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ECAT Pre General Science Mathematics Chapter 10 Mathematical Induction Online Test MCQs With Answers
Question # 1
n! > 2
n
-1 is true when
Choose an answer
n≤ 3
n≤ 6
n≥ 4
n≤ 6
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Question # 2
(x3-1/x)12
Choose an answer
295
495
395
722
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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
The third term in the expansion of (1+2x) is
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-2x2
-4x2
2x2
4x2
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Question # 5
The sum of coefficients in the binomial expansion equals to
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2
2
n+1
2
n-1
2
n
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Question # 6
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n < 8/5
n < 5/8
|n| < 8/5
|n|>8/5
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Question # 7
If n is not natural number, then the expansion (1 + x)
n
is valid for
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Question # 8
The term involving x4 the expansion (3-2x)7 is
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217 x4
15120x4
313x4
-25x4
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Question # 9
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 # 10
Number of terms in the expansion of (a+x)
n
is
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n - 1
n + 1
n + 2
n + 3
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Question # 11
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 # 12
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2 and 9
3 and 2
2/3 and 9
3/2 and 6
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Question # 13
(0.90)
1/2
is equal to
Choose an answer
0.99
0.90
0.80
0.88
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Question # 14
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 # 15
If n is any positive integer then n! > n
2
for
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Question # 16
If n € N , then n(n+3) is always
Choose an answer
Multiple of 3
Multiple of 6
odd
even
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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
If the 4th term in the expansion of (px + x
-1
)
m
is 2.5 for all x
∈ R, then
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Question # 19
The no of term is the expansion of (a+x)n-1 is
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n+1
n-1
n
n-2
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Question # 20
The exponent of x in 10th term in the expansion of (a+x)n
Choose an answer
10
12
11
9
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Question # 21
The proposition S(n) for any n∈ N is only true if k∈ N and
Choose an answer
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 # 22
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 # 23
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 # 24
The number of terms in the expansion of (a + x)
12
is
Choose an answer
13
12
11
10
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Question # 25
Choose an answer
28 / 81
28 / 243
81 / 28
243 / 82
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Question # 26
for n€ N, 3
2n + 7 is divisible by
Choose an answer
7
8
9
10
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Question # 27
n
C
2
= exists when n is ______
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Question # 28
If n is any positive integer then 4
n
>3
n
+ 4 is true for all
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Question # 29
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 # 30
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 # 31
Choose an answer
n
C
r
n+1
C
r+1
n
C
r+1
None
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Question # 32
The sum of co-efficient in (1+x-3x
2
)
4163
is
Choose an answer
0
1
-1
None
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Question # 33
The fifteenth term of (3-a)
15
is
Choose an answer
-17a
12
-945a
13
-941a
13
-515a
12
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Question # 34
The coefficient of the third term of (8a-b)
1/3
, after simplification is
Choose an answer
-228
1/288
1/220
-1/177
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Question # 35
The coefficient of the second term of (a+b)
4
is
Choose an answer
1
9
3
5
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Question # 36
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 # 37
When we expand (a + 2b)
5
then
Choose an answer
a
5
+ 10a
4
b + 40a
3
b
2
+ 80a
2
b
3
+ 80ab
4
+ 32b
5
a
5
+ a
4
b + a
3
b
2
+ a
2
b
3
+ ab
4
+ b
5
5a
5
+ 4a
4
b + 3a
3
b
2
+ 2a
2
b
3
+ 1 ab
4
+ b
5
None
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