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Relations and Functions (Class 12)

JEE Main 2025 (Online) 28th January Evening ShiftMCQMedium📈 Topic in 17% papers+4−1
Ques. 1JEE Main 2025, 28 January (Evening Shift)

Let f : [0, 3] A be defined by f(x) = 2x3 - 15x2 + 36x + 7 and g : [0, ) B be defined by g(x) = x2025x2025 + 1. If both the functions are onto and S = \x Z; x A or x B\, then n(S) is equal to :

  1. 29
  2. 31
  3. 30
  4. 36

Answer

(3) 30

Solution

Since f and g are onto, A = range of f and B = range of g.

f'(x) = 6x2 - 30x + 36 = 6(x - 2)(x - 3)

f increases on [0, 2] and decreases on [2, 3].

f(0) = 7, f(2) = 16 - 60 + 72 + 7 = 35, f(3) = 54 - 135 + 108 + 7 = 34

A = [7, 35] integers 7, 8, …, 35: 29 integers

g(x) = 1 - 1x2025 + 1 increases from g(0) = 0 towards 1 (never reaching 1)

B = [0, 1) only integer 0

n(S) = 29 + 1 = 30

Answer: (3)

Keep practising — Relations and Functions (Class 12)

Ques. 2JEE Main 2025, 24 January (Morning Shift)

Let f:R-\0\ be a function such that f(x)-6f ( 1x )= 353x- 52. If x 0 ( 1 x+f(x) )= ; , , then +2 is equal to

  1. 6
  2. 5
  3. 3
  4. 4
Ques. 3JEE Main 2025, 24 January (Morning Shift)

Let f(x)= 2x+2+1622x+1+2x+4+32. Then the value of 8 (f ( 115 )+f ( 215 )+ +f ( 5915 ) ) is equal to

  1. 108
  2. 92
  3. 118
  4. 102
Ques. 4JEE Main 2025, 24 January (Evening Shift)

The function f:(- , ) (- ,1), defined by f(x)= 2x-2-x2x+2-x is :

  1. One-one but not onto
  2. Onto but not one-one
  3. Both one-one and onto
  4. Neither one-one nor onto
Ques. 5JEE Main 2025, 24 January (Evening Shift)

Number of functions f:\1,2, ,100\ \0,1\, that assign 1 to exactly one of the positive integers less than or equal to 98, is equal to .

Ques. 6JEE Main 2025, 23 January (Morning Shift)

Let R=\(1,2),(2,3),(3,3)\ be a relation defined on the set \1,2,3,4\. Then the minimum number of elements, needed to be added in R so that R becomes an equivalence relation, is:

  1. 9
  2. 8
  3. 7
  4. 10
Ques. 7JEE 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
Ques. 8JEE 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. 9JEE 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. 10JEE 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. 11JEE 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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All JEE Main Mathematics chapters
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