M0IITU11 - Binomial theorem qns

M0IITU11 - Binomial theorem qns - Binomial Theorem 1. The...

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1 Binomial Theorem QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439 1. The fourth term in the expansion of (1 - 2x) 3/2 will be : (A) - 3 4 x 4 (B) x 3 2 (C) x 3 2 (D) 3 4 x 4 2. 10 C 1 + 10 C 3 + 10 C 5 + 10 C 7 + 10 C 9 = 2 9 2 10 2 10 - 1 None of these 3. C 0 C r + C 1 C r + 1 2 C r + 2 + . .... + C n - r C n is equal to : () ! ! ! 2n nr nr -+ n rn r ! ! ( ) ! n nr ! ! - 4. If the coefficient of r th term & (r + 4) th term are equal in the expansion of (1 + x) 20 , then the value of r will be 7 8 9 10 5. C C C C C C 1 0 2 1 3 2 23 ++ .... + n n n C C - 1 = (A) nn - 1 2 + 2 2 + 1 2 (D) -- 12 2 6. C 1 + 2 C 2 + 3 C 3 + 4 C 4 ..... + nC n = 2 n n . 2 n n - 1 n + 1 7. If p & q be positive, then the coefficients of x p & x q in the expansion of (1 + x) p + q Equal Equal in magnitude but opposite in sign Reciprocal to each other 8. The term independent of x expansion of x x 3 3 2 2 10 + & ± ± ± ± ± ± ± 3 2 5 4 5 2 9. If the coefficients of 5 th , 6 and 7 terms in the expansion of (1 + x) n be in A.P., then n = 7 only 14 only 7 or 14 10. The sum of the coefficients in the (1 + x - 3x 2 ) 2163 0 1 - 1 2 2163 11. C C C C C C 1 0 2 1 3 2 + 15 C C 15 14 = 100 120 - 12. In the expansion of x x - & ± ± ± ± ± 1 6 , the constant term is : - 20 20 30 - 30 20. In the expansion of (x 2 - 2x)
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2 Binomial Theorem QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439 coefficient of x 16 is : (A) - 1680 (B) 1680 (C) 3360 (D) 6720 13. If (1 + ax) n = 1 + 8x + 24x 2 + . ..... , then the value of a and n 2, 4 2, 3 3, 6 1, 2 14. If for positive integers r > 1, n > 2, the coefficient of the (3 r) th & (r + 2) th powers of x in the expansion of (1 + x) 2n are equal, then : n = 2r n = 3r n = 2r + 1 None of these 15. The sum of the series, r n = & 0 (-1) r n C r 1 2 3 2 7 2 15 2 234 r r r r r r r mterms ++++ & ± ± ± ± ± ....
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M0IITU11 - Binomial theorem qns - Binomial Theorem 1. The...

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