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Relations and Functions (Class 12)

JEE Main 2024 (Online) 29th January Morning ShiftMCQMedium📈 Topic in 10% papers+4−1
Ques. 1JEE Main 2024, 29 January (Morning Shift)

If f(x)= cases2+2x, & -1 x<0\ 1- x3, & 0 x 3 cases; g(x)= cases-x, & -3 x 0\ x, & 0<x 1 cases, then range of (f g)(x) is

  1. [0,1)
  2. [0,3)
  3. (0,1]
  4. [0,1]

Answer

(4) [0,1]

Solution

-3 x 0: g(x)=-x [0,3]; 0<x 1: g(x)=x (0,1]

∴ g(x) [0,3] always use f(u)=1- u3

(f g)(x)= cases1+ x3, & -3 x 0\ 1- x3, & 0<x 1 cases

[figure]

Values run from 0 (at x=-3) to 1 (at x=0), every value in between taken

∴ Range =[0,1]

Answer: (4)

Keep practising — Relations and Functions (Class 12)

Ques. 2JEE Main 2024, 29 January (Evening Shift)

If R is the smallest equivalence relation on the set \1,2,3,4\ such that \(1,2),(1,3)\ , then the number of elements in R is .

  1. 15
  2. 10
  3. 12
  4. 8
Ques. 3JEE Main 2024, 27 January (Morning Shift)

Let S=\1,2,3, ,10\. Suppose M is the set of all the subsets of S, then the relation R=\(A, B):A B ; A, B M\ is :

  1. symmetric only
  2. reflexive only
  3. symmetric and reflexive only
  4. symmetric and transitive only
Ques. 4JEE Main 2024, 27 January (Morning Shift)

The function f:N-\1\ ; defined by f(n)= the highest prime factor of n, is :

  1. one-one only
  2. neither one-one nor onto
  3. onto only
  4. both one-one and onto
Ques. 5JEE Main 2024, 27 January (Evening Shift)

Let f:R- \ -12 \ and g:R- \ -52 \ be defined as f(x)= 2x+32x+1 and g(x)= |x|+12x+5. Then, the domain of the function fog is :

  1. R- \- 74 \
  2. R
  3. R- \- 52,- 74 \
  4. R- \- 52 \

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All JEE Main Mathematics chapters
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