Home
Class 12
MATHS
Let X=(\ ^(10)C1)^2+2(\ ^(10)C2)^2+3(\ ^...

Let `X=(\ ^(10)C_1)^2+2(\ ^(10)C_2)^2+3(\ ^(10)C_3)^2+\ ddot\ +10(\ ^(10)C_(10))^2` , where `\ ^(10)C_r` , `r in {1,\ 2,\ ddot,\ 10}` denote binomial coefficients. Then, the value of `1/(1430)\ X` is _________.

Text Solution

Verified by Experts

The correct Answer is:
D
`X = underset(r=1)overset(10)sumr.(.^(10)C_(r))^(2)= underset(r=1)overset(10)sumr..^(10)C_(r)..^(10)C_(r)`
`= 10. underset(r=1)overset(10)sum .^(9)C_(r-1)..^(10)C_(10-r) = 10..^(19)C_(9)`
Now, `(X)/(1430) = (10..^(19)C_(9))/(1430) = (.^(19)C_(9))/(143) = (.^(19)C_(9))/(11xx13)`
`= (19xx17xx16)/(8) = 19xx34 = 646`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE|Exercise Single correct Answer|62 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Multiple Correct Answer|4 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise (Numerical)|25 Videos

  • AREA UNDER CURVES

    CENGAGE|Exercise Question Bank|10 Videos

  • CIRCLE

    CENGAGE|Exercise MATRIX MATCH TYPE|6 Videos

Similar Questions

Explore conceptually related problems

10C_1=

Prove that ""^(10)C_(2)+2xx^(10)C_(3)+^(10)C_(4)=^(12)C_(4)

The coefficient of x^(4) in the expansion of (x/2-3/x^(2))^(10) is

Find the sum ^10 C_1+^(10)C_3+^(10)C_5+^(10)C_7+^(10)C_9dot

If the variance of 1,2,3,4,5,….., x is 10, then the value of x is

"^(30)C_(0)*^(20)C_(10)+^(31)C_(1)*^(19)C_(10)+^(32)C_(2)*18C_(10)+....^(40)C_(10)*^(10)C_(10) is equal to

Find the value of .^(20)C_(0) xx .^(13)C_(10) - .^(20)C_(1) xx .^(12)C_(9) + .^(20)C_(2) xx .^(11)C_(8) - "……" + .^(20)C_(10) .

If (10)^9 + 2(11)^1 (10)^8 + 3(11)^2 (10)^7+...........+10 (11)^9= k (10)^9 , then k is equal to :