Official PYQ · 2011Q32Normal FormsMCQ1 mark

GATE CS 2011 Q32 — Normal Forms

Consider a database table T containing two columns $\text{X}$ and $\text{Y}$ each of type $\text{integer}$ . After the creation of the table, one record $\text{(X=1, Y=1)}$ is inserted in the table.

Let $\text{MX}$ and $\text{MY}$ denote the respective maximum values of $\text{X}$ and $\text{Y}$ among all records in the table at any point in time. Using $\text{MX}$ and $\text{MY}$ , new records are inserted in the table $128$ times with $\text{X}$ and $\text{Y}$ values being $\text{MX+1, 2*MY+1}$ respectively. It may be noted that each time after the insertion, values of $\text{MX}$ and $\text{MY}$ change.

What will be the output of the following SQL query after the steps mentioned above are carried out?

SELECT Y FROM T WHERE X=7;

View worked solution

Answer: A

Let us trace the values of $X$ and $Y$ inserted into the table $T$ step-by-step.

Initial State (Step 0):
Only one record exists in the table:
$(X_0, Y_0) = (1, 1)$
Here, the maximum values are $MX = 1$ and $MY = 1$ .

Step 1:
New record inserted: $(MX + 1, 2 \cdot MY + 1) = (1 + 1, 2 \cdot 1 + 1) = (2, 3)$ .
Now, $MX = 2$ and $MY = 3$ .

Step 2:
New record inserted: $(2 + 1, 2 \cdot 3 + 1) = (3, 7)$ .
Now, $MX = 3$ and $MY = 7$ .

Step 3:
New record inserted: $(3 + 1, 2 \cdot 7 + 1) = (4, 15)$ .
Now, $MX = 4$ and $MY = 15$ .

By observing the pattern for the $n$ -th insertion step:

$X_n = n + 1$
$Y_n = 2^{n+1} - 1$

We are looking for the record where $X = 7$ :

X_n = 7 \implies n + 1 = 7 \implies n = 6

For $n = 6$ , the corresponding value of $Y$ is:

Y_6 = 2^{6+1} - 1 = 2^7 - 1 = 128 - 1 = 127

Thus, the query SELECT Y FROM T WHERE X=7; will return 127.

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Published 10 Oct 2026

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