If the system of equations ( nC3)x+( nC4)y+35z=0, ( nC4)x+35y+( nC3)z=0 and 35x+( nC3)y+( nC4)z=0 has a non-trivial solution, then the value of n is equal to (∀ n ∈ N , n ≥ 4)

Question

If the system of equations ( nC3)x+( nC4)y+35z=0, ( nC4)x+35y+( nC3)z=0 and 35x+( nC3)y+( nC4)z=0 has a non-trivial solution, then the value of n is equal to (∀ n ∈ N , n ≥ 4) (A) 6 (B) 7 (C) 8 (D) 9

Tardigrade Admin · Accepted Answer

For non trival solution. Δ=0 | beginarrayccc n C3 n C4 35 n C4 35 n C3 35 n C3 n C4 endarray|=0 ⇒ n C3+ n C4+35=0 (not possible) or n C3= n C4=35 ⇒ n=7

Q. If the system of equations $(_^{n} C_{3}) x + (_^{n} C_{4}) y + 35 z = 0, (_^{n} C_{4}) x + 35 y + (_^{n} C_{3}) z = 0$ and $35 x + (_^{n} C_{3}) y + (_^{n} C_{4}) z = 0$ has a non-trivial solution, then the value of $n$ is equal to $(\forall n \in N, n \geq 4)$

$6$

$7$

$8$

$9$

For non trival solution.
$Δ = 0$ $∣ ∣^{n} C_{3}^{n} C_{4} 35^{n} C_{4} 35^{n} C_{3} 35^{n} C_{3}^{n} C_{4} ∣ ∣ = 0$
$\Rightarrow^{n} C_{3} +^{n} C_{4} + 35 = 0$ (not possible)
or $^{n} C_{3} =^{n} C_{4} = 35 \Rightarrow n = 7$

Q. If the system of equations (_nC3​)x+(_nC4​)y+35z=0,(_nC4​)x+35y+(_nC3​)z=0 and 35x+(_nC3​)y+(_nC4​)z=0 has a non-trivial solution, then the value of n is equal to (∀n∈N,n≥4)

6

7

8

9

For non trival solution. Δ=0 ∣∣​nC3​nC4​35​nC4​35nC3​​35nC3​nC4​​∣∣​=0 ⇒nC3​+nC4​+35=0 (not possible) or nC3​=nC4​=35⇒n=7

Q. If the system of equations $(_^{n} C_{3}) x + (_^{n} C_{4}) y + 35 z = 0, (_^{n} C_{4}) x + 35 y + (_^{n} C_{3}) z = 0$ and $35 x + (_^{n} C_{3}) y + (_^{n} C_{4}) z = 0$ has a non-trivial solution, then the value of $n$ is equal to $(\forall n \in N, n \geq 4)$

$6$

$7$

$8$

$9$

For non trival solution.
$Δ = 0$ $∣ ∣^{n} C_{3}^{n} C_{4} 35^{n} C_{4} 35^{n} C_{3} 35^{n} C_{3}^{n} C_{4} ∣ ∣ = 0$
$\Rightarrow^{n} C_{3} +^{n} C_{4} + 35 = 0$ (not possible)
or $^{n} C_{3} =^{n} C_{4} = 35 \Rightarrow n = 7$