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1
BT
LEVEL−I
1
...


If the fourth term in the expansion of (px+1/x)n is 5/2 then the value of p is
(A) 1
(B) 1/ 2
(C) 6
(D) 2

3
...


4

4
(B) 56  
3

5

2
(D) 56  
5

6
...


2!
3!
n!


 nn

(B)

n!
1

2


 is



 2 n

(D) –

n!2

n!
1

n!2

1

The sum of coefficients of even powers of x in the expansion of  x  
x

11 11
(A) 11  11C5
(B)
 C6
2
(C) 11 11 C 5  11 C 6
(D) 0



9
...


5

 3 i
 3 i
If z= 
  
  , then
 2
 2
2
2




(A) Re(z) =0
(C) Re(z) >0, Im(z) >0

(A)

7
...


5

11

is



1
 1

The number of irrational terms in the expansion of  5 8  2 6 




(A) 97
(B) 98
(C) 96
(D) 99

100

is equal to;

In the expansion of (1 + ax)n, n  N, then the coefficient of x and x2 are 8 and 24
respectively
...


In the coefficients of the (m + 1)th term and the (m + 3) th term in the expansion of (1 +x)20
are equal then the value of m is
(A) 10
(B) 8
(C) 9
(D) none of these

11
...


The coefficient of x5 in the expansion of (1 –x + 2x2)4 is…………

13
...


The expression n C 0  4
...
4 n C n , equals

n

(A) 2 2n (B) 2 3n
15
...


The sum of the coefficients in the expansion of (1  x  3 x 2 ) 2163 is
(A) 1
(B) –1
(C) 0
(D) None of these

17
...


1


The sum of the rational terms in the expansion of  2  3 5 





n

n
n


C 
C 
 1  n 2  ………
...


If in the expansion of (1 + x)m (1 –x)n, the co-efficient of x and x2 are 3 and –6 respectively,
then m is ……………

20
...


If (1 + x + 2x2)20 = a0 + a1x + a2x2 + ……………+ a40x40 then a1 + a3 + a5 + ………
...


The largest term in the expansion of (3 + 2x)50 where x =

23
...


23n –7n –1 is divisible by …………





2n1

1
is ……………
5

and f = R –[R] where [
...


If (1 –x + x2)n = a0 + a1x + a2x2 + ………………+a2nx2n, then a0 + a2 + a4 + …………+ a2n
equals to …………

26
...


1
...
nC2 + 3
...
+ n
...
2
(B) 2n+1 –3
4
(C) n
...


If the coefficient of (2r + 2)th and (r + 1)th terms of the expansion (1 +x)37 are equal then r =
(A) 12
(B) 13
(C) 14
(D) 18

29
...


If the co-efficient of rth, (r+1)th and (r+2)th terms in the expansion of (1+x)14 are in A
...
, then
the value of r is
(A) 5
(B) 6
(C) 7
(D) 9

31
...


C1
C
C
C
 2 3 2  2 4 3 
...


Co-efficient of x5 in the expansion of (1+x2)5 (1+x)4 is
(A) 40
(B) 50
(C) 30
(D) 60

2
...
3
...
 ( 2n  1)
...
3
...
 ( 2n  1)
...
3
...
 ( 2n  1)
1
...
5
...


 1

If 6 term in the expansion of  8 / 3  x 2 log10 x  is 5600, then x is equal to
x

(A) 5
(B) 4
(C) 8
(D) 10
th

4

4
...


The coefficient of x6 in {(1 + x)6 + (1 + x)7 + ………
...


If (1 +x)10 = a0 +a1x +a2x2 + ……+a10x10 then (a0 –a2 +a4 –a6 +a8 –a10)2 + (a1 –a3 +a5 –a7 +a9)2
is equal to
(A) 310
(B) 210
9
(C) 2
(D) none of these

7
...


2

The term independent of x in the expansion of  1  2x   is…………
x


3

9
...


1
 1

The number of irrational terms in the expansion of  2 2  3 10 




(A) 47
(B) 56
(C) 50
(D) 48

55

is;

If ab  0 and the co-efficient of x7 in (ax2+(1/bx))11 is equal to the co-efficient of x-7 in
11

1 

 ax  2  , then a and b are connected by the relation
bx 

(A) a= 1/b
(B) a =2/b
(C) ab= 1
(D) ab=2
20

11
...


(B) 620
(D) none of these

If Pn denotes the product of all the co-efficients in the expansion of (1+x)n, then
to
(A)
(C)

n  1n

(B)

n!

n  1n1

(D)

n!
n

13
...


If a  b  1 , then



n

Cr ar bn  r equals

r 0

(B) n

(A) 1

15
...


(D) nb

(D) None of these
...
(1  x) n , m  n is
(A)

n 1

C m 1

(B)

n 1

(C) n C m

C m 1

(D) n C m 1

5

17
...


19
...
10C2 –22
...
10C10 is equal to
2

1
2
1
(C)
...


(B) 0
(D) none of these

If the second, third and fourth terms in the expansion of (a+b)
respectively, then
(A) a = 3
(B) b = 1/3
(C) n = 5
(D) all the above

n

are 135, 30 and 10/3

LEVEL−III

100

1
...


(B) - 100C53
(D) 100C65

If n is an even natural number and coefficient of xr in the expansion of
then
(A) r  n/2
(C) r 

n2
2

(B) r 

n2
2

(D) r  n

1  x n
1 x

is 2n, (|x| < 1),

6

n1
2

3
...
Then value of

Cr
(B) n( A+1)

r 1

(A) n( A-1)
nA
(C)
2
4
...


The greater of two numbers 300! and

6
...


Value of

n

 r n


C r  r C m  is equal to;


r 1  m  0


 

(A) 2n –1
(C) 3n –2n

(B) 3n -1
(D) none of these
n

Value of

r 

n

Cr



2

is equal to

r 0

n  2n C n
2
2 2n
n  Cn
(C)
2

(A) n
...
2nCn
n

If



r
n

r 1

Cr

n

= , then value of


r 0

1
n

Cr

n
2
n
(C)
2
(A)

is equal to;
(B)

2
n

(D) none of these
n

10
...


r
is equal to
Cr

1
1
1



...


r 1

n

(D) nA

(A)

8
...
2
(C) n(n –1)
...
2n –3
(D) none of these

7

12
...
( x+(2n + 1) nCn) is
(A) n2n
(B) n2n + 1
n
(C) (n +1)2
(D) n2n + 1

13
...


r 0

2

(A)

 2n

2

 n  1  2

(B)

 2n  1 2n  2 
22 n1  2n 2  2 n  1

(C)

14
...
I
...
, then R  f is equal to

2n

(B) 112 n1
(D) 11

(A) 11
(C) 112n1
15
...
Cn  2 2 n

(B)  n  1 2 n Cn  22 n

(C)  n  1 2 n Cn  2 2 n

(D)  n  1 2 n Cn  2 2 n

16
...


The number 101100  1 is divisible by
(A) 10
(C) 103

18
...


Let f (n)  10 n  3  4 n  2  5; n  N
...


If

n

r 2n

  r 1 


r 0

(A) 8
(C) 6

Cr 

28  1
, then ‘n’ is
6
(B) 4
(D) 5

8

ANSWERS
LEVEL −I
1
...

9
...

17
...

25
...


C
B
A
C
B
239 − 219
3n  1
2
n 1
3 1
n1

2
...

10
...

18
...


B
B
C
C
41
50
C6 344 (2x)6

3
...

11
...

19
...


B
D
B
A
12
42n+1

4
...

12
...

20
...


A
A
−56
B
n+2
Cr
49

26
...


C

28
...


D

31
...


C

D
A
B
B
7

2
...

10
...

18
...

7
...

15
...


D
−7
A
C
A

4
...

12
...

20
...

6
...

14
...


D
B
A
C
...

7
...

15
...


B
B
C
D
B

4
...

12
...

20
...

5
...

13
...


3

C0  2  3C1

A
A
D

LEVEL −III
1
...

9
...

17

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