Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
COMEDK2012MathematicsMathematical Induction

The last digit of 583 !+7²⁹¹ is

Options

  1. A1
  2. B2
  3. C0
  4. D3

Correct answer

D. 3

Step-by-step solution

We have, 583 ! 0( 10) and 7²=-1( 10) So, (7² )¹⁴⁵ 7¹=(-1)¹⁴⁵ 7¹( 10) 7²⁹¹=-7( 10) 3( 10) So, 583 !+7²⁹¹=3( 10) Hence, last digit is 3 .

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