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Relations and Functions

JEE Main 2025 (Online) 2nd April Evening ShiftMCQMedium📈 Topic in 9% papers+4−1
Ques. 1JEE Main 2025, 2 April (Evening Shift)

Let A = \1, 2, 3, , 100\ and R be a relation on A such that R = \(a, b) : a = 2b + 1\. Let (a1, a2), (a2, a3), (a3, a4), , (ak, ak+1) be a sequence of k elements of R such that the second entry of an ordered pair is equal to the first entry of the next ordered pair. Then the largest integer k, for which such a sequence exists, is equal to :

  1. 6
  2. 8
  3. 7
  4. 5

Answer

(4) 5

Solution

(ai, ai+1) R means ai = 2ai+1 + 1, i.e. ai + 1 = 2(ai+1 + 1), so repeating this,

a1 + 1 = 2k(ak+1 + 1)

ak+1 1 and a1 100, 2k(ak+1 + 1) 101

2k 2 101 2k+1 101 k + 1 6 k 5

k = 5 is possible: (63, 31), (31, 15), (15, 7), (7, 3), (3, 1).

largest k = 5

Answer: (4)

Keep practising — Relations and Functions

Ques. 2JEE Main 2025, 2 April (Evening Shift)

If the domain of the function f(x) = 1 10 + 3x - x2 + 1 x + |x| is (a, b), then (1 + a)2 + b2 is equal to :

  1. 29
  2. 30
  3. 25
  4. 26
Ques. 3JEE Main 2025, 29 January (Evening Shift)

Let S = N \0\. Define a relation R from S to R by : R = \(x, y) : e y = x e ( 25 ), x S, y R \. Then, the sum of all the elements in the range of R is equal to :

  1. 32
  2. 109
  3. 52
  4. 53
Ques. 4JEE Main 2025, 29 January (Evening Shift)

If the domain of the function 5(18x - x2 - 77) is ( , ) and the domain of the function (x-1) ( 2x2 + 3x - 2x2 - 3x - 4 ) is ( , ), then 2 + 2 + 2 is equal to:

  1. 186
  2. 179
  3. 195
  4. 174
Ques. 5JEE Main 2025, 28 January (Morning Shift)

Let f : R R be a function defined by f(x) = (2 + 3a)x2 + ( a+2a-1 )x + b, a 1. If f(x + y) = f(x) + f(y) + 1 - 27xy, then the value of 28 i=15|f(i)| is

  1. 735
  2. 675
  3. 715
  4. 545
Ques. 6JEE Main 2025, 24 January (Evening Shift)

The number of real solution(s) of the equation x2+3x+2= \|x-3|,|x+2|\ is :

  1. 2
  2. 3
  3. 1
  4. 0
Ques. 7JEE Main 2025, 23 January (Morning Shift)

Let f(x)= e x and g(x)= x4-2x3+3x2-2x+22x2-2x+1. Then the domain of f g is

  1. (0, )
  2. [1, )
  3. R
  4. [0, )
Ques. 8JEE Main 2025, 22 January (Morning Shift)

The product of all solutions of the equation e5( ex)2+3=x8, x>0, is :

  1. e2
  2. e
  3. e6/5
  4. e8/5
Ques. 9JEE Main 2024, 6 April (Evening Shift)

Let f(x) = 17 - 5x be a function defined on R. Then the range of the function f(x) is equal to :

  1. [ 18, 15 ]
  2. [ 17, 16 ]
  3. [ 17, 15 ]
  4. [ 18, 16 ]
Ques. 10JEE Main 2024, 5 April (Morning Shift)

If S = \a R : |2a - 1| = 3[a] + 2\a\\, where [t] denotes the greatest integer less than or equal to t and \t\ represents the fractional part of t, then 72 a S a is equal to .

Ques. 11JEE Main 2024, 4 April (Morning Shift)

If the domain of the function -1 ( 3x-222x-19 )+ e ( 3x2-8x+5x2-3x-10 ) is ( , ], then 3 +10 is equal to:

  1. 95
  2. 100
  3. 97
  4. 98

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All JEE Main Mathematics chapters
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