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Relations and Functions (Class 12)

JEE Main 2025 (Online) 23rd January Evening ShiftMCQEasy📈 Topic in 47% papers+4−1
Ques. 1JEE Main 2025, 23 January (Evening Shift)

Let X=R . Define a relation R on X as : (a1,b1)R(a2,b2) b1=b2 In the light of the above statements, choose the correct answer from the options given below :

  1. Both Statement I and Statement II are true
  2. Statement I is true but Statement II is false
  3. Both Statement I and Statement II are false
  4. Statement I is false but Statement II is true

Answer

(2) Statement I is true but Statement II is false

Solution

R, "same second coordinate", is reflexive (b1=b1), symmetric and transitive (equality of b) equivalence relation: Statement I true.

[figure]

Related points of (a,b) are all (x,y) with y=b: the horizontal line y=b (slope 0), never parallel to y=x (slope 1).

Statement II false.

Answer: (2)

Keep practising — Relations and Functions (Class 12)

Ques. 2JEE Main 2025, 22 January (Morning Shift)

Let f(x) be a real differentiable function such that f(0)=1 and f(x+y)=f(x)f'(y)+f'(x)f(y) for all x,y . Then n=1100 ef(n) is equal to :

  1. 2406
  2. 5220
  3. 2525
  4. 2384
Ques. 3JEE Main 2025, 22 January (Morning Shift)

The number of non-empty equivalence relations on the set \1,2,3\ is :

  1. 7
  2. 4
  3. 5
  4. 6
Ques. 4JEE Main 2025, 22 January (Evening Shift)

Let A=\1,2,3,4\ and B=\1,4,9,16\. Then the number of many-one functions f:A B such that 1 f(A) is equal to :

  1. 151
  2. 139
  3. 163
  4. 127
Ques. 5JEE Main 2025, 22 January (Evening Shift)

Let A=\1,2,3\. The number of relations on A, containing (1,2) and (2,3), which are reflexive and transitive but not symmetric, is .

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