Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202316 May 2023Morning ShiftMathematicsMathematical InductionActual

If 2^ n divides 16 ! and 2^ n +1 does not divide 16 !, then n =

Options

  1. A14
  2. B15
  3. C16
  4. D17

Correct answer

B. 15

Step-by-step solution

Since 2^n divides 16 ! and 2^ n+1 does not divide 16 !. n= Number of times 2 occurs in 16 != [ 16 2 ]+ [ 16 2^2 ]+ [ 16 2^3 ]+ [ 16 2^4 ]=8+4+2+1=15

Practice Mathematical Induction on Quantrex Academy →

More from Mathematical Induction

Using mathematical induction, the numbers a_n s are defined by a₀=1, a_ n+1 =3 n^2+n+a_n , (n 0) . Then, a_n is equal to 2023If 49^n+16^n+k is divisible by 64 for n N , then the least negative integral value of k is 20232^ 3 n -7 n-1 is divisible by 2023Using mathematical induction, the numbers a_n are defined by a₀=1, a_ n+1 =3 n^2+n+a_n, (n 0) . Then, a_n is equal to 20232^ 3 n -7 n-1 is divisible by 2023The given following circuit is equivalent to 2023The shaded area in the figure given below is a solution set of a system of inequations. The minimum value of objective function 3 x+5 y , subject to the linear constraints given by 2023Using mathematical induction, the numbers a n 's are defined by a 0 = 1 , a n + 1 = 3 n 2 + n + a n , n ≥ 0 , then a n = 2021 Full Mathematical Induction list All AP EAMCET PYQs