If the value of the sum 29(( 30C)0)+28(( 30C)1)+27(( 30C)2)+. ldots ldots .+1(( 30C)28)+0⋅ (( 30C)29)-(( 30C)30) is equal to K⋅ 232, then the value of K is equal to

Question

If the value of the sum 29(( 30C)0)+28(( 30C)1)+27(( 30C)2)+. ldots ldots .+1(( 30C)28)+0⋅ (( 30C)29)-(( 30C)30) is equal to K⋅ 232, then the value of K is equal to (A) 7 (B) 14 (C) (5/2) (D) (7/2)

Tardigrade Admin · Accepted Answer

S=29(( 30C)0)+28(( 30C)1)+27(( 30C)2)+. ldots ldots .+1(( 30C)28)+0⋅ (( 30C)29)-(( 30C)30) Also, S=-(( 30C)0)+0⋅ (( 30C)1)+1(( 30C)2)+. ldots ldots .+27(( 30C)28)+28(( 30C)29)+29(( 30C)30) Adding we get, 2S=28 30C0 + 30C1 + 30C2 + . ldots . . + 30C28 + 30C29 + 30C30 ⇒ S=14⋅ 230=(14/4)232=(7/2)⋅ 232 ⇒ K=(7/2)

Q. If the value of the sum $29 ((_^{30} C)_{0}) + 28 ((_^{30} C)_{1}) + 27 ((_^{30} C)_{2}) + . \dots\dots . + 1 ((_^{30} C)_{28}) + 0 \cdot ((_^{30} C)_{29}) - ((_^{30} C)_{30})$ is equal to $K \cdot 2^{32},$ then the value of $K$ is equal to

$7$

$14$

$\frac{5}{2}$

$\frac{7}{2}$

Q. If the value of the sum 29((_30C)0​)+28((_30C)1​)+27((_30C)2​)+.…….+1((_30C)28​)+0⋅((_30C)29​)−((_30C)30​) is equal to K⋅232, then the value of K is equal to

7

14

25​

27​

Q. If the value of the sum $29 ((_^{30} C)_{0}) + 28 ((_^{30} C)_{1}) + 27 ((_^{30} C)_{2}) + . \dots\dots . + 1 ((_^{30} C)_{28}) + 0 \cdot ((_^{30} C)_{29}) - ((_^{30} C)_{30})$ is equal to $K \cdot 2^{32},$ then the value of $K$ is equal to

$7$

$14$

$\frac{5}{2}$

$\frac{7}{2}$