Jamia Millia Islamia MCA Puzzle Previous Year Questions (PYQs)
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Branches of 5 nationalized banks A, B, C, D and E in Uttar Pradesh are as follows:
A, B, C, D and E are in Lucknow and Kanpur.
A, B and E are in Kanpur and Allahabad.
B, C and D are in Lucknow and Varanasi.
B, E and D are in Allahabad and Saharanpur.
C, E and D are in Saharanpur and Moradabad.
Which bank has branches in all the cities except Moradabad?
1
2
3
4
Solution
List all cities for each bank:
A → Lucknow, Kanpur, Allahabad
B → Lucknow, Kanpur, Allahabad, Varanasi, Saharanpur
C → Lucknow, Kanpur, Varanasi, Saharanpur, Moradabad
D → Lucknow, Kanpur, Varanasi, Allahabad, Saharanpur, Moradabad
E → Lucknow, Kanpur, Allahabad, Saharanpur, Moradabad
Bank B covers all except Moradabad.
In a family, each daughter has the same number of brothers as she has sisters,
and each son has twice as many sisters as he has brothers.
How many sons are there in the family?
1
2
3
4
Solution
Let number of sons = $s$, and number of daughters = $d$.
For a daughter: number of brothers = $s$, number of sisters = $d - 1$
⇒ $s = d - 1$
For a son: number of sisters = $d$, number of brothers = $s - 1$
⇒ $d = 2(s - 1)$
Solving:
$s = d - 1$
$d = 2s - 2$
Substitute: $s = (2s - 2) - 1 ⇒ s = 3$.
A ten-rupee coin is placed on a plain paper. How many coins of the same size can be placed around it so that each one touches the central and adjacent coins?
1
2
3
4
Solution
In 2D, at most 6 equal circles can touch another equal circle (kissing number).
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