Home
Class 12
MATHS
Find the value of (.^(10)C(10))+(.^(10)C...

Find the value of `(.^(10)C_(10))+(.^(10)C_(0)+.^(10)C_(1))+(.^(10)C_(0)+.^(10)C_(1)+.^(10)C_(2))+"...."+(.^(10)C_(0)+.^(10)C_(1)+.^(10)C_(2)+"....." + .^(10)C_(9))`.

Text Solution

Verified by Experts

The correct Answer is:
`10 xx 2^(9)`
`(.^(10)C_(0)+.^(10)C_(1))+(.^(10)C_(0)+.^(10)C_(1)+.^(10)C_(2))+"...."+(.^(10)C_(0)+.^(10)C_(1)+.^(10)C_(2)+"...."+.^(10)C_(9))`
`= 10.^(100)C_(0) + 9.^(10)C_(1)+8.^(10)C_(2)+"...."+.^(10)C_(9)`
`= .^(10)C_(1) +2.^(10)C_(2)+3.^(10)C_(3)+"...."+10.^(10)C_(10)`
`= underset(r=1)overset(10)sum..^(10)C_(r) = 10 underset(r=1)overset(10)sum.^(9)C_(r-1)=10 xx 2^(9)`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise Concept Application Exercise 8.7|9 Videos

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise Concept Application Exercise 8.8|10 Videos

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise Concept Application Exercise 8.5|8 Videos

  • AREA

    CENGAGE PUBLICATION|Exercise Comprehension Type|2 Videos

  • CIRCLE

    CENGAGE PUBLICATION|Exercise For problems 3 and 4|2 Videos

Similar Questions

Explore conceptually related problems

Find the values of .^(10)C_(4)

Find the value of .^10 C_2

Find the value of .^10 C_4

Find the value of .^11 C_10

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) .

The value of (.^(21)C_(1) - .^(10)C_(1)) + (.^(21)C_(2) - .^(10)C_(2)) + (.^(21)C_(3) - .^(10)C_(3)) + (.^(21)C_(4) - .^(10)C_(4)) + … + (.^(21)C_(10) - .^(10)C_(10)) is

Find the sum .^(10)C_1+^(10)C_3+^(10)C_5+^(10)C_7+^(10)C_9

Find the sum 2..^(10)C_(0) + (2^(2))/(2).^(10)C_(1) + (2^(3))/(3).^(10)C_(2)+(2^(4))/(4).^(10)C_(3)+"...."+(2^(11))/(11).^(10)C_(10) .

Find the value of .^(20)C_(0) - .^(20)C_(1)+ .^(20)C_(2) - .^(20)C_(3) +"……"-"....." + .^(20)C_(10) . is

The value of sum_(r=2)^(10) ""^(r)C_(2).""^(10)C_(r) is