Home
Class 12
MATHS
Let S = {1, 2, 3, 4, 5, 6, 7, 8,9,10}. D...

Let S = {1, 2, 3, 4, 5, 6, 7, 8,9,10}. Define `f : S to S`as
`f(n) = {{:(2n",",if,n=1", 2, 3, 4, 5"),(2n-11",",if," n=6,7,8,9,10"):}`
Let `g : S to S` be a function such that `fog(n) = {{:(n + 1",",if,"n is odd"),(n - 1",",if,"n is even"):}`
Then `g(10) (g(1) + g(2) + g(3) + g(4) + g(5))` is equal to _______ .

Text Solution

AI Generated Solution

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • JEE MAINS 2022

    JEE MAINS PREVIOUS YEAR|Exercise MATHEMATICS (SECTION - A)|20 Videos

  • JEE MAINS 2021

    JEE MAINS PREVIOUS YEAR|Exercise Mathematics (Section A )|20 Videos

  • JEE MAINS 2023 JAN ACTUAL PAPER

    JEE MAINS PREVIOUS YEAR|Exercise Question|360 Videos

Similar Questions

Explore conceptually related problems

IF A ={1,3,5,2,4,1,3,5,7,8,9,6,10} , then n(A) = ________.

Let S_n = 1 (n - 1) + 2. (n -2) + 3. (n - 3) +…+ (n -1).1, n ge 4. The sum sum_(n = 4)^oo ((2S_n)/(n!) - 1/((n - 2)!)) is equal to :

Knowledge Check

  • If A= {1,3,5,2,4,1,3,5,7,8,9,6,10}, then n(A) =________.

    A
    13
    B
    8
    C
    10
    D
    9

  • If S_(n) = sum_(n=1)^(n) (2n + 1)/(n^(4) + 2n^(3) + n^(2)) then S_(10) is less then

    A
    `0`
    B
    `1`
    C
    `2`
    D
    `3`

  • If f:NrarrZ defined as f(n)={{:((n-1)/(2),":"," if n is odd"),((-n)/(2),":", " if n is even"):} and g:NrarrN defined as g(n)=n-(-1)^(n) , then fog is (where, N is the set of natural numbers and Z is the set of integers)

    A
    one - one and onto
    B
    one - one and into
    C
    many - one and onto
    D
    many - one and into

    • Similar Questions

    Explore conceptually related problems

    Let S_n = 1 (n - 1) + 2. (n -2) + 3. (n - 3) +…+ (n -1).1, n ge 4. The sum sum_(n = 4)^oo ((2S_n)/(n!) - 1/((n - 2)!)) is equal to :

    Let g(x)= x^6 + ax^5 + bx^4 + cx^3+dx^2 + ex + f be a polynomial such that g(1) = 1, g(2) = 2, g(3) = 3,g(4) = 4,g(5) = 5 and g(6) = 6 . And if g(7) = n then find n

    Let S= {1,2,3,4 5,6, 7} . Then the number of possible functions f: S rarr S such that f(m.n)= f(m).f(n) for every m, n in S and m.n in S is equal to ____

    Let f:N rarr R and g:N rarr R be two functions and f(1)=08,g(1)=0.6f(n+1)=f(n)cos(g(n))-g(n)sin(g(n)) and g(n+1)=f(n)sin(g(n))+g(n)cos(g(n)) for n>=1.lim_(n rarr oo)f(n) is equal to

    Let N be the set of numbers and two functions f and g be defined as f,g:N to N such that f(n)={((n+1)/(2), ,"if n is odd"),((n)/(2),,"if n is even"):} and g(n)=n-(-1)^(n) . Then, fog is (A) one-one but not onto (B) onto but not one-one (C) both one-one and onto (D) neither one-one nor onto

    Home
    Profile