Latest IIT-JEE Aptitude Question SOLUTION: Which of the following is correct ? option (A) a17 = a16 + a15 (B) c17 = c16 + c15 (C) b17 = b16 + c16 (D) a17 = c17 + b16

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(#M40027993) IIT-JEE question 2012 question Keep an EYE

Which of the following is correct ?
option
(A) a17 = a16 + a15
(B) c17 = c16 + c15
(C) b17 = b16 + c16
(D) a17 = c17 + b16

Asked In IIT-JEE MAN (10 years ago)

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chaitanya  (10 years ago)

a17 = a16 + a15

lets us consider the condition that the number which we write are the combination of 1&0

also consider that no two consecutive zeros comes together

consider

no of zeros 0 1 2 3 4 5 6 7 8 9

a15 1 +14c1 + 13c2 + 12c3+11c4+10c5+9c6+8c7 X X

a16 1 +15c1+ .............................+ 8c8 X

a17 1 +16c1+...............................+ 9c8 X




now let us consider the formula nCr+nC(r-1)=(n+1)Cr
=>1+15C1=16C1
therefore
a15+a16=a17

answer 1 satisfies
a17 = a16 + a15

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