The total number of functions, f: {1, 2, 3, 4} → {1, 2, 3, 4, 5, 6} such that f(1) + f(2) = f(3), is equal to

(A) 60

(B) 90

(C) 108

(D) 126

## Solution:

Tip for solving this question:

First, find f(3) at different values.

Calculate the number of ways at different values of f(3) to find the total number of functions

### Step 1 of 2:

Given, f: {1, 2, 3, 4} → {1, 2, 3, 4, 5, 6}

Total number of ways = {No. of ways of selecting f(1), f(2), f(3)}

*{No. of ways of selecting f(4)}

Now, No. of ways of selecting f(4) = 6

Here f(3) can be 2, 3, 4, 5, 6

Also, Given f(1) + f(2) = f(3)

Different cases at different values of f(3) are

### Case 1:

One Condition

Therefore, No. of ways = 6*1 = 6 ……(1)

### Case 2:

Two conditions

Therefore, No. of ways = 6*2 = 12 ……(2)

### Case 3:

Three Conditions

Therefore, No. of ways = 6*3 = 18 ……(3)

### Case 4:

Four Conditions

Therefore, No. of ways = 6*4 = 24 ……(4)

### Case 5:

Five Conditions

Therefore, No. of ways = 6*5 = 30 ……(5)

### Step 2 of 2:

From (1), (2), (3), (4), (5)

Total no. of ways = 6 + 12 + 18 + 24 + 30 = 90

i.e. Total no. of functions = 90

## Final Answer:

Hence, Option (B) is correct.

JEE Main 2022 July 25th Shift 1 Mathematics Question Paper and Solutions

## Leave a Reply