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ECAT Pre General Science Mathematics Chapter 10 Mathematical Induction Online Test MCQs With Answers
Question # 1
The sum of the odd coefficients in the expansion of (a + x)
4
is
Choose an answer
14
12
8
4
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Question # 2
The third term in the expansion of (1+2x) is
Choose an answer
-2x2
-4x2
2x2
4x2
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Question # 3
If n is any positive integer ,t hen 2+4+6+......+2 n=
Choose an answer
2
n
-1
2
n
+1
n
2
+1
n(n+1)
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Question # 4
There are two middle terms in the expansion of (a+x)n if n is
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Even +ve integer
+ve integer
Odd +ve integer
All
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Question # 5
The number of terms in the expansion of (a + x)
12
is
Choose an answer
13
12
11
10
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Question # 6
If n is add the expansion (a + x)
n
has middle terms
Choose an answer
2
3
4
5
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Question # 7
Choose an answer
n < 8/5
n < 5/8
|n| < 8/5
|n|>8/5
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Question # 8
The no of term is the expansion of (a+x)n-1 is
Choose an answer
n+1
n-1
n
n-2
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Question # 9
1st four terms of the expansion (1-x)
-2
are
Choose an answer
1 + 2x + 3x
2
+ 4x
3
3x
2
+ 2x + 1
1 + 3x + 4x
2
+ 5x
3
None of these
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Question # 10
In the expansion of (a + x)
n
the sum of exponents of a and x in each term of the expansion is
Choose an answer
n + 1
n - 1
n
2n
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Question # 11
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 # 12
There is no integer n for which 3
n
is
Choose an answer
Odd
even
Natural
Prime
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Question # 13
Digit in the unit place of the number 183! + 3
183
Choose an answer
7
6
3
0
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Question # 14
Choose an answer
Even
Odd
Prime
None of these
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Question # 15
For each natural number n, n (n+1) is
Choose an answer
an even
an odd
multiple of 3
Irrational
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Question # 16
The fifth term of (a+2x3)17 is
Choose an answer
4013 x3a13
2208a13 x12
223x7a18
38080a13 x12
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Question # 17
(1 - x)
3
= ______
Choose an answer
1 + 3x + 3x
2
+ x
3
1 + x + x
2
+ x
3
1 - x + x
2
- x
3
1 - 3x + 3x
2
- x
3
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Question # 18
The middle term(s) of (a+x)11 is
Choose an answer
6th term
6thor 7th
7th term
6thand7th
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Question # 19
Choose an answer
2
7
8
12
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Question # 20
The middle term of the expansion (1 + 2x)
6
is ______
Choose an answer
1st term
4th term
2nd term
5th term
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Question # 21
The 7th term of (3
8
+ 6
4
x)
11/4
is
Choose an answer
-19217/3 x
6
189/2 6
4
x
2227/12 x
3
-19712/3 x
6
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Question # 22
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 # 23
For≥ -2 , 1+3+5+......+(2n+5)
Choose an answer
(n+2)
2
(n-2)
2
2n+1
(n+3)
2
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Question # 24
n
C
2
= exists when n is ______
Choose an answer
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Question # 25
If n is any positive integer then n! > 2
n-1
for
Choose an answer
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Question # 26
The coefficient of x
10
in the expansion (x
3
+3/x
2
)
10
is
Choose an answer
1700
17023
17027
17010
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Question # 27
(x
3
-1/2x)
6
is
Choose an answer
15/16 x
2
2/13 x
2
17/7 x
2
16/15 x
2
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Question # 28
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 # 29
1+3x+6x2 +10x3 +....=
Choose an answer
(1+x)-3
(1-x)-2
(1-x)-3
(1+x)-2
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Question # 30
The last term of (1+2x)-2
Choose an answer
(-1)-2 (2x)-2
(-1)-4(-2x)-2
(-1)-3(2x)-3
Does not exist
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Question # 31
The middle term of [1/x-x]
10
is
Choose an answer
-152
-252
371
-421
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Question # 32
Choose an answer
ab=-1
ab = 1
ab = 2
None
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Question # 33
If n is any positive integer then n
2
> n + 3 for
Choose an answer
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Question # 34
The sum of coefficients in the binomial expansion equals to
Choose an answer
2
2
n+1
2
n-1
2
n
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Question # 35
The first three terms in the expansion of (1 + x)
-2
are ______
Choose an answer
1 - 2x + 3x
2
1 - 2x - 3x
2
1 + 2x + 3x
2
-2 -2x + 3x
2
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Question # 36
The sum of first n even number is
Choose an answer
n2
n(n+1)
n+1
n+2
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Question # 37
If n is any positive integer then 2
n
> 2(n + 1) is true for all
Choose an answer
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