The value of 15 C 0 2 - 15 C 1 2 - 15 C 2 2 - - 15 C 15 2 is

The correct option is C 0 ^15C^2_0 ^15C^2_1+ ^15C^2_2... ^15C^2_7+ ^15C^2_8... ^15C^2_15 Pairing the terms. ( ^15C^2_0 ^15C^2_15)+( ^15C^2_1+ ^15C^2 ...

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

Byju's Answer

Standard XII

Mathematics

Implicit Differentiation

The value of ...

Question

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

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!

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

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

Open in App

Solution

The correct option is C 0
$^{15} C_{0}^{2} -^{15} C_{1}^{2} +^{15} C_{2}^{2} . . . -^{15} C_{7}^{2} +^{15} C_{8}^{2} . . .^{15} C_{15}^{2}$
Pairing the terms.
$(^{15} C_{0}^{2} -^{15} C_{15}^{2}) + (-^{15} C_{1}^{2} +^{15} C_{14}^{2}) + . . . (-^{15} C_{7}^{2} +^{15} C_{8}^{2})$
By using the property of binomial coefficient.
$^{n} C_{r} =^{n} C_{n - r}$
$(^{15} C_{0}^{2} -^{15} C_{0}^{2}) + (-^{15} C_{1}^{2} +^{15} C_{1}^{2}) + . . . (-^{15} C_{7}^{2} +^{15} C_{7}^{2})$
$= 0$

Suggest Corrections

Similar questions

Q. If

{(1 + x)}^{n} = n \sum r = 0 C_{r} x^{r} = C_{0} + C_{1} x + C_{2} x^{2} + . . . + C_{n} x^{n}

, then calculated value of

C_{0}^{2} - C_{1}^{2} + C_{2}^{2} - C_{3}^{2} + . . . (- 1)^{n} C_{n}^{2}

n = 15

is equals

Q. The value of the expression

C_{0}^{2} - C_{1}^{2} + C_{2}^{2} - \dots + (- 1)^{n} C_{n}^{2}

Q. Value of the expression

C_{0}^{2} + C_{1}^{2} + C_{2}^{2} + . . . . . + (n + 1) C_{n}^{2}

Q. The value of expression

C_{0}^{2} - C_{1}^{2} + C_{2}^{2} - . . . . . . {(- 1)}^{n} (n + 1) C_{n}^{2}

{C_{0}}^{2} + {C_{1}}^{2} + {C_{2}}^{2} + {C_{3}}^{2} + . . . . . . . ?

Join BYJU'S Learning Program

The value of 15C02−15C12+15C22−⋅⋅⋅⋅⋅⋅⋅⋅−15C152 is

The correct option is C 015C20−15C21+15C22...−15C27+15C28...15C215Pairing the terms.(15C20−15C215)+(−15C21+15C214)+...(−15C27+15C28)By using the property of binomial coefficient.nCr=nCn−r(15C20−15C20)+(−15C21+15C21)+...(−15C27+15C27)=0

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