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JEE Questions for Maths Binomial Theorem And Mathematical Lnduction Quiz 2 - MCQExams.com
JEE
Maths
Binomial Theorem And Mathematical Lnduction
Quiz 2
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0%
0.2
0%
4.8
0%
1.02
0%
5.2
If (1 + χ )
15
= a
0
+ a
1
χ +...+ a
15
χ
15
, then
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0%
110
0%
115
0%
120
0%
135
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0%
± 1
0%
± 3
0%
± 4
0%
± 2
Middle term in the expansion
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0%
n!/(n!)2
0%
(2n)!/(n!)2
0%
(2n - n)!/n!
0%
(2n)!/n!
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0%
(n - 5)/6
0%
(n - 4)/5
0%
5/(n -4)
0%
6/(n - 5)
The 13th term in the expansion of
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0%
36
0%
37
0%
38
0%
39
In the expansion (1 - 3χ + 3χ
2
- χ
3
)
2n
, the middle term is
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0%
(n + 1)th term
0%
(2n + 1)th term
0%
(3n + 1)th term
0%
None of these
The coefficient of the middle term in the expansion of ( χ + 2y)
6
is
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0%
6C3
0%
8(6C
0%
8(6C
0%
6C4
0%
8(6C
The coefficient of the term independent of χ in the expansion of
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0%
210
0%
105
0%
70
0%
112
For |χ| < 1, the constant term in the expansion of
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0%
2
0%
1
0%
0
0%
-(1/2)
If m the expansion
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0%
6
0%
10
0%
9
0%
12
The greatest term in the expansion of
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0%
26840/9
0%
24840/9
0%
25840/9
0%
None of these
The coefficient of the middle term in the binomial expansion in powers of χ in expansion of (1 + αχ)
2
and (1 - αχ)
6
is the same, if α equals
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0%
-(5/3)
0%
10/3
0%
-(3/10)
0%
3/5
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0%
10
0%
5
0%
6
0%
4
0%
11
The term independent of χ in the expansion of
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0%
- 3
0%
0
0%
3
0%
1
The term independent of χ in the expansion of
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0%
5th term
0%
6th term
0%
11th term
0%
No term
The sum of coefficients in the expansion of
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0%
16 8C4
0%
8C4
0%
8C5
0%
None of these
The middle term in the expansion of
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0%
18C9
0%
-18C9
0%
18C10
0%
-18C10
The value of (
n
C
1
)
2
+ (
n
C
2
)
2
+ (
n
C
3
)
2
+...+(
n
C
n
)
2
is
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0%
(2nCn)2
0%
2nCn
0%
2nCn + 1
0%
2nCn - 1
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0%
0%
2)
0%
0%
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0%
0%
2)
0%
0%
None of these
If n is an integer with 0 ≤ n ≤ 11, then the minimum value of n!(11 -! is attained, when a value of n equals
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0%
11
0%
5
0%
7
0%
9
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0%
0%
2)
0%
0%
None of these
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0%
5
0%
10
0%
15
0%
20
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0%
0%
2)
0%
0%
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0%
4
0%
8
0%
16
0%
32
If the binomial coefficients of (3r)th and (r+2)th terms in the binomial expansion of (1 + χ )
2n
are equal, then
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0%
n = r
0%
n = r + 1
0%
n = 2r
0%
n = 2r - 1
If
n
C
4
,
n
C
5
, and
n
C
6
are in AP, then n is
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0%
7 or 14
0%
7
0%
14
0%
14 or 21
15
C
3
+
15
C
5
+ ...+
15
C
15
is equal to
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0%
214
0%
214 - 15
0%
214 + 15
0%
214 - 1
If C
0
, C
1
,...C
n
denote the binomial coefficients in the expansion of (1 + χ)
n
. Then, the value of C
1
- 2C
2
+ 3C
3
- 4C
4
+ ....(up to n terms) is
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0%
2n
0%
2-n
0%
0
0%
1
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0%
Statement I is correct, Statement II is corrrect; Statement II is correct explanation for Statement I
0%
Statement I is correct, Statement II is corrrect; Statement II is not a correct explanation for Statement I
0%
Statement I is correct, Statement II is incorrect;
0%
Statement I is incorrect, Statement II is correct;
If the sum of the coefficients in the expansion of (a
2
χ
2
- 6aχ + 11 )
10
, where a is constant is 1024, then the value of a is
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0%
5
0%
1
0%
2
0%
3
0%
4
15
C
0
.
5
C
5
+
15
C
1
.
5
C
4
+
15
C
2
.
5
C
3
+
15
C
3
.
5
C
2
+
15
C
4
.
5
C
1
is equal to
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0%
220 - 25
0%
20! / 5! 15!
0%
(20!/5! 15!) - 1
0%
0%
15! / 5! 10!
The value of
15
C
8
+
15
C
9
–
15
C
6
–
15
C
7
is
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0%
– 1
0%
0
0%
1
0%
None of these
8
C
0
/ 6 –
8
C
1
+
8
C
2
. 6 –
8
C
3
. 6
2
+...+
8
C
8
. 6
7
is equal to
Report Question
0%
0
0%
67
0%
68
0%
58/6
The value of sum of the series 3 .
n
C
0
– 8
n
C
1
+ 13
n
C
2
– 18
n
C
3
+ ... up to (n +terms is
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0%
0
0%
3n
0%
5n
0%
None of these
Coefficient of t
24
in (1 +t
2
)
12
(1+t
12
) (1 + t
24
) is
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0%
0%
2)
0%
0%
If (1 + χ)
n
= C
0
+ C
1
χ + C
2
χ
2
+ ... + C
n
χ
n
. Then, C
0
C
1
+ C
1
C
2
+ ...+C
n –1
C
n
is equal to
Report Question
0%
0%
2)
0%
0%
None of these
If (1 + χ – 3χ
2
)
10
= 1 + a
1
χ +a
2
χ
2
+ a
20
χ
20
, then a
2
+ a
4
+ a
6
+ ..+ a
20
is equal to
Report Question
0%
0%
2)
0%
0%
If C
0
, C
1
, C
2
.., C
n
denote the binomial coefficients in the expansion of (1 + χ)
n
, then
Report Question
0%
0%
2)
0%
0%
If n = 5, then (
n
C
0
)
2
+ (
n
C
1
)
2
+ (
n
C
2
)
2
+ ...+ (
n
C
5
)
2
Report Question
0%
250
0%
254
0%
245
0%
252
0%
258
For natural numbers and m and n , if (1 – y)
m
(1 + y)
n
= 1 + a
1
y + a
2
y
2
+ ...and a
1
= a
2
= 10, then (m , n) is
Report Question
0%
(35 , 20)
0%
(45 , 35)
0%
(35 , 45)
0%
(20 , 45)
If
18
C
15
+ 2(
18
C
16
) +
17
C
16
+ 1 =
n
C
3
, then n is equal to
Report Question
0%
19
0%
20
0%
8
0%
24
0%
21
The value of 1
2
. C
1
+ 3
2
. C
3
+ 5
2
. C
5
+ ... is
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0%
n(n – 1)n–2 + n . 2n–1
0%
n(n – 1)2n-2
0%
n(n –1)2n–3
0%
None of these
If C
1
, C
2
, C
3
are the usual binomial coefficients and S = C
1
+ 2C
2
+ 3C
3
+ ...+nC
n
, then S equals
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0%
n 2n
0%
2n –1
0%
n 2 n –1
0%
2n + 1
The sum of the coefficients in the expansion of (1 + χ - 3χ
2
)
3148
is
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0%
8
0%
7
0%
1
0%
- 1
If n is an integer greater than 1, then a -
n
C
1
(a -+
n
C
2
(a -+ ...+ (- 1)
n
(a - n) is equal to
Report Question
0%
a
0%
0
0%
a2
0%
2n
20
C
4
+ 2 .
20
C
3
+
20
C
2
-
22
C
18
is equal to
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0%
0
0%
1242
0%
7315
0%
6345
If (1 + 2
x
+ 3
x
2
)
10
= a
0
+ a
1
x
+ a
2
x
2
+ ...+ a
20
x
20
, then a
1
equals
Report Question
0%
10
0%
20
0%
210
0%
None of these
The number of terms in the expansion of (a + b + c)
10
is
Report Question
0%
11
0%
21
0%
55
0%
66
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