Munna is the jigri of:

Step 1: Identify Munna’s pattern
Munna got exactly 9 out of 10 answers correct. From the final answer key (last row — Sastry), we compare Munna’s row: Sastry:b , d , d , c , b , d , a , c , a , b
Munna: b , d , d , c , b , d , a , c , b , b] Only mismatch is at Q9 ⇒ Munna changed this intentionally (as per passage).
Step 2: Find two students who can be jigri to Munna
A student’s answer key is copied from either one or two jigri(s). If two: identical ⇒ copied, else blank. Let’s check whose answers closely match Munna except Q9.
Niran: b d d c b d a c b b (Only Q9 differs from Sastry) ✔️
Praveen: b d d c b d a c b b ✔️ These match Munna exactly ⇒ Both could be jigri.
Therefore, Munna is the jigri of Niran and Praveen.





For any natural number $k$, let $a_k = 3^k$. The smallest natural number $m$ for which \[ (a_1)^1 \times (a_2)^2 \times \dots \times (a_{20})^{20} \;<\; a_{21} \times a_{22} \times \dots \times a_{20+m} \] is: