Principle Of Mathematical Induction(11th And 12th > Mathematics ) Questions and Answers
Explanation:-
Answer: Option D. ->
None of these
:
D
P(n) = n2 + n. It is always odd (statement) but
square of any odd number is always odd and
also, sum of odd number is always even. So
for no any 'n' for which this statement is true.
Explanation:-
Answer: Option D. ->
n≥ 3
:
D
Check through option, condition (n!)2 > nn is
true when n ≥ 3.
Explanation:-
Answer: Option C. ->
n≥ 4
:
C
Check through option, the condition 3n > n3 is
true when n ≥ 4.
Explanation:-
Answer: Option B. ->
n≥ 1
:
B
Check through option, the condition
(n+12)n ≥ n ! is true for n ≥ 1.
Explanation:-
Answer: Option B. ->
n≥ 5
:
B
Check through option, the condition
10n−2 > 81n is satisfied if n ≥ 5.
Explanation:-
Answer: Option B. ->
n≥ 4
:
B
Check through option, the condition 2n < n! is
true when n ≥ 4.
Explanation:-
Answer: Option B. ->
6
:
B
n(n2−1) = (n - 1)(n)(n + 1)
It is product of three consecutive natural
numbers, so according to Langrange's theorem
it is divisible by 3 ! i.e., 6.
Explanation:-
Answer: Option B. ->
n<2n
:
B
Let n = 1 then option (a) and (d) is eliminated.
Equality can't be attained for any value of n so,
option (b) satisfied.
Explanation:-
Answer: Option A. ->
25
:
A
Putting n = 1 in 72n+23n−3.3n−1
=50, divisible by 25
Explanation:-
Answer: Option A. ->
x + y
:
A
x2n−1+y2n−1 is always contain equal odd power.
So it is always divisible by x + y.