UGC NET Computer Science Computer Previous Year Questions (PYQs) – Page 2 of 111

Complement of fuzzy set:

$\mu_{A'}(x) = 1 - \mu_A(x)$

Compute:

$x_1$: $1 - 0.3 = 0.7$

$x_2$: $1 - 0.7 = 0.3$

$x_3$: $1 - 0.4 = 0.6$

Thus,

$A' = {(x_1,0.7),(x_2,0.3),(x_3,0.6)}$

Using Kruskal's algorithm, edges are selected in increasing order of weight.

From the graph:

$a-b = 1$

$d-f = 1$

$b-f = 2$

$d-c = 2$

$d-e = 3$

So, the valid order must follow:

Weight $1$ edges first:

$I, II$ in any order

Then weight $2$ edges:

$III, IV$ in any order

Then weight $3$ edge:

$V$

Now check option (c):

II, I, III, V, IV

Here, edge $V = d-e$ has weight $3$, but edge $IV = d-c$ has weight $2$.

So, selecting $V$ before $IV$ violates Kruskal's increasing weight rule.

Therefore, this order cannot be used.

Interrupt Service Routine (ISR) steps:

Save processor registers → C

Check which device raised interrupt → D

Service the device → B

Restore processor registers → E

Re-enable interrupt facility → A

Correct sequence:

C, D, B, E, A

While simplifying a CFG, the safest order is:

First remove $\epsilon$-productions.

Then remove unit productions.

Finally remove useless symbols and productions.

Reason:

After removing $\epsilon$-productions, new unit productions may be created.

After removing unit productions, some symbols may become useless.

So, useless symbols should be removed at the end.

Correct order is:

$\epsilon$-productions → Unit productions → Useless symbols and productions