CUET UG 2025 — General Test Logical Reasoning

The series H4Q, K10N, N20K, Q43H, T90E follows three consistent patterns:

$\bullet$∙ First letters: H($8$8th) $\to$→ K($11$11th) $\to$→ N($14$14th) $\to$→ Q($17$17th) $\to$→ T($20$20th), increasing by $+3$+3 positions each time.

$\bullet$∙ Last letters: Q($17$17th) $\to$→ N($14$14th) $\to$→ K($11$11th) $\to$→ H($8$8th) $\to$→ E($5$5th), decreasing by $-3$−3 positions each time.

$\bullet$∙ Numbers: Follow the recursive rule $a_n = 2 \times a_{n-1} + (n-1)$an​=2×an−1​+(n−1), where $n$n is the term position:

$$\quad a_1 = 4$$a1​=4

$\quad a_2 = 2 \times 4 + 1 = 9$a2​=2×4+1=9 (but given as $10$10, mismatch)

$$\quad a_3 = 2 \times 9 + 2 = 20$$a3​=2×9+2=20

$$\quad a_4 = 2 \times 20 + 3 = 43$$a4​=2×20+3=43

$\quad a_5 = 2 \times 43 + 4 = 90$a5​=2×43+4=90.

Why K$10$10N?

K10N breaks the number pattern (should be $9$9 instead of $10$10), while all other components fit perfectly across the series. This matches option $2$2 in the provided choices.