MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Greatest Binomial Coefficients

If 1+2x+3x2...

Question

If ${(1 + 2 x + 3 x^{2})}^{10} = a_{0} + a_{1} x + a_{2} x^{2} + . . . . . + a_{20} x^{20}$ , then $a_{1}$ equals

A

6

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

8

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

210

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

None of these

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is C None of these
Given
$(1 + 2 x + 3 x^{2})^{10} = a_{0} + a_{1} x + a_{2} x^{2} + - - - + a_{20} x_{20}$
Differentiating Both the sides w.r.t 'x'
$\Rightarrow 10 (1 + 2 x + 3 x^{2})^{9} (2 + 6 x) = a_{1} + 2 a_{2} x + - - - + a^{20} .20 x^{19}$
put x = 0
$\Rightarrow 10 \times 1 \times 2 = a_{1}$
$∴ a_{1} = 20$

Suggest Corrections

thumbs-up

0

Similar questions

{(1 + 2 x + 3 x^{2})}^{10} = a_{0} + a_{1} x + a_{2} x^{2} + . . . . + a_{20} x^{20}

(1 + 2 x + 3 x^{2})^{10} = a_{0} + a_{1} x + a_{2} x^{2} + . . . + a_{20} x^{20},

a_{1}

(1 + 2 x + 3 x^{2})^{10} = a_{0} + a_{1} x + a_{2} x^{2} + . . . + a_{20} x^{20}

a_{1}

i f (1 + x)^{10} = a_{0} + a_{1} x + . . . . a_{10} x^{10}, t h e n (a_{0} - a_{2} + a_{4} - a_{6} + a_{8} - a_{10})^{2} + (a_{1} - a_{3} + a_{5} - a_{7} + a_{9})^{2}

{(1 + x + 2 x^{2})}^{20} = a_{0} + a_{1} x + a_{2} x^{2} + . . . . . + a_{10} x^{40}

a_{1} + a_{3} + a_{5} + . . . . . . + a_{39}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Visualising the Terms

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Greatest Binomial Coefficients

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon