CAT Question Bank - Binomial Theorem

[Rowdy Rathore]

Q20) What is the highest power of 4 that divides 5^12 - 1 ?

[Rowdy Rathore]

Q21) A positive real number is increased by 10% and then decreased by 10%. This process is repeated 99 more times. What can be said about the new number obtained?
a. It is less than 30% of the original number.
b. It is between 30% and 45% of the original number.
c. It is between 45% and 55% of the original number.
d. It is greater than 55% of the original number

[Soumya Ranjan Patra]

@rowdy-rathore c is the ans

[Soumya Ranjan Patra]

@rowdy-rathore 1

[badalravi]

@rowdy-rathore put x =1
(1+1-3)^2163 = (-1)^2163 = -1

[badalravi]

@rowdy-rathore x=10

[Rowdy Rathore]

@badalravi
put logx = y and solve.
we will get 2y^2 + 3y = 5
solve the quadratic and the roots are y = 1 and -5/2
logx = 1 or logx = -5/2
x = 10 or 10^(-5/2)
2 values possible.

[Rowdy Rathore]

@Soumya-Ranjan-Patra
nC4 * a^(n - 4) * (-b)^4 = nC5 * a^(n - 5) * (-b)^5
n! / 4! (n - 4)! * a^(n - 4) * b4 - n!/5!(n - 5)! * a^(n - 5) * b^5 = 0
n!/4!(n - 5)! * a^(n - 5) * b4 [a/(n - 4) - b/5] = 0
a/(n - 4) = b/5
a/b = (n - 4)/5
How you got 1 ?

[Kushal Khandelwal]

@rowdy-rathore 108

[zabeer]

General term - nCr * (x^2)^(n-r) (3y)^r

It is given that 2n - 2r + r = 5
2n - r = 5
n = 4 => r = 3

So the term we have here is 4C3 * (x^2)^1 (3y)^3
Coefficient = 4C3 * 3^3 = 4 * 27 = 108