Step 1: Find the elements of set .
Step 2: Find the elements of set .
Step 3: Find the intersection of and .
Step 4: Compare with the given options. The correct intersection is not present in any of the options.
02
PYQ 2024
medium
mathematicsID: lpunest-
The symbolic form of logic of the circuit given below is
1
2
3
4
Official Solution
Correct Option: (1)
Step 1: Examine the diagram conceptually. The circuit shows the following gate sequence: - Input goes to a NOT gate → . - Input goes to a NOT gate → . Step 2: The upper branch combines with using an AND operation as per diagram marking:
Step 3: This output is joined with through an OR gate:
Step 4: The final stage ANDs with :
Step 5: Compare options—only option (A) matches this exact Boolean trace. Hence → (A).
03
PYQ 2025
medium
mathematicsID: lpunest-
In how many ways can the number be resolved into two factors?
1
2
3
4
Official Solution
Correct Option: (3)
Step 1: Express as a perfect square. Step 2: Find the prime factorisation of . Step 3: Find the total number of factors. If , then number of factors:
Step 4: Find the number of ways to resolve into two factors. Since is a perfect square, the number of distinct factor pairs is:
Step 5: Final conclusion. The number can be resolved into two factors in ways.
