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Mathematics ECAT Pre Engineering Chapter 10 Mathematical Inductions Online Test MCQs With Answers
Question # 1
The expansion of (1 - 3x)
-1
is valid if
Choose an answer
| x | < 1
| x | < 3
| x | < 1/3
None of these
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Question # 2
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 # 3
The third term in the expansion of (1+2x) is
Choose an answer
-2x2
-4x2
2x2
4x2
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Question # 4
For all positive integral value of n,3
n
< n! , when
Choose an answer
n> 6
n< 6
n<11
n>11
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Question # 5
Choose an answer
405 / 256
504 / 259
450 / 263
None
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Question # 6
The term independent of x is the expansion (x
3
+1/x)
12
Choose an answer
295
495
395
722
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Question # 7
If the sum of even coefficients in the expansion of (1+x)n is 128 then
Choose an answer
n=7
n=9
n=8
None
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Question # 8
There is no integer n for which 3
n
is
Choose an answer
Odd
even
Natural
Prime
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Question # 9
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 # 10
Choose an answer
2
7
8
12
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Question # 11
The coefficient of the second term of (a+b)
4
is
Choose an answer
1
9
3
5
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Question # 12
If n is any positive integer then 4
n
>3
n
+ 4 is true for all
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Question # 13
(51)
4
is equal to
Choose an answer
7065201
8065201
6765201
6565201
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Question # 14
If n is any positive integer then 3 + 6 + 9 + ....+ 3n = ______
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Question # 15
The fifth term of (a+2x3)17 is
Choose an answer
4013 x3a13
2208a13 x12
223x7a18
38080a13 x12
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Question # 16
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 # 17
The proposition S(k+1) is true when ______ is true∀K∈N
Choose an answer
S(n)
S(k)
S(1)
S(k-1)
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Question # 18
In the expansion of (x+y)n the coefficient of 5th and 12th terms are equal then n=
Choose an answer
12
n=14
17
n=15
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Question # 19
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 # 20
If the 4th term in the expansion of (px + x
-1
)
m
is 2.5 for all x
∈ R, then
Choose an answer
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Question # 21
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 # 22
The seventh term of (x3+1/x)8is
Choose an answer
71
-22
27
28
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Question # 23
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 # 24
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 # 25
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 # 26
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 # 27
The number of terms in the expansion of (a + b)
9
is
Choose an answer
10
11
9
12
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Question # 28
If the sum of co-efficient in the expansion of (a+b)
n
is 4096, then the greatest co-efficient in the expansion is
Choose an answer
1594
792
924
2924
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Question # 29
Number of terms in the expansion of (a+x)
n
is
Choose an answer
n - 1
n + 1
n + 2
n + 3
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Question # 30
For every positive integers n 1+5+9+....+ (4n - 3) is
Choose an answer
n(2n - 1)
(2n - 1)
n - 1
n
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Question # 31
In the expansion of (a + x)
n
the general term T
r + 1
is
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