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

Index of (r+1)th Term from End When Counted from Beginning

If the expans...

Question

If the expansion of $(1 + x)^{m} (1 - x)^{n}$ , the coefficients of x and $x^{2}$ are 3 and -6 respectively. then m is

6

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

9

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

12

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

24

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

Open in App

Solution

The correct option is D $12$
$(1 +^{m} C_{1} x +^{m} C_{2} x^{2} + . . .) (1 -^{n} C_{1} x +^{n} C_{2} x^{2} - . . . .)$

$^{m} C_{1} -^{n} C_{1} = 3 \Rightarrow m - n = 3$

$^{m} C_{2} +^{n} C_{2} -^{m} C_{1}^{n} C_{1} = - 6$ $m (m - 1) + n (n - 1) - 2 m n = - 12$

$(m - n)^{2} - (m + n) = - 12$

$9 - (2 m - 3) = - 12$ $∴ m = 12$

Suggest Corrections

Similar questions

(1 + x)^{m} (1 - x)^{n}

x^{2}

In the expansion of $(1 + x)^{m} (1 - x)^{n}$ , the coefficients of x and $x^{2}$ are respectively 3 and -6. Then m equals :

(1 + x)^{m} \cdot (1 - x)^{n}

x

x^{2}

3

- 6

{(1 + x)}^{m} {(1 - x)}^{n}

x

x^{2}

3

- 6

m

(1 + x)

^{m}

(1 - x)

^{n}

x

x^{2}

3

- 6

Join BYJU'S Learning Program