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ECAT Pre General Science Mathematics Chapter 10 Mathematical Induction Online Test MCQs With Answers
Question # 1
Choose an answer
2
7
8
12
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Question # 2
The middle term in the expansion of (a +x)
12
is
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7th
8th
9th
6th
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Question # 3
The seventh term of (x3+1/x)8is
Choose an answer
71
-22
27
28
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Question # 4
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 # 5
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 # 6
n! > 2
n
-1 is true when
Choose an answer
n≤ 3
n≤ 6
n≥ 4
n≤ 6
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Question # 7
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 # 8
The general term in the expansion of (a+x)n is
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(r-1)th term
(r+1)th term
rth term
none
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Question # 9
If n is add the expansion (a + x)
n
has middle terms
Choose an answer
2
3
4
5
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Question # 10
The sum of the cubes of three consecutive natural number is divisible by
Choose an answer
9
6
5
10
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Question # 11
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 # 12
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 # 13
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 # 14
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 # 15
The greatest term in the expansion of (3+2x)
9
, when x=1 is
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4th
4th and 5th
5th
6th
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Question # 16
The first three terms in the expansion of (1 - x)
-2
are
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1 - 2x + 3x
2
1 - 2x - 3x
2
1 + 2x + 3x
2
-2 - 2x +3x
2
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Question # 17
The number of terms in the expansion of (a + x)
12
is
Choose an answer
13
12
11
10
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Question # 18
Choose an answer
2 and 9
3 and 2
2/3 and 9
3/2 and 6
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Question # 19
Choose an answer
n
C
r
n+1
C
r+1
n
C
r+1
None
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Question # 20
The term involving x4 the expansion (3-2x)7 is
Choose an answer
217 x4
15120x4
313x4
-25x4
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Question # 21
The sum of co-efficient in (1+x-3x
2
)
4163
is
Choose an answer
0
1
-1
None
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Question # 22
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 # 23
If n is odd then the middle terms in the expansion of (a + x)
n
are
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Question # 24
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 # 25
(0.90)
1/2
is equal to
Choose an answer
0.99
0.90
0.80
0.88
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Question # 26
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 # 27
The coefficient of the second term of (a+b)
4
is
Choose an answer
1
9
3
5
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Question # 28
(1 + 2x)
4
= ______
Choose an answer
1 + 4x + 6x
2
+ 4x
3
+ x
4
1 - 4x + 6x
2
- 4x
3
+ x
4
1 - 8x + 24x
2
- 32x
3
+ 16x
4
1 + 8x+ 24x
2
+ 32x
3
+ 16x
4
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Question # 29
The expansion of (1 - 3x)
-1
is valid if
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| x | < 1
| x | < 3
| x | < 1/3
None of these
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Question # 30
The middle term of (x-y)
8
is
Choose an answer
25 x
4
y
4
70 x
4
y
4
120 x
4
y
4
97x
4
y
4
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Question # 31
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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Question # 32
The fifteenth term of (3-a)
15
is
Choose an answer
-17a
12
-945a
13
-941a
13
-515a
12
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Question # 33
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 # 34
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 # 35
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 # 36
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 # 37
If a statement S(n) is true for n = 1 and the truth of S(n) for n = k implies the truth of S(n) for = k + 1, then S(n) is true for all
Choose an answer
Real numbers n
Integers n
Positive integers n
None of these
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