CUET UG 2025 — General Test Logical Reasoning

Looking at the table:

6	10	14
9	15	21
12	20	?

Examining the rows, each row forms an arithmetic sequence:

Row 1: $6, 10, 14$6,10,14 with common difference $4$4

Row 2: $9, 15, 21$9,15,21 with common difference $6$6

Row 3: $12, 20, ?$12,20,? with common difference $8$8

Following this pattern: $? = 20 + 8 = 28$?=20+8=28

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Examining the columns to verify:

Column 1: $6, 9, 12$6,9,12 with common difference $3$3

Column 2: $10, 15, 20$10,15,20 with common difference $5$5

Column 3: $14, 21, ?$14,21,? with common difference $7$7

Following this pattern: $? = 21 + 7 = 28$?=21+7=28

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Alternatively, observing the structure as products:

Column 1: $6 = 2 \times 3$6=2×3, $9 = 3 \times 3$9=3×3, $12 = 4 \times 3$12=4×3

Column 2: $10 = 2 \times 5$10=2×5, $15 = 3 \times 5$15=3×5, $20 = 4 \times 5$20=4×5

Column 3: $14 = 2 \times 7$14=2×7, $21 = 3 \times 7$21=3×7, $? = 4 \times 7 = 28$?=4×7=28

Each column multiplies consecutive odd numbers $(3, 5, 7)$(3,5,7) by the row position $(2, 3, 4)$(2,3,4).

Therefore, the missing number is $28$28.