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    Assignment-1 Binomial Theorem 1685019641490

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    mr.astrophysicist1109

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    Assignment-1 Binomial Theorem 1685019641490

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    mr.astrophysicist1109
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    Assignment-1_Binomial_theorem__1685019641490

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    Assignment-1 Binomial Theorem 1685019641490

    Uploaded by

    mr.astrophysicist1109

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    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
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    of 2

    MATHEMATICS : VIKAS GUPTA

    ASSIGNMENT-1
    11 11
     2 1   1 
    1. Find the coefficients : (i) x7 in  a x   (ii) x7 in  ax  2 
     bx   bx 

    (iii) Find the relation between a & b , so that these coefficients are equal.

    2. If the coefficients of (2r + 4)th , (r  2)th terms in the expansion of (1 + x)18 are equal , find r.

    3. If the coefficients of the rth, (r + 1)th & (r + 2)th terms in the expansion of (1 + x)14 are in AP, find r.

    10 8
     x 3   1 1/3 1/5 
    4. Find the term independent of x in the expansion of (a)   2 (b)  x  x
     3 2 x  
    2 

    5. If the coefficients of 2nd, 3rd & 4th terms in the expansion of (1 + x)2n are in AP, show that 2n²  9n + 7 = 0.

    6. If a, b, c & d are the coefficients of any four consecutive terms in the expansion of (1 + x)n, n  N, prove

    VIBRANT ACADEMY
    a c 2b
    that a  b  c  d  b  c .

    11
     7
    7. In the expansion of  1  x   find the term not containing x.
     x

    8. Show that coefficient of x5 in the expansion of (1 + x²)5 . (1 + x)4 is 60.

    9.
    unacademy  2
    Prove that the ratio of the coefficient of x10 in (1  x²)10 & the term independent of x in  x  
     x
    10

    is 1 : 32 .

    n 4
    10. Let (1+x²)² . (1+x)n = a K . xK . If a1 , a2 & a3 are in AP, find n.
    K0

    8
     2 log 4x  44 1 
    Find the value of x for which the fourth term in the expansion,  5
    5 5
    11.   is 336.
    3 2 x 1  7 
     5log5 

    12. Find the coefficient of xr in the expression of :


    (x + 3)n1 + (x + 3)n2 (x + 2) + (x + 3)n3 (x + 2)2 + ..... + (x + 2)n1

    n
    r  1 3r 7r 15r 
    13. Find the sum of the series  (1) . nC r    3r  4 r  .....up to m terms 
    r 2r
    r0  2 2 2 2 

    Join with code VIBRANTLIVE for 10% discount on your subscription. [1]
    ANSWERS

    11C
    a6 11
    1C
    a5 5
    1. (i) (ii) (iii) ab = 1 2. r = 6 3. r = 5 or 9 4. (a) (b) T6 = 7
    5
    b5 6
    b6 12

    5
    7. 1+  11
    1C
    2k . 2kC
    k 7k 10. n = 2 or 3 or 4 11. x = 0 or 1 12. nC (3nr 
    r 2nr)
    k1

    2 mn
    1
    13.
     2  1  2 
    n mn

    VIBRANT ACADEMY

    unacademy

    Join with code VIBRANTLIVE for 10% discount on your subscription. [2]

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