CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If ∣ ∣ ∣(1+x)(1+x)2(1+x)3(1+x)4(1+x)5(1+x)6(1+x)7(1+x)8(1+x)9∣ ∣ ∣ =a0+a1x+a2x2+. , then, a1 is equal to

A
1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is D 0
∣ ∣ ∣(1+x)(1+x)2(1+x)3(1+x)4(1+x)5(1+x)6(1+x)7(1+x)8(1+x)9∣ ∣ ∣=a0+a1x+a2x2+.....
Put x=0
∣ ∣111111111∣ ∣=a0
a0=0
So,∣ ∣ ∣(1+x)(1+x)2(1+x)3(1+x)4(1+x)5(1+x)6(1+x)7(1+x)8(1+x)9∣ ∣ ∣=a1x+a2x2+.....
Differentiating w.r.t. x,
∣ ∣ ∣12(1+x)3(1+x)2(1+x)4(1+x)5(1+x)6(1+x)7(1+x)8(1+x)9∣ ∣ ∣+∣ ∣ ∣(1+x)(1+x)2(1+x)34(1+x)35(1+x)46(1+x)5(1+x)7(1+x)8(1+x)9∣ ∣ ∣+
∣ ∣ ∣(1+x)(1+x)2(1+x)3(1+x)4(1+x)5(1+x)67(1+x)68(1+x)79(1+x)8∣ ∣ ∣=a1+2a2x+....
Put x=0
∣ ∣123111111∣ ∣+∣ ∣111456111∣ ∣+∣ ∣111111789∣ ∣=a1
a1=0

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Operations on Sets
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon