Latest TCS Aptitude Question SOLUTION: What is summation(k=0 to 28) k^2(28Ck) where 28Ck is the number of ways of choosing k items from 28 items? a) 406 * 2^27 b) 306 * 2^26 c) 28 * 2^27 d) 56 * 2^27 from practice que

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(#M40040126) TCS Category question Keep an EYE

What is summation(k=0 to 28) k^2(28Ck) where 28Ck is the number of ways of choosing k items from 28 items?
a) 406 * 2^27
b) 306 * 2^26
c) 28 * 2^27
d) 56 * 2^27
from practice ques. at seesame

Asked In TCS aastha huria (9 years ago)

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mohit  (9 years ago)

n(n+1)*2^n-2...option a..

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Kethineni Vinodh  (9 years ago)

Consider (1+x)n=C0+C1x+C2x2+.....+Cnxn .......(1)
Differentiating w.r.t x we get
n(1+x)n−1=C1+2C2x+3C3x2+.....+nCnxn−1
Multiplying by x on both sides,
x.n(1+x)n−1=x.C1+2C2x2+3C3x3+.....
Now again differentiating w.r.t to x
n(1+x)n−1+n(n−1)x(1+x)n−2=C0+22C1x+32C2x2+42C3x3.....
Putting x = 1, we get
n(n+1)2n−2=C1+22C2+32C3+42C4
Now substituting n = 28
28(28+1)228−2 = 812.226 = 406*2^27

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