PREVIOUS YEAR SOLVED PAPERS MCQ - GATE 2017 Shift 1

46 Consider the following two functions.
void fun1 (int n) {
if (n == 0 ) return;
printf (“%d” , n);
fun2 (n - 2); printf (“%d” , n);
}
void fun2 (int n) {
if (n = = 0) return ;
printf (“%d” , n);
fun1(++n) ;
printf (“%d” , n);
}
The output printed when fun1(5) is called is

47 Let A be real valued square symmetric matrix of rank 2 with

Consider the following statements.
(I) One eigen value must be in [-5, 5]
(II) The eigen value with the largest magnitude must be strictly greater than 5.
Which of the above statements about eigen values of A is/are necessarily CORRECT?

ρ(A) = n|A| = 0 ⇒ one eigen value must be ‘0’ ∈ [-5, 5]
∴ (I) is true

but eigen values of A are 0, −5,5
∴ The eigen value with the largest magnitude is not greater than 5
For and Let

⇒ eigen values = 5,5
∴ One eigen value must be in [−5,5] and largest eigen value magnitude is not greater than 5
∴ (II) is false

48 Consider the context-free grammars over the alphabet {a,b,c} given below. S and T are non-terminals
G₁: S → aSb|T,T → cT|∈
G₂: S → bSa|T,T → cT|∈
The language L(G₁)∩L(G₂) is

The Context free grammar given over alphabets ∑{a, b, c} with S and T as non terminals are:
G₁: S → aSb|T,T → cT|∈
G₂: S → bSa|T,T → cT|∈
Lets L(G₁) is the language for grammar G₁ and L(G₂) is the language for grammar G₂
L(G₁) = {aⁿc^mbⁿ|n,m ≥ 0}
L(G₂) = {bⁿc^maⁿ|n,m ≥ 0}
L(G₁) ∩ L(G₁) = {c^maⁿ|m ≥ 0}; which is infinite and regular

49 Let X be a Gaussian random variable mean 0 and variance σ². Let Y = max(X, 0) where max (a, b) is the maximum of a and b. The median of Y is _____.

Note – Numerical Type question

‘X’ is Gaussian random variable
⇒ X ∼ N(0, σ²) for -∞ < x < ∞
Given

Since median is positional average
Therefore, median of Y is '0'.

50 Consider the Karnaugh map given below, where x represents “don’t care” and blank represents 0.

Assume for all inputs (a, b, c, d) the respective complements (a, b, c, d) are also available. The above logic is implemented 2-input NOR gates only. The minimum number of NOR gates required is _____.

Note – Numerical Type question

From K-map simplification we get the min-term as CA' . So We can simplify it for NOR gate expression
i.e. C' NOR A = (C'+A)' = CA'
Now complemented inputs are also given to us so for 2 input NOR gate we need only 1 NOR gate.
1 is correct answer