NIMCET 2023 — Reasoning PYQ

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Question

NIMCET 2023 — Reasoning PYQ

NIMCET | Reasoning | 2023

If DENMARK in coded on FCPKCPM Then code SINGAPORE of which option.

Choose the correct answer:

Explanation

Let

$B = - 1 00 am p; - 1 am p; - 1 am p; 0 am p; 2 am p; - 1 am p; - 1 = - I + N, N = 000 am p; - 1 am p; 0 am p; 0 am p; 2 am p; - 1 am p; 0, N^{3} = 0.$

So

$B^{19} = (- I + N)^{19} = - I + 19 N - 171 N^{2},$

Now

$N^{2} = 000 am p; 0 am p; 0 am p; 0 am p; 1 am p; 0 am p; 0 .$

Sum of entries is linear, hence

$Sum (B^{19}) = Sum (- I) + 19 Sum (N) - 171 Sum (N^{2}) = - 3 + 19 \cdot 0 - 171 \cdot 1 = - 174.$
Pattern in coding DENMARK – FCPKCPM is alternating:
+2, -2, +2, -2, +2, -2, +2

Apply same to SINGAPORE with 9 letters → pattern becomes:
+2, -2, +2, -2, +2, -2, +2, -2, +2

Apply shifts:
S(+2) = U
I(-2) = G
N(+2) = P
G(-2) = E
A(+2) = C
P(-2) = N
O(+2) = Q
R(-2) = P
E(+2) = G

Final code: UGPECNQPG

Answer: (a) UGPECNQPG