Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
COMEDK2014MathematicsMathematical Induction

7⁹+9⁷ is divisible by

Options

  1. A128
  2. B24
  3. C64
  4. D72

Correct answer

C. 64

Step-by-step solution

Now, 7⁹=(8-1)⁹=-1(1-8)⁹=-1+ 9 1 8- 9 2 8²+ + 9 9 8⁹ and 9⁷=(1+8)⁷=1+ 7 1 8+ 7 2 8²+ 7 3 8³+ .+ 7 7 8⁷ 7⁹+9⁷=8 ( 9 1 + 7 1 )+8² ( 7 2 - 9 2 )+ =8(9+7)+8²(21-36)+ =64 2+64(-15)+ Hence, it is divisible by 64 .

Practice Mathematical Induction on Quantrex Academy →

More from Mathematical Induction

If 2^ n divides 16 ! and 2^ n +1 does not divide 16 !, then n = 2023Using 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 2023 Full Mathematical Induction list All COMEDK PYQs