Home
Class 11
MATHS
Let P(n) denote the statement that n^(2)...

Let `P(n)` denote the statement that `n^(2) +n` is odd. It is seen that `P(n) rArr P(n+1), P(n)` is true for all

A

`n gt 1`

B

`n`

C

`n gt 2`

D

no value of n

Text Solution

Verified by Experts

The correct Answer is:
D
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • MATHEMATICAL INDUCTION

    AAKASH SERIES|Exercise PRACTICE SHEET (EXERCISE-I) LEVEL-I (Principle of Mathematical Induction) (Straight Objective Type Questions)|55 Videos

  • LOCUS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|37 Videos

  • MATRICES

    AAKASH SERIES|Exercise LINEAR EQUATIONS - PRACTICE EXERCISE|15 Videos

Similar Questions

Explore conceptually related problems

A coin has probability p of showing head when tossed. It is tossed n times. Let P_(n) denote the probabilty that no two (or more) consecutive heads occur. Prove that P_(1) = 1, P_(2) = 1 - P^(2) and P_(n) = (1 -P) P_(n-1) + P(1 - P) P_(n-2) for all n ge 3 .

Let f: N toN be defined by f (n) = {{:((n +1)/( 2 ), if n " is odd" ), ( (n)/(2), "if n is even "):} for all n in N. State whether the function f is bijective. Justify your answer.

Knowledge Check

  • If P(n) be the statement n (n+1)+1 is an integer, then which of the following is even

    A
    `P(4)`
    B
    `P(4) +2`
    C
    `P(4) + 4`
    D
    `P(4) +1`

  • A student was asked to prove a statement by induction. He proved (i) P(5) is true and (ii) truth of P(n) rArr truth of P(n+1), n in N . On the basis of this, he could conclude that P(n) is true

    A
    for no `n in N`
    B
    for all `n ge 5, n in N`
    C
    for all `n in N`
    D
    for all `n ge 1, n in N`

  • Let P(n) : 1+ (1)/(4) + (1)/(9) + …. + (1)/(n^2) lt 2 - (1)/( n) is true for

    A
    `AA in in N`
    B
    `n =1`
    C
    `n gt 1, AA n in N`
    D
    `n gt 2`

    • Similar Questions

    Explore conceptually related problems

    The statement P(n) (1xx1!) + (2 xx2!) + (3 xx 3!) + … …. + (nxx n!) = (n+1)! - 1 is

    If a is any set such that n [P (A) ] = 64 , then n(A) =

    If P_1, P_2, P_3 ,………, P_n are n points on the line y = x all lying in the first quadrant, such that (OP_n) = n (OP_(n-1) ) (O is origin ) , OP_1 = and P_n = (2520 sqrt2 , 2520 sqrt2) , then n =

    If 0 < p

    Let n in N . If (1 + x)^n = a_0 + a_1 x + a_2x^2+…. + a_nx^n and a_(n-3), a_(n-2) , a_(n-1) are in A.P then Statement - I : a_1, a_2, a_3 are in A.P. Statement -II : n = 7 The true statements are :

    Home
    Profile