Dear student, The expansion of x+ynx+yn=C0nxn y0+C1nxn-1y1+C2nxn-2y2+ +Cn-1nx1yn-1+Cnnx0yn (1)Given series is C0np+C1npq+C2npq2+ +CnnpqnTaking p common=pC0n+C1nq+C2nq2+ +Cnnqn =p1+qn [ from (1) ] Hence option 1 is the answer Regards

sir

Dear student,

T h e e x p a n s i o n o f {(x + y)}^{n} {(x + y)}^{n} = {}^{n}C_{0} x^{n} y^{0} + {}^{n}C_{1} x^{n - 1} y^{1} + {}^{n}C_{2} x^{n - 2} y^{2} + . . . . . . + {}^{n}C_{n - 1} x^{1} y^{n - 1} + {}^{n}C_{n} x^{0} y^{n} . . (1) G i v e n s e r i e s i s {}^{n}C_{0} p + {}^{n}C_{1} p q + {}^{n}C_{2} p q^{2} + . . . . . . + {}^{n}C_{n} p q^{n} T a k i n g p c o m m o n = p ({}^{n}C_{0} + {}^{n}C_{1} q + {}^{n}C_{2} q^{2} + . . . . . . + {}^{n}C_{n} q^{n}) = p {(1 + q)}^{n} . . . [f r o m (1)] H e n c e o p t i o n 1 i s t h e a n s w e r

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​sir

sir