The value of 15C02- 15C12- 15C22- 15C152 is

Let f(n)=C_0^2 C_1^2+C_2^2 C_3^2+⋯+( 1)^n C_n^2 We know that f(n)= 0 , amp; if n is odd ( 1)^n/2 C_n/2 , amp; if n is even Since, here n is odd (n=15) ∴ ^ ...

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

Byju's Answer

Standard XII

Mathematics

Sum of Binomial Coefficients with Alternate Signs

The value of ...

Question

The value of $^{15} C_{0}^{2} -^{15} C_{1}^{2} +^{15} C_{2}^{2} - \dots -^{15} C_{15}^{2}$ is

15

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

- 15

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

0

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

51

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

Open in App

Solution

The correct option is C $0$
Let $f (n) = C_{0}^{2} - C_{1}^{2} + C_{2}^{2} - C_{3}^{2} + \dots + (- 1)^{n} C_{n}^{2}$
We know that
$f (n) = {\begin{matrix} 0, & if n is odd (- 1)^{n / 2} C_{n / 2}, & if n is even \end{matrix}$

Since, here $n$ is odd $(n = 15)$
$∴^{15} C_{0}^{2} -^{15} C_{1}^{2} +^{15} C_{2}^{2} - \dots -^{15} C_{15}^{2} = 0$

Suggest Corrections

Similar questions

Q. The value of

^{15} C_{0}^{2} -^{15} C_{1}^{2} +^{15} C_{2}^{2} - \dots -^{15} C_{15}^{2}

The value of $\sqrt{2 \sqrt{2} \sqrt{2 \dots \dots \dots \infty}}$ is 2.

Q. The value of

cos 1^{\circ} \cdot cos 2^{\circ} \cdot cos 3^{\circ} \dots cos 180^{\circ}

Q. The value of the determinant of

n^{t h}

order, given by

∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} x & 1 & 1 & \dots 1 & x & 1 & \dots 1 & 1 & x & \dots \cdot & \cdot & \cdot & \dots \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣

Q. The value of

1 \cdot 1! + 2 \cdot 2! + 3 \cdot 3! + . . . + n \cdot n!

Join BYJU'S Learning Program

Explore more

Sum of Binomial Coefficients with Alternate Signs

Standard XII Mathematics

Join BYJU'S Learning Program

The value of 15C20− 15C21+ 15C22−⋯− 15C215 is

The correct option is C 0 Let f(n)=C20−C21+C22−C23+⋯+(−1)n C2n We know that f(n)={0 ,if n is odd(−1)n/2 Cn/2 ,if n is even Since, here n is odd (n=15) ∴ 15C20− 15C21+ 15C22−⋯− 15C215=0

The value of $^{15} C_{0}^{2} -^{15} C_{1}^{2} +^{15} C_{2}^{2} - \dots -^{15} C_{15}^{2}$ is