1
GATE CSE 2021 Set 1
Numerical
+2
-0.67

Consider the following representation of a number in IEEE 754 single-precision floating point format with a bias of 127.

S: 1 E:   10000001    F : 11110000000000000000000

Here S, E and F denote the sign, exponent and fraction components of the floating point representation.

The decimal value corresponding to the above representation (rounded to 2 decimal places) is ______

2
GATE CSE 2021 Set 1
+2
-0.67

Let p and q be two propositions. Consider the following two formulae in propositional logic.

S1 : (¬p ∧ (p ∨ q)) → q

S2 : q → (¬p ∧ (p ∨ q))

Which one of the following choices is correct?

A
Neither S1 nor S2 is a tautology.
B
S1 is not a tautology but S2 is a tautology.
C
Both S1 and S2 are tautologies.
D
S1 is a tautology but S2 is not a tautology.
3
GATE CSE 2021 Set 1
Numerical
+2
-0.67

There are 6 jobs with distinct difficulty levels, and 3 computers with distinct processing speeds. Each job is assigned to a computer such that:

- The fastest computer gets the toughest job and the slowest computer gets the easiest job.

- Every computer gets at least one job.

The number of ways in which this can be done is ______

4
GATE CSE 2021 Set 1
+2
-0.67

Consider the two statements.

S1 : There exist random variables X and Y such that

(E[X - E(X)) (Y - E(Y))])2 > Var[X] Var[Y]

S2 : For all random variables X and Y,

Cov[X, Y] = E [|X - E[X]| |Y - E[Y]|]

Which one of the following choices is correct?

A
S1 is false, but S2 is true.
B
S1 is true, but S2 is false.
C

Both S1 and S2 are true.

D
Both S1 and S2 are false.
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