If the number of terms in a-bn2-3 and c-d3 n-4 are same- where a- b- c- -0- n - N- then the number of possible values of n isA- 0B- 1C- 2D- More than 2 but finite-

The correct option is A 0Given expansions are nbsp;(a+b)^n^2+3 and (c+d)^3n+4 As the number of terms are same, so n^2+3+1 = 3n+4+1 ⇒ n^2 3n 1 = 0 ⇒ n = 3±√(9 ...

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

Byju's Answer

Standard XII

Mathematics

Pascal Triangle

If the number...

Question

If the number of terms in $(a + b)^{n^{2} + 3}$ and $(c + d)^{3 n + 4}$ are same, where $a, b, c, d \neq 0, n \in N$ , then the number of possible value(s) of $n$ is

0

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

1

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

2

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

More than

2

but finite.

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

Open in App

Solution

The correct option is A $0$
Given expansions are $(a + b)^{n^{2} + 3}$ and $(c + d)^{3 n + 4}$
As the number of terms are same, so
$n^{2} + 3 + 1 = 3 n + 4 + 1 \Rightarrow n^{2} - 3 n - 1 = 0 \Rightarrow n = \frac{3 \pm \sqrt{9 + 4}}{2}$
As $n \in N$ , so there is no possible value of $n$ .

Suggest Corrections

Similar questions

Q. If the number of terms in

(a + b)^{n^{2} + 3}

and

(c + d)^{3 n + 4}

are same, where

a, b, c, d \neq 0, n \in N

, then the number of possible value(s) of

n

Q. If

^{n} C_{2} +^{n} C_{3} =^{n + 1} C_{r}

, then the minimum possible value of

r

Mark the correct option:

The number of pairs positive integers (m, n) such that mⁿ = 25 is

A. 0

B. 1

C. 2

D. more than 2

Q. The number of real values of

x,

satisfying

3^{2 {log}_{3} x} - 2 x - 3 = 0

Q. If the number of terms in the expansion of

(a + b)^{n^{2} + 3}

7

, then the number of value(s) of

n, (n \in N)

Join BYJU'S Learning Program

If the number of terms in (a+b)n2+3 and (c+d)3n+4 are same, where a,b,c,d≠0,n∈N, then the number of possible value(s) of n is

The correct option is A 0Given expansions are (a+b)n2+3 and (c+d)3n+4 As the number of terms are same, so n2+3+1=3n+4+1⇒n2−3n−1=0⇒n=3±√9+42 As n∈N, so there is no possible value of n.

If the number of terms in $(a + b)^{n^{2} + 3}$ and $(c + d)^{3 n + 4}$ are same, where $a, b, c, d \neq 0, n \in N$ , then the number of possible value(s) of $n$ is

The correct option is A $0$
Given expansions are $(a + b)^{n^{2} + 3}$ and $(c + d)^{3 n + 4}$
As the number of terms are same, so
$n^{2} + 3 + 1 = 3 n + 4 + 1 \Rightarrow n^{2} - 3 n - 1 = 0 \Rightarrow n = \frac{3 \pm \sqrt{9 + 4}}{2}$
As $n \in N$ , so there is no possible value of $n$ .