Match the values of the following expressions. Column I: (A) If 2 n + 1 P n − 1 : 2 n − 1 P n = 3 : 5 , find n . (B) Find the position of the constant term in ( x 2 − 1/ ( 3 x ) ) 9 . (C) Find

Question

Match the values of the following expressions. Column I: (A) If $_{2 n + 1} P_{n - 1} :_{2 n - 1} P_{n} = 3 : 5$ , find $n$ . (B) Find the position of the constant term in $(x^{2} - 1/ (3 x))^{9}$ . (C) Find the coefficient of $x^{50}$ in $(1 + x)^{41} (1 - x + x^{2})^{40}$ . (D) If $(2 n) = (5 n)$ , find $n$ . Column II: (p) 0 (q) 4 (r) 6 (s) 7

Column I	Column II
(A) If $_{2 n + 1} P_{n - 1} :_{2 n - 1} P_{n} = 3 : 5$ , find $n$ .	(p) 0
(B) Find the position of the constant term in $(x^{2} - 1/ (3 x))^{9}$ .	(q) 4
(C) Find the coefficient of $x^{50}$ in $(1 + x)^{41} (1 - x + x^{2})^{40}$ .	(r) 6
(D) If $(2 n) = (5 n)$ , find $n$ .	(s) 7

TestHub · Accepted Answer

This repeats source Q8. The permutation ratio reduces to 2 ( 2 n + 1 ) / [( n + 1 ) ( n + 2 )] = 3/5 , giving n = 4 . A term of B has exponent 18 − 3 k = 0 at k = 6 , the seventh term. In C , ( 1 − x + x 2 ) = ( 1 + x 3 ) / ( 1 + x ) , so the product is ( 1 + x ) ( 1 + x 3 ) 40 ; degree 50 is impossible. In D , symmetry of binomial coefficients gives n = 2 + 5 = 7 .

Mathematics - Binomial Theorem Question with Solution | TestHub

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