Home
Class 12
MATHS
Show that |^x Cr^x C(r+1)^x C(r+2)^y Cr^...

Show that `|^x C_r^x C_(r+1)^x C_(r+2)^y C_r^y C_(r+1)^y C_(r+2)^z C_r^z C_(r+1)^z C_(r+1)|=|^x C_r^(x+1)C_(r+1)^(x+2)C_(r+2)^y C_r^(y+1)C_(r+1)^(y+2)C_(r+2)^z C_r^(z+1)C_(r+1)^(z+2)C_(r+1)|` .

A

`0`

B

`2^(n)`

C

`"^(x+y+z)C_(r )`

D

`"^(x+y+z)C_(r +2)`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` `|{:(.^(x)C_(r),.^(x)C_(r+1),.^(x)C_(r+2)),(.^(y)C_(r ),.^(y)C_(r+1),.^(y)C_(r+2)),(.^(z)C_(r ),.^(z)C_(r+1),.^(z)C_(r+2)):}|-|{:(.^(x)C_(r),.^(x+1)C_(r+1),.^(x+2)C_(r+2)),(.^(y)C_(r ),.^(y+1)C_(r+1),.^(y+2)C_(r+2)),(.^(z)C_(r ),.^(z+1)C_(r+1),.^(z+2)C_(r+2)):}|`
In first determinant apply `C_(3)toC_(3)+C_(2)` and `C_(2)toC_(2)+C_(1)` and then agan `C_(3)toC_(3)+C_(2)`
Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE|Exercise Comprehension|2 Videos

  • DETERMINANT

    CENGAGE|Exercise Multiple Correct Answer|5 Videos

  • DEFINITE INTEGRATION

    CENGAGE|Exercise JEE Advanced Previous Year|38 Videos

  • DETERMINANTS

    CENGAGE|Exercise All Questions|268 Videos

Similar Questions

Explore conceptually related problems

Evaluate |^x C_1^x C_2^x C_3^y C_1^y C_2^y C_3^z C_1^z C_2^z C_3|

|{:(.^(x)C_(r),,.^(x)C_(r+1),,.^(x)C_(r+2)),(.^(y)C_(r),,.^(y)C_(r+1),,.^(y)C_(r+2)),(.^(z)C_(r),,.^(z)C_(r+1),,.^(z)C_(r+2)):}| is equal to

Prove that "^n C_r+^(n-1)C_r+...+^r C_r=^(n+1)C_(r+1) .

Prove that (r+1)^n C_r-r^n C_r+(r-1)^n C_2-^n C_3++(-1)^r^n C_r = (-1)^r^(n-2)C_rdot

If .^(15)C_(2r-1)=.^(15)C_(2r+4) find r

If .^(15)C_(2r-1) = .^(15)C_(2r + 4) " find " r

The value of determinant |[ ^n C_(r-1), ^n C_r, (r+1)^(n+2)C_(r+1)],[ ^n C_r, ^n C_(r+1),(r+2)^(n+2)C_(r+2)],[ ^n C_(r+1), ^n C_(r+2), (r+3)^(n+2)C_(r+3)]| is n^2+n-2 b. 0 c. ^n+3C_(r+3) d. ^n C_(r-1)+^n C_r+^n C_(r+1)

Find the sum sum_(r=1)^n r^2(^n C_r)/(^n C_(r-1)) .

.^((n-1)C_(r) + ^((n-1)) C_((r-1)) is