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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 x 50 in (1 + x) 41 (1 - x + x 2 ) 40 is 1. 1 2. 2 3. 3 4. 0 Given that the term of the expansion (x 1/3 - 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 (2 1/3 + 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 x 49 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 (3 P + 2) is : where P = 3 4n 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 x 4 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 + x 2 ) 25 = a 0 + a 1 x + a 2 x 2 + ..... + a 50 . x 50 then a 0 + a 2 + a 4 + ..... + a 50 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 14a 5/2 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 + x 2 ) (1 + x + x 2 + x 3 ) ...... (1 + x + x 2 + x 3 + ...... + x n ) a 0 + a 1 x + a 2 x 2 + a 3 x 3 + ...... + a m x m 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 { n C 1 + 4 . n C 2 + 4 2 . n C 3 + ...... + 4 n - 1 } is : 1. 0 2. 5 n + 1 3. 5 n 4. 5 n - 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 x 5 is equal to that of x 15 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. 10 C 0 2. 10 C 7 3. 10 C 4 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










 






























  The greatest term of the expansion (2x + 5y)13 where x = 10, y = 2 is
 
 
 
 
 
 
 
  None

 


 











 






























  The binomial expansion of n N contain a term independent of x :
 
   only if k is an integers
 
  only if k is a natural numbers.
 
  only if k is rational
 
  for any real k.

 


 











 






























  The coefficient of x50 in (1 + x)41 (1 - x + x2)40 is
 
  1
 
  2
 
  3
 
  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 =
1100
1010
1001
none










0 out of 4 marks (content provider)

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 =
6
9
12
15










0 out of 4 marks (content provider)

Correct Answer: 2
Solution:
Ans: 2





























Q. 9 The coefficient of x49 in the expansion of (x - 1) ..... is equal to
- 2
+ ve coefficient of x
- ve coefficient of x
- 2










0 out of 4 marks (content provider)

Correct Answer: 1
Solution:
Ans: 1





























Q. 10 The last digit of (3P + 2) is :
where P = 34n and n N
1
2
4
5










0 out of 4 marks (content provider)

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
1120
2110
1210
none










0 out of 4 marks (content provider)

Correct Answer: 1
Solution:
Ans: 1





























Q. 12 The coefficient of x4 in is :










0 out of 4 marks (content provider)

Correct Answer: 1
Solution:
Ans: 1





























Q. 13 If (1 + x + x2)25 = a0 + a1x + a2x2 + ..... + a50 . x50 then a0 + a2 + a4 + ..... + a50 is :
even
odd & of the form 3n
odd & of the form (3n - 1)
odd & of the form (3n + 1)










0 out of 4 marks (content provider)

Correct Answer: 1
Solution:
Ans: 1





























Q. 14 If the second term of the expansion is 14a5/2 then the value of is :
4
3
12
6










0 out of 4 marks (content provider)

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
n!
(n + 1) !
(n - 1)!
none










0 out of 4 marks (content provider)

Correct Answer: 2
Solution:
Ans: 2





























Q. 16 The value of 4 {nC1 + 4 . nC2 + 42 . nC3 + ...... + 4n - 1} is :
0
5n + 1
5n
5n - 1










0 out of 4 marks (content provider)

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 :
12
13
14
15










0 out of 4 marks (content provider)

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










0 out of 4 marks (content provider)

Correct Answer: 1
Solution:
Ans: 1





























Q. 19 In the expansion of , the term which does not contain x is :
10C0
10C7
10C4
none










0 out of 4 marks (content provider)

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 :
 
 
 
 
 
 
 
 
 










0 out of 4 marks (content provider)

Correct Answer: 2
Solution:
Ans: 2

Grade:12th Pass

3 Answers

VISHWESH RAVI
31 Points
11 years ago
answer soon. pls !!!!!!!!!!!!!! its urgent by VISHWESH RAVI
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

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Badiuddin



 

VISHWESH RAVI
31 Points
11 years ago

thanks a lot sir for the solution.

 

PLEASE PAY ATTENTION TO MY OTHER ASKED QUESTIONS (WITH TITLE PLEASE HELP).

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

 

THANKING YOU,

VISHWESH RAVI

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