# Sample Multiple Choice Questions Sample Questions for JGEEBILS Part 4

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1. A function f: {0,1} n ⇾ {0,1} is called symmetric if for every x1, x2, … , xn ∈ {0,1} and every permutation σ of {1,2, … , n} , we have f (x1, x2, … , xn) = f (xσ (1) , xσ (2) , … , xσ (n) ) . The number of such symmetric functions is:

(a) 2n + 1

(b) 2n

(c) 22n/n!

(d) 22n

(e) n!

2. Let r, s and t be regular expressions. Which of the following is wrong?

(a) (r + s) ∗ = (r ∗ s ∗) ∗

(b) r (s + t) = ₹ + rt

(c) (r + s) ∗ = (s + r) ∗

(d) (₹ + r) ∗ r = r (sr + r) ∗

(e) All are correct.

3. Consider the following program

x:= 0; y:= 1; z:= 1;

while y <= N do begin x:= x + 1;

y:= y + z + 2;

z:= z + 2;

end

Which of the following holds on termination of the program?

(a) (x + 1) 2 = N (b) x = √ N

(c) x^{2} = N (d) x 2 ⩽ N < (x + 1) ^{2}

(e) x^{2} < N ⩽ (x + 1) ^{2}

4. The maximum height of a rooted binary tree (all nodes have either two children or none) with N nodes is

(a) N (b) log N (c) (N − 1) /2 (d) (N2) /2 (e) N (N − 1) /2.

5. If a graph G has n vertices and m edges then the depth first traversal of G can

be carried out in time

(a) O (n + m) (b) O (nm) but not O (n + m)

(c) O (n^{2}) but not O (n + m) (d) O (n) (e) O (m)

## Systems Science

1. Engineering Mathematics: Complex Analysis, Linear Algebra, Elementary Numerical Analysis, Basic Optimization Theory and Algorithms, Introduction to Probability Theory and Statistics.

2. Electrical and Computer Sciences: Introduction to Signals and Linear Systems Analysis, Control Systems, Digital Signal Processing, Basic Circuit Theory, Introduction to Digital Communications, Digital Computer Fundamentals, Introduction to Computer Programming.

## Sample Questions [Systems Science]

1. The probability density of a random variable is f (x) = ax^{2} exp (− kx) (k > 0,0 ⩽ x ⩽ ∞) Then, the coefficient a equals

(a) k^{3/2}

(b) k^{3}

(c) k^{2}

(d) k

(e) 2k/π.

2. Discrete sequences x (n) is non-zero for 0 ⩽ n ⩽ Nx and y (n) for 0 ⩽ n ⩽ Ny. The sequence z (n) is obtained by convolving x (n) and y (n) . z (n) assumes nonzero values for N1 ⩽ n ⩽ N2, where N1 and N2 can be expressed in terms of Nx and Ny as,

(a) N1 = 0; N2 = MAX (Nx, Ny)

(b) N1 = Nx; N2 = Ny

(c) N1 = MIN (Nx, Ny) ; N2 = Nx + Ny

(d) N1 = 0; N2 = Nx + Ny

(e) N1 = MIN (Nx, Ny) ; N2 = MAX (Nx, Ny)

3. This is a portion of FORTRAN-77 program for assigning values to a N × N

matrix A:

DO I = 1, N

DO J = I, N

A (I, J) = ABS (I − J) + 1

ENDDO

ENDDO

What is the matrix A called?

(a) Anti-symmetric (b) Sparse (c) Upper triangular (d) Toeplitz

(e) Irregular.

4. logb (logbx) equals

(a) (ln ln x − ln ln b) / ln b

(b) (ln x − ln b) / ln b

(c) (ln ln x − ln ln b)

(d) (ln x − ln b) / [ (ln x) (ln b) ]

(e) None of the Above.

5. The Laplace Transform G (s) of the transfer function of a linear time invariant

system is given by

G (s) = 1 (s + a)

2 + b^{2}

For the system to be stable it is necessary that

(a) a < 0 (b) a ⩾ 0 (c) a = b (d) b = 0 (e) a = − b.