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Relations and Functions (Class 12)

JEE Main 2024 (Online) 29th January Morning ShiftMCQEasy📈 Topic in 48% papers+4−1
Ques. 1JEE Main 2024, 29 January (Morning Shift)

Let R be a relation on Z Z defined by (a, b)R(c, d) if and only if ad-bc is divisible by 5. Then R is

  1. Reflexive and transitive but not symmetric
  2. Reflexive and symmetric but not transitive
  3. Reflexive but neither symmetric nor transitive
  4. Reflexive, symmetric and transitive

Answer

(2) Reflexive and symmetric but not transitive

Solution

Reflexive: ab-ba=0, divisible by 5 (a,b)R(a,b)

Symmetric: 5 (ad-bc) 5 (cb-da) (c,d)R(a,b)

Transitive: (3,1)R(10,5) ∵ 3 5-1 10=5

and (10,5)R(1,1) ∵ 10 1-5 1=5

but 3 1-1 1=2 (3,1) is not related to (1,1) not transitive

∴ R is reflexive and symmetric but not transitive

Answer: (2)

Keep practising — Relations and Functions (Class 12)

Ques. 2JEE 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]
Ques. 3JEE 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. 4JEE 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. 5JEE 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. 6JEE 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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