Home
Class 12
MATHS
If 10^m divides the number 101^(100)-1 t...

If `10^m` divides the number `101^(100)-1` then, find the greatest value of `mdot`

Text Solution

Verified by Experts

The correct Answer is:
m = 4
`(1+100)^(100) = 1+100 xx 100 + (100 xx 99)/(1 xx 2) xx (100^(2)) + (100 xx 99 xx 98)/(1xx2xx3)xx(100^(3))+"…."`
`rArr (101)^(100) - 1`
`= 100 xx 100 [ 1+(100 xx 99)/(1xx2)+(100xx9xx98)/(1xx2xx3)xx100+"….."]`
From above, it is clear that `(101)^(100) - 1` is divisible by
`(100)^(2) = 10000`. So, the greatest value of m is 4.
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise 8.3|7 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise 8.4|13 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise 8.1|17 Videos

  • AREA UNDER CURVES

    CENGAGE|Exercise Question Bank|10 Videos

  • CIRCLE

    CENGAGE|Exercise MATRIX MATCH TYPE|6 Videos

Similar Questions

Explore conceptually related problems

If z is any complex number such that |z+4|lt=3, then find the greatest value of |z+1|dot

If the third term in the expansion of (1+x)^mi s-1/8x^2, then find the value of mdot

The approximate value of 1/(10.1) .

If the tangent at any point (4m^2,8m^3) of x^3-y^2=0 is a normal to the curve x^3-y^2=0 , then find the value of mdot

When the polynomial 5x^3+M x+N is divided by x^2+x+1, the remainder is 0. Then find the value of M+Ndot

If p(m)=m^(2)-3m+1 , then find the value of p(1) and p(-1) .

If he roots of the equation 12 x^2-m x+5=0 are in the ratio 2:3 then find the value of mdot