JEE Mains Super40 Revision Series
BINOMIAL THEOREM
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1 11598
JEE Mains Super40 Revision Series BINOMIAL THEOREM
The term independent of x in expansion of is (1) 120 (2) 210 (3)
310 (4) 4
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2 11636
JEE Mains Super40 Revision Series BINOMIAL THEOREM
If the coefficients of and in the expansion of in powers of x
are both zero, then (a, b) is equal to (1) (3) (2) (4)
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3 11644
JEE Mains Super40 Revision Series BINOMIAL THEOREM
The sum of coefficients of integral powers of x in the binomial expansion of is: (1)
(2) (3) (4)
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( − )x + 1
x − x + 123
13
x − 1
x − x12
x3 x4 (1 + ax + bx2)(1 − 2x)18
(16, )251
3(14, )
251
3(14, )
272
3
(16, )272
3
(1 − 2√x)50
(350 + 1)1
2(350)
1
2(350 − 1)
1
2(250 + 1)
1
2
4 11684 JEE Mains Super40 Revision Series BINOMIAL THEOREM
If the number of terms in the expansion of is 28, then the sum of the
coefficients of all the terms in this expansion, is : (1) 64 (2) 2187 (3) 243 (4) 729
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5 31984
JEE Mains Super40 Revision Series BINOMIAL THEOREM
If denotes the rth order
derivative of with respect to is b. c. d. none of these
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6 31985
JEE Mains Super40 Revision Series BINOMIAL THEOREM
The fractional part of is (a) (b) (c) (d) non of these
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7 31990
JEE Mains Super40 Revision Series BINOMIAL THEOREM
If the sum of the coefficients in the expansion of is 4096, then the greatest coefficient inthe expansion is b. c. d. none of these
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8 31992
JEE Mains Super40 Revision Series BINOMIAL THEOREM
The sum of the coefficients of even power of in the expansion of is b. c. d.
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9 32014 JEE Mains Super40 Revision Series BINOMIAL THEOREM
(1 − + )n
, x ≠ 0,2
x
4
x2
f(x) = xn, f(1) + + + , wheref r(x)f 1(1)
1
f 2(1)
2 !
f n(1)
n !f(x) x, n 2n 2n− 1
24n
15(n ∈ N)
1
15
2
15
4
15
(a + b)n
924 792 1594
x (1 + x + x2 + x3)5
256128 512 64
If the last tem in the binomial expansion of , then 5th term from
the beginning is b. c. d. none of these
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10 32018
JEE Mains Super40 Revision Series BINOMIAL THEOREM
The total number of terms which are dependent on the value of in the expansion of
is equal to b. c. d.
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11 32020
JEE Mains Super40 Revision Series BINOMIAL THEOREM
If is an integer between 0 and 21, then the minimum value of is attained for b. c. d.
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12 32039
JEE Mains Super40 Revision Series BINOMIAL THEOREM
If occurs in the expansion , then the coefficient of is b.
c. d. none of these
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13 32040
JEE Mains Super40 Revision Series BINOMIAL THEOREM
If the coefficients of 5th, 6th , and 7th terms in the expansion of are in A.P., then a. 7 only b. 14 only c. 7 or 14 d. none of these
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(2 − )n
is( )
log3 813
1
√2
1
353
210 420 105
x
(x2 − 2 + )n
1
x22n + 1 2n n n + 1
n n !(21 − n) ! n =1 10 12 20
xm (x + 1/x2)n
xm(2n) !
(m) !(2n − m) !(2n) !3 !3 !
(2n − m) !
(2n) !
( ) !( ) !2n−m
34n+m
3
(1 + x)n n =
14 32042 JEE Mains Super40 Revision Series BINOMIAL THEOREM
In the expansion of , if the sum of the coefficients of is 0 , then
is a. 25 b. 20 c. 15 d. none of these
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15 32044
JEE Mains Super40 Revision Series BINOMIAL THEOREM
In the expansion of , the coefficient of is a. 144 b. 288 c. 216 d. 576
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16 32051
JEE Mains Super40 Revision Series BINOMIAL THEOREM
Coefficient of in the expansion of is 1051 b. 1106 c. 1113 d.1120
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17 32057
JEE Mains Super40 Revision Series BINOMIAL THEOREM
The term independent of in the expansion of is (a) (b)
(c) (d) non of these
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18 32058
JEE Mains Super40 Revision Series BINOMIAL THEOREM
The coefficient of in the expansion is b.
c. d. none of these
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19 32061 JEE Mains Super40 Revision Series BINOMIAL THEOREM
(x3 − )n
, n ∈ N1
x2x5andx10
n
(1 + 3x + 2x2)6
x11
x11 (1 + x2)4(1 + x3)
7(1 + x4)
12
a (1 + √a + )− 30
1
√a − 130C20 0
30C10
x53100
∑m= 0
^ (100)Cm(x − 3)100 −m2m ^ 100C47
^ 100C53 −100C53
If coefficient of (where ) is then in same expansion
coefficient of will be (a) (b) (c) (d)
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20 32064
JEE Mains Super40 Revision Series BINOMIAL THEOREM
The coefficient of in lthe expansion of is
b. c. d. none of these
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21 32066
JEE Mains Super40 Revision Series BINOMIAL THEOREM
In the expansion of the number of integral terms is b. c. d.
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22 32080
JEE Mains Super40 Revision Series BINOMIAL THEOREM
If , then is b. c. d.
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23 32084 JEE Mains Super40 Revision Series BINOMIAL THEOREM
If is equal to b. c. d. none of
these
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a2b3c4 ∈ (a + b + c)m
n ∈ N L(L ≠ 0),
a4b4c1 LL
3
mL
4
L
2
xr[0 ≤ r ≤ (n − 1)]
(x + 3)n− 1 + (x + 3)n− 2(x + 2) + (x + 3)n− 3(x + 2)2 + + (x + 2)n− 1
^ nCr(3r − 2n) ^ nCr(3n− r − 2n− r) ^ nCr(3r + 2n− r)
(51 / 2 + 71 / 8)1024
, 128 129 130
131
10
∑r= 0
( ) ∧ nCr =r + 2
r + 1
28 − 1
6n 8 4 6 5
= a0 + a1x + a2x2 + , then
50
∑r= 1
arx2 + x + 1
1 − x148 146 149
24 32085
JEE Mains Super40 Revision Series BINOMIAL THEOREM
is a prime number and `n Watch Free Video Solution on Doubtnut
25 32089
JEE Mains Super40 Revision Series BINOMIAL THEOREM
The value of is equal to b. c. d.
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26 32090
JEE Mains Super40 Revision Series BINOMIAL THEOREM
The coefficient of in the expansion of is b. c. d.
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27 32091
JEE Mains Super40 Revision Series BINOMIAL THEOREM
If the term independent of in the is 405, then equals b. c.
d.
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p
20
∑r= 0
r(20 − r)( ^ (20)Cr)2 40039C20 40040C19 40039C19
40038C20
x10 (1 + x2 − x3)8
476 496 506 528
x (√x − )10
k
x2k 2, − 2 3, − 3
4, − 4 1, − 1
28 32094
JEE Mains Super40 Revision Series BINOMIAL THEOREM
The coefficient of in is b. c. d. none
of these
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29 32095
JEE Mains Super40 Revision Series BINOMIAL THEOREM
If the coefficient of equal the coefficient of in satisfy the
satisfy the relation b. c. d.
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30 32097
JEE Mains Super40 Revision Series BINOMIAL THEOREM
The coefficient of in the expansion of is b. c. d.
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31 32112
JEE Mains Super40 Revision Series BINOMIAL THEOREM
If then the coefficient of in expansion of is b. c. d.
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a8b4c9d9 (abc + abd + acd + bcd)10
10!10!
8 !4 !9 !9 !2520
x7 ∈ [ax2 − ( )]11
1
bx2x− 7
[ax − ( )]11
, thenaandb1
bx2a + b = 1 a − b = 1 b = 1
= 1a
b
xn (1 − x)(1 − x)n n − 1 ( − 1)n(1 − n)
( − 1)n− 1
(n − 1)2
( − 1)n− 1
n
|x| < 1, xn (1 + x + x2 + x3 + )2
n n − 1n + 2 n + 1
32 32114
JEE Mains Super40 Revision Series BINOMIAL THEOREM
If is so small that and higher powers of may be neglectd, then
may be approximated as b. c. d.
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33 32119
JEE Mains Super40 Revision Series BINOMIAL THEOREM
The sum of rational term in is equal to b. c. d. none ofthese
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34 32140
JEE Mains Super40 Revision Series BINOMIAL THEOREM
a. b. c. d.
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35 32141
JEE Mains Super40 Revision Series BINOMIAL THEOREM
The coefficient of in the expansion of in ascending powers of when
b. c. d.
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x x3 x
(1 + x)3 / 2
− (1 + x)31
2
(1 − x)1 / 23x + x23
81 − x23
8−
x
2
3
×2
− x23
8
(√2 + 33 + 56)10
12632 1260 126
∞
∑k= 1
k(1 − )k− 1
=1
nn(n − 1) n(n + 1) n2 (n + 1)
2
x4 {√1 + x2 − x}− 1
x,
|x| < 1, is 01
2−
1
2−
1
8
36 32143
JEE Mains Super40 Revision Series BINOMIAL THEOREM
The value of is b. c. d.
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37 32161
JEE Mains Super40 Revision Series BINOMIAL THEOREM
If are the binomial coefficient, then
equals b. c. d.
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38 32164
JEE Mains Super40 Revision Series BINOMIAL THEOREM
If then the value of
is b. c. d. none of these
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39 32167
JEE Mains Super40 Revision Series BINOMIAL THEOREM
If
b. c. d. none of these
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15
∑r= 1
r2r
(r + 2)!
(17) ! − 216
(17) !
(18) ! − 217
(18) !
(16) ! − 215
(16) !
(15) ! − 214
(15) !
^ C0,C 1,C 2,C n 2 × C1 + 23 × C 3 + 25 × C5 +3n + ( − 1)n
2
3n − ( − 1)n
2
3n + 1
2
3n − 1
2
(3 + x2008 + x2009)2010
= a0 + a1x + a2x2 + + anx
n,
a0 − a1 − a2 + a3 − a4 − a5 + a6 −1
2
1
2
1
2
1
232010 1 22010
(1 + x)n
= C0 + C1x + C2x2 + + Cnx
n, thenC0C2 + C1C3 + C2C4 + + Cn− 2Cn =(2n) !
(n !)2
(2n) !
(n − 1)!(n + 1)!
(2n) !
(n − 2)!(n + 2)!
40 32174
JEE Mains Super40 Revision Series BINOMIAL THEOREM
The number of real negative terms in the binomial expansion of isa. b. c. d.
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(1 + ix)4n− 2, n ∈ N , x > 0n n + 1 n − 1 2n