"^10(C0)^2-"^10(C1)^2+"^10(C2)^2-......-...

`"^10(C_0)^2``-``"^10(C_1)^2``+``"^10(C_2)^2``-`......`-`(`"^10C_9)^2``+`(`"^10C_10)^2=`

`10!`

`(""^(10)C_(5))^(2)`

`""^(_10)C_(5)`

`""^(10)C_(5)`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

BIONMIAL THEOREM
VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise-2 : One or More than One Answer is/are Correct|9 Videos
BIONMIAL THEOREM
VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise-3 : Matching Type Problems|2 Videos
AREA UNDER CURVES
VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise AXERCISE (SUBJECTIVE TYPE PROBLEMS)|8 Videos
CIRCLE
VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise - 5 : Subjective Type Problems|13 Videos

Similar Questions

Explore conceptually related problems

Observe the following statements : Statement - I : 1/2 . ""^10C_0 - ""^10C_1 + 2. ""^10C_2 - 2^2. ""^10C_3 + ……+ 2^9. ""^10C_10 = -1/2 Statement - II : ""^20C_1 - 2(""^20C_2) + 3.(""^20C_3)-…..-20.(""^20C_20) = 0 Then the false statements are :

Find 1/2.""^10C_0 -""^10C_1 +2.""^10C_2 - 2^2.""^10C_3+…..+2^9. ""^10C_10 = ?

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)) .

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 _________.

Evaluate the following : (i) 1+.^(20)C_(1)+^(20)C_(2)+^(20)C_(3)+....+^(20)C_(19)+^(20)C_(20) (ii) ^(10)C_(1)+^(10)C_(2)+^(10)C_(3)+.....+^(10)C_(9) (iii)^(25)C_(1)+^(25)C_(3)+^(25)C_(5)+.....+^(25)C_(25) (iv) ^(18)C_(2)+^(18)C_(4)+^(18)C_(4)+^(18)C_(6)+....+^(18)C_(18)

Prove that ^10 C_1(x-1)^2-^(10)C_2(x-2)^2+^(10)C_3(x-3)^2+-^(10)C_(10)(x-10)^2=x^2

Each question has four choices a, b, c and d, out of which only one is correct. Each question contains STATEMENT 1 and STATEMENT 2. Both the statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT1. Both the statements are TRUE but STATEMENT 2 is NOT the correct explanation of STATEMENT 1. STATEMENT 1 is TRUE and STATEMENT 2 is FALSE. STATEMENT 1 is FALSE and STATEMENT 2 is TRUE. Statement 1: The value of (^(10)^C_0)+(^(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) is 10 2^9 . Statement 2: ^n C_1+2^n C_2+3^n C_3+ n^n C_n=n2^(n-1) .

In the expansion off (1+x)^(10)=.^(10)C_(0)+.^(10)C_(1)x+.^(10)C_(2)x^(2)+ . . .+.^(10)C_(10)x^(10) , then value of 528[(.^(10)C_(0))/(2)-(.^(10)C_(1))/(3)+(.^(10)C_(2))/(4)-(.^(10)C_(3))/(5)+ . . .+(.^(10)C_(10))/(12)] is equal to________.

"^(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

""^10C_1 . ""^9C_5 + ""^10C_2. ""^9C_4 + ""^10C_3. ""^9C_3 + ""^10C_4. ""^9C_2 + ""^10C_5. ""^9C_1 + ""^10C_6 = ""^19C_6 + x then x =

VIKAS GUPTA (BLACK BOOK) ENGLISH-BIONMIAL THEOREM-Exercise-4 : Subjective Type Problems

"^10(C0)^2-"^10(C1)^2+"^10(C2)^2-......-("^10C9)^2+("^10C10)^2=
Text Solution
|
The sum of series 3*""^(2007)C(0)-8*""^(2007)C(1)+13*""^(2007)C(2)-18...
Text Solution
|
In the polynomial function f(x)=(x-1)(x^(2)-2)(x^(3)-3)……..(x^(11)-11...
Text Solution
|
If 3^(101)-2^(100) is divided by 11, the remainder is
Text Solution
|
Find the hundred's digit in the co-efficient of x^(17) in the expansio...
Text Solution
|
Let x=(3sqrt(6)+7)^(89). If {x} denotes the fractional part of 'x' the...
Text Solution
|
Let n in N, Sn=sum(r=0)^(3n)^(3n)Cr and Tn=sum(r=0)^n^(3n)C(3r), then ...
Text Solution
|
Find the sum of possible real values of x for which the sixth term of ...
Text Solution
|
Let q be a positive with q le 50. If the sum ""^(98)C(30)+2" "^(97)C...
Text Solution
|
The remainder when (sum(k=1)^(5) ""^(20)C(2k-1))^(6) is divided by 11,...
Text Solution
|
Let a=3^(1/(223))+1 and for all geq3,l e tf(n)=^n C0dota^(n-1)-^n C1do...
Text Solution
|
In the polynomial (x-1)(x^(2)-2)(x^(3)-3)…(x^(11)-11), the coefficient...
Text Solution
|
Let the sum of all divisior of the form 2^(p)*3^(q) (with p, q positi...
Text Solution
|
Find the sum of possible real values of x for which the sixth term of ...
Text Solution
|
Let 1+sum(r=1)^(10)(3^r.^(10)Cr+r.^(10)Cr)=2^(10)(alpha. 4^5+beta) whe...
Text Solution
|
If S(n) = ""^(n)C(0) ""^(n)C(1) + ""^(n)C(1) ""^(n)C(2) + ...+ ""^(n)...
Text Solution
|