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Mathematics ECAT Pre Engineering Chapter 10 Mathematical Inductions Online Test MCQs With Answers
Question # 1
The sum of the coefficient in the expansion of (a + x)
5
is
Choose an answer
32
16
8
5
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Question # 2
The coefficient of x
10
in the expansion (x
3
+3/x
2
)
10
is
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1700
17023
17027
17010
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Question # 3
The coefficient of the second term of (a+b)
4
is
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1
9
3
5
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Question # 4
The seventh term of (x3+1/x)8is
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71
-22
27
28
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Question # 5
The positive integer just greater than (1+0.0001)
10000
is
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4
5
2
3
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Question # 6
The middle term of (x-y)
8
is
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25 x
4
y
4
70 x
4
y
4
120 x
4
y
4
97x
4
y
4
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Question # 7
7
2n
+ 3
n-1
. 2
3n-3
is divisible by
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24
25
9
13
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Question # 8
For all positive integral value of n,3
n
< n! , when
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n> 6
n< 6
n<11
n>11
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Question # 9
The proposition S(n) for any n∈ N is only true if k∈ N and
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S(k +1) is true
S(1) is true and S(k+1) is true whenever S (k) is true
S(k+1) is true whenever S (k) is true
S(k) is true
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Question # 10
Choose an answer
28 / 81
28 / 243
81 / 28
243 / 82
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Question # 11
for n€ N, 3
2n + 7 is divisible by
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7
8
9
10
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Question # 12
If n is any positive integer then 2
n
> 2(n + 1) is true for all
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Question # 13
If n is any positive integer then n! > 2
n-1
for
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Question # 14
In the expansion of (a + x)
n
the general term T
r + 1
is
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Question # 15
If x+y+z+......+2n = 2n+1-1∀n∈W,then cube root of xyz is equal to
Choose an answer
1
4
2
8
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Question # 16
The proposition S(k+1) is true when ______ is true∀K∈N
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S(n)
S(k)
S(1)
S(k-1)
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Question # 17
For≥ -2 , 1+3+5+......+(2n+5)
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(n+2)
2
(n-2)
2
2n+1
(n+3)
2
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Question # 18
The term involving x
4
in the expansion (3-2x) is
Choose an answer
217x
4
15120x
4
313x
4
-25x
4
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Question # 19
n
2
- 1 divisible by 8 when n is
Choose an answer
an odd integer
an even integer
Irrational
Prime Number
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Question # 20
Choose an answer
10
C
6
10
C
5
10
C
4
None
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Question # 21
The first three terms in the expansion of (1 + x)
3
are
Choose an answer
1 + 3x +6x
2
1- 3x + 6x
2
\
-3 -3x -6x
2
1- 3x -6x
2
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Question # 22
If the expansion of (1 + x)
20
, then co-efficient of rth ad (r + 4)th term are equal, then r is
Choose an answer
7
8
9
10
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Question # 23
The expansion (1 + x)
-3
holds when
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|x| > 1
|x| < 1
x < 1
x > 1
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Question # 24
Choose an answer
Even
Odd
Prime
None of these
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Question # 25
If n is any positive integer then n
2
> n + 3 for
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Question # 26
The coefficient of xn in the expansion of (1-x)-1 is
Choose an answer
(-1)n2n
1
(-1)n(n+1)
(n+1)
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Question # 27
The term involving x4 the expansion (3-2x)7 is
Choose an answer
217 x4
15120x4
313x4
-25x4
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Question # 28
(0.90)
1/2
is equal to
Choose an answer
0.99
0.90
0.80
0.88
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Question # 29
The sum of the even coefficients in the expansion (1 + x)
n
is
Choose an answer
n
2
2
n-2
2
n-1
2
n
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Question # 30
If n is any positive integer then 3 + 6 + 9 + ....+ 3n = ______
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Question # 31
The sum even binomial coefficient of (3+2x)5 is ______term
Choose an answer
16
30
8
32
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Question # 32
If (1+x)
n
=C
0
+ C
1
x +C
2
x
2
+ ......+C
n
x
1
then C
0
C
2
+ C
1
C
3
+ C
2
C
4
+ .....+C
n-2
C
n
=
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Question # 33
The first three terms in the expansion of (1 + x)
-1
are
Choose an answer
1 + x + x
2
1 - x - x
2
-1 -x + x
2
1 - x + x
2
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Question # 34
(x3-1/x)12
Choose an answer
295
495
395
722
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Question # 35
There is no integer n for which 3
n
is
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Odd
even
Natural
Prime
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Question # 36
If the exponent in the binomial expansion is 6, then the middle term is
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2nd term
3rd term
4th term
5th term
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Question # 37
If (1+x-2x
3
)
6
= 1+a
1
x + a
2
x
2
+ a
3
x
3
+ ..... the the value of a
2
+ a
4
+ a
6
+ .....+a
12
will be
Choose an answer
32
31
64
1024
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