (i) 14, , 22 2^7=128 (ii) 15, , 21 2^5=032 (iii) 16, , 20 2^3=008 (iv) 17, . ., 19 2^1= 002 170 N=170=2 5 17