If the coefficients of x 3 and x 4 in the expansion of 1 + a x + b x 2 1 - 2 x 18 in powers of x are both…

If the coefficients of x3 and x4 in the expansion of 1+ax+bx21-2x18 in powers of x are both zero, then a,b is equal to
  1. 1 4 ,  2 7 2 3
  2. 1 6 ,  2 7 2 3
  3. 1 6 ,  2 5 1 3
  4. 1 4 ,  2 5 1 3

Solution

We have, 1+ax+bx21-2x18=a0+a1x+a2x2+.......
=1+ax+bx21-18C1·2x+18C2·22x2+.....18C182x18

⇒a3=-18C3×8+18C2×4a-36b

⇒a4=18C4×16-18C3×8a+18C2×4×b

102a-6b=1088  ...i

64a-6b=480  ...ii

Solution of the above two equation gives.

a=16
b = 2 7 2 3

Asked in: JEE Main 2014 (06 Apr)

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