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# The greatest term of the expansion (2x + 5y)13 where x = 10, y = 2 is           1. 2. 3. 4. None   The binomial expansion of n N contain a term independent of x :           1.  only if k is an integers           2. only if k is a natural numbers.           3. only if k is rational           4. for any real k.   The coefficient of x50 in (1 + x)41 (1 - x + x2)40 is           1. 1           2. 2           3. 3           4. 0 Given that the term of the expansion (x1/3 - x-1/2)15 which does not contain x is 5 m where m N , then m =       1. 1100       2. 1010       3. 1001       4. none 0 out of 4 marks (content provider) Contributed by  Correct Answer: 3 Solution:Ans: 3 Q. 8 In the binomial (21/3 + 3-1/3)n, if the ratio of the seventh term from the beginning of the expansion to the seventh term from its end is 1/6 , then n =       1. 6       2. 9       3. 12       4. 15 0 out of 4 marks (content provider) Contributed by  Correct Answer: 2 Solution:Ans: 2 Q. 9 The coefficient of x49 in the expansion of (x - 1)  ..... is equal to       1. - 2 2. + ve coefficient of x       3. - ve coefficient of x       4. - 2 0 out of 4 marks (content provider) Contributed by  Correct Answer: 1 Solution:Ans: 1 Q. 10 The last digit of (3P + 2) is : where P = 34n and n N       1. 1       2. 2       3. 4       4. 5 0 out of 4 marks (content provider) Contributed by  Correct Answer: 4 Solution:Ans: 4 Q. 11 The sum of the binomial coefficients of is equal to 256 . The constant term in the expansion is       1. 1120       2. 2110       3. 1210       4. none 0 out of 4 marks (content provider) Contributed by  Correct Answer: 1 Solution:Ans: 1 Q. 12 The coefficient of x4 in is :       1. 2. 3. 4. 0 out of 4 marks (content provider) Contributed by  Correct Answer: 1 Solution:Ans: 1 Q. 13 If (1 + x + x2)25 = a0 + a1x + a2x2 + ..... + a50 . x50 then a0 + a2 + a4 + ..... + a50 is :       1. even       2. odd & of the form 3n       3. odd & of the form (3n - 1)       4. odd & of the form (3n + 1) 0 out of 4 marks (content provider) Contributed by  Correct Answer: 1 Solution:Ans: 1 Q. 14 If the second term of the expansion is 14a5/2 then the value of is :       1. 4       2. 3       3. 12       4. 6 0 out of 4 marks (content provider) Contributed by  Correct Answer: 1 Solution:Ans: 1 Q. 15 If (1 + x) (1 + x + x2) (1 + x + x2 + x3) ...... (1 + x + x2 + x3 + ...... + xn) a0 + a1x + a2x2 + a3x3 + ...... + amxm then has the value equal to       1. n!       2. (n + 1) !       3. (n - 1)!       4. none 0 out of 4 marks (content provider) Contributed by  Correct Answer: 2 Solution:Ans: 2 Q. 16 The value of 4 {nC1 + 4 . nC2 + 42 . nC3 + ...... + 4n - 1} is :       1. 0       2. 5n + 1       3. 5n       4. 5n - 1 0 out of 4 marks (content provider) Contributed by  Correct Answer: 4 Solution:Ans: 4 Q. 17 In the expansion of (1 + x)43 if the co-efficients of the (2r + 1)th and the (r + 2)th terms are equal, the value of r is :       1. 12       2. 13       3. 14       4. 15 0 out of 4 marks (content provider) Contributed by  Correct Answer: 3 Solution:Ans: 3 Q. 18 The positive value of a so that the co-efficient of x5 is equal to that of x15 in the expansion of is       1. 2. 3. 1       4. 2 0 out of 4 marks (content provider) Contributed by  Correct Answer: 1 Solution:Ans: 1 Q. 19 In the expansion of , the term which does not contain x is :       1. 10C0       2. 10C7       3. 10C4       4. none 0 out of 4 marks (content provider) Contributed by  Correct Answer: 3 Solution:Ans: 3 Q. 20 Co-efficient of t in the expansion of, ( + p)m - 1 + ( + p)m - 2 ( + q) + ( + p)m - 3 ( + q)2 + ...... ( + q)m - 1 where  - q and p q is :           1. 2. 3. 4. 0 out of 4 marks (content provider) Contributed by Correct Answer: 2 Solution:Ans: 2  Badiuddin askIITians.ismu Expert
148 Points
11 years ago

Dear Vishesh

1:

first calculate

r= (n+1)/{1+(x/a)}

here n = 13 , x= 2x = 2*10=20

a = 5y=5*2=10

so r = 14/3

integer value r=4

so Tr+1 will be the greatest term

i.e   T5

now T5 = 13C4 209 104

please post seperate question in seperate post

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11 years ago

thanks a lot sir for the solution.

I WILL BE VERY GRATEFUL TO YOU FOR THIS KIND STEP.

THANKING YOU,

VISHWESH RAVI