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The coefficient of $x^{7}$ in the expression ${(1 + x)}^{10} + x {(1 + x)}^{9} + x^{2} {(1 + x)}^{8} + ...... + x^{10}$ is-

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Correct option is A

Given series = 1+x101−x1+x111−x1+x =1+x101+x11−x111+x11×11+x =1+x11−x11Coefficient of x7 is 11C7=11C4=330

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The coefficient of x7 in the expression 1+x10+x1+x9+x21+x8+......+x10 is-

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The coefficient of $x^{7}$ in the expression ${(1 + x)}^{10} + x {(1 + x)}^{9} + x^{2} {(1 + x)}^{8} + ...... + x^{10}$ is-