Binomial Theorem Practice Questions - DPP for JEE

 Page 1


PART-I (Single Correct MCQs)
1. If x = 99
50
 + 100
50
 and y = (101)
50
 then
(a) x = y
(b) x < y
(c) x > y
(d) None of these
2.
(a)
(b)
(c)
(d) None of these
3. The value of the term independent of x in the expansion of 
Page 2


PART-I (Single Correct MCQs)
1. If x = 99
50
 + 100
50
 and y = (101)
50
 then
(a) x = y
(b) x < y
(c) x > y
(d) None of these
2.
(a)
(b)
(c)
(d) None of these
3. The value of the term independent of x in the expansion of 
 is equal to
(a) 1
(b) – 6
(c) –5
(d) 6
4. If x is so small that  and higher powers of x may be neglected, then 
 may be approximated as
(a)
(b)
(c)
(d)
5. Coefficient of x
25
 in expansion of expression
 is
(a)
50
C
25
(b) – 
50
C
30
(c)
50
C
30
(d) – 
50
C
25
6. If (1 + x)
2n
 = a
0
 + a
1
x + a
2
x
2
 + ..... + a
2n
x
2n
, then
(a) a
0
 + a
2
 + a
4
 + .... =  (a
0
 + a
1
 + a
2
 + a
3
 + ....)
Page 3


PART-I (Single Correct MCQs)
1. If x = 99
50
 + 100
50
 and y = (101)
50
 then
(a) x = y
(b) x < y
(c) x > y
(d) None of these
2.
(a)
(b)
(c)
(d) None of these
3. The value of the term independent of x in the expansion of 
 is equal to
(a) 1
(b) – 6
(c) –5
(d) 6
4. If x is so small that  and higher powers of x may be neglected, then 
 may be approximated as
(a)
(b)
(c)
(d)
5. Coefficient of x
25
 in expansion of expression
 is
(a)
50
C
25
(b) – 
50
C
30
(c)
50
C
30
(d) – 
50
C
25
6. If (1 + x)
2n
 = a
0
 + a
1
x + a
2
x
2
 + ..... + a
2n
x
2n
, then
(a) a
0
 + a
2
 + a
4
 + .... =  (a
0
 + a
1
 + a
2
 + a
3
 + ....)
(b) a
n+1
 < a
n
(c) a
n–3
 = a
n+3
? (d) All of these
7. Number of ways of selection of 8 letters from 24 letters of which 8 are
a, 8 are b and the rest unlike, is given by
(a) 2
7
(b) 8.2
8
(c) 10.2
7
(d) None of these
8. The expression is a
polynomial of
degree:
(a) 5
(b) 6
(c) 7
(d) 8
9. The value of
is where 
(a)
(b)
(c)
(d)
Page 4


PART-I (Single Correct MCQs)
1. If x = 99
50
 + 100
50
 and y = (101)
50
 then
(a) x = y
(b) x < y
(c) x > y
(d) None of these
2.
(a)
(b)
(c)
(d) None of these
3. The value of the term independent of x in the expansion of 
 is equal to
(a) 1
(b) – 6
(c) –5
(d) 6
4. If x is so small that  and higher powers of x may be neglected, then 
 may be approximated as
(a)
(b)
(c)
(d)
5. Coefficient of x
25
 in expansion of expression
 is
(a)
50
C
25
(b) – 
50
C
30
(c)
50
C
30
(d) – 
50
C
25
6. If (1 + x)
2n
 = a
0
 + a
1
x + a
2
x
2
 + ..... + a
2n
x
2n
, then
(a) a
0
 + a
2
 + a
4
 + .... =  (a
0
 + a
1
 + a
2
 + a
3
 + ....)
(b) a
n+1
 < a
n
(c) a
n–3
 = a
n+3
? (d) All of these
7. Number of ways of selection of 8 letters from 24 letters of which 8 are
a, 8 are b and the rest unlike, is given by
(a) 2
7
(b) 8.2
8
(c) 10.2
7
(d) None of these
8. The expression is a
polynomial of
degree:
(a) 5
(b) 6
(c) 7
(d) 8
9. The value of
is where 
(a)
(b)
(c)
(d)
10. If ‘n’  is positive integer and three consecutive coefficient in the
expansion of (1 + x)
n
 are in the ratio 6 : 33 : 110, then n is equal to :
(a) 9
(b) 6
(c) 12
(d) 16
11. If the coefficient of  in  equals the coefficient of 
in , then a and b satisfy the relation
(a) a – b = 1
(b) a + b = 1
(c) = 1
(d) ab = 1
12. If (1 + x)
n
 = , then the value of
+ ......
+ is
(a)
(b)
(c) 2
n
(d) (n + 2) . 2
n – 1
13. Find the value of 
4n
C
0
 + 
4n
C
4
 + 
4n
C
8
 + ...... + 
4n
C
4n
(a)
(b)
(c)
(d) None of these
14. The sum of the series
  is
(a) 0
Page 5


PART-I (Single Correct MCQs)
1. If x = 99
50
 + 100
50
 and y = (101)
50
 then
(a) x = y
(b) x < y
(c) x > y
(d) None of these
2.
(a)
(b)
(c)
(d) None of these
3. The value of the term independent of x in the expansion of 
 is equal to
(a) 1
(b) – 6
(c) –5
(d) 6
4. If x is so small that  and higher powers of x may be neglected, then 
 may be approximated as
(a)
(b)
(c)
(d)
5. Coefficient of x
25
 in expansion of expression
 is
(a)
50
C
25
(b) – 
50
C
30
(c)
50
C
30
(d) – 
50
C
25
6. If (1 + x)
2n
 = a
0
 + a
1
x + a
2
x
2
 + ..... + a
2n
x
2n
, then
(a) a
0
 + a
2
 + a
4
 + .... =  (a
0
 + a
1
 + a
2
 + a
3
 + ....)
(b) a
n+1
 < a
n
(c) a
n–3
 = a
n+3
? (d) All of these
7. Number of ways of selection of 8 letters from 24 letters of which 8 are
a, 8 are b and the rest unlike, is given by
(a) 2
7
(b) 8.2
8
(c) 10.2
7
(d) None of these
8. The expression is a
polynomial of
degree:
(a) 5
(b) 6
(c) 7
(d) 8
9. The value of
is where 
(a)
(b)
(c)
(d)
10. If ‘n’  is positive integer and three consecutive coefficient in the
expansion of (1 + x)
n
 are in the ratio 6 : 33 : 110, then n is equal to :
(a) 9
(b) 6
(c) 12
(d) 16
11. If the coefficient of  in  equals the coefficient of 
in , then a and b satisfy the relation
(a) a – b = 1
(b) a + b = 1
(c) = 1
(d) ab = 1
12. If (1 + x)
n
 = , then the value of
+ ......
+ is
(a)
(b)
(c) 2
n
(d) (n + 2) . 2
n – 1
13. Find the value of 
4n
C
0
 + 
4n
C
4
 + 
4n
C
8
 + ...... + 
4n
C
4n
(a)
(b)
(c)
(d) None of these
14. The sum of the series
  is
(a) 0
(b)
(c)
(d)
15. If 7
103
 is divided by 25, then the remainder is
(a) 20
(b) 16
(c) 18
(d) 15
16. If x is very small in magnitude compared with a, then 
 can be approximately equal to
(a)
(b)
(c)
(d)
17. If C
0
, C
1
, C
2
, ......, C
n
 be the coefficients in the expansion of (1 + x)
n
,
then  is equal to
(a)
(b)