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Relations and Functions (Class 12)

JEE Main 2025 (Online) 22nd January Morning ShiftMCQMedium📈 Topic in 29% papers+4−1
Ques. 1JEE 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

Answer

(3) 2525

Solution

x=y=0: 1=2f'(0) f'(0)= 12

y=0: f(x)= 12f(x)+f'(x) f'(x)= 12f(x) f(x)=ex/2

ef(n)= n2

n=1100 n2= 12 100 1012=2525

Answer: (3)

Keep practising — Relations and Functions (Class 12)

Ques. 2JEE 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. 3JEE 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. 4JEE 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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