Gate Computer Science Sample Paper

The min-degree of G is defined as min degree v ) .

Therefore, min-degree of G cannot be (A)341. Consider the following system of linear equations 4 5 ...

43 12"' V 1/7 12 8 Notice that the second and the third columns of the coefficient matrix are linearly dependent. For how many values of < , does this ystem of equations have infinitely many solutions? (A) O (B) 1 (C) 2 (D) infinitely many 42. A piecewise linear function f(x) is plotted using thick solid lines in the figure below (the plot is drawn to scale).If we use the Newton-Arapaho method to find the roots of (x) using ox, XSL , and xx respectively as initial guesses, the roots obtained would be (A) 1.

3, 0. 6, and 0. 6 respectively (B) 0. 6, 0.

6, and 1. 3 respectively (D) 1. 3, 0. 6, and 1.

3 respectively (C) 1. 3, 1. 3, and 0. 6 respectively 43.

The following is a scheme for floating point number representation using 16 bits. Bit Position 15 s 14 8 Owe m Mantissa Sign Exponent Let s, e, and m be the numbers represented in binary in the sign, exponent, and mantissa fields respectively.Then the floating point number represented is: Г? 31 What is the maximum difference between two successive real numbers reprehensible in this system? (A) 2-40 (B) 2-9 (C) 222 (D) 231 44. A I-input, 2-output synchronous sequential circuit behaves as follows: Let z, knotted the number of Co's and Xi's respectively in initial bits of the input (Zen=k). The circuit outputs 00 until one of the following conditions holds.

; z ink=2. In this case, the output at the k-the ND all subsequent clock ticks is 10. ink z = 2. In this case, the output at the k-the and all subsequent clock ticks is 01 .What is the minimum number of states required in the state transition graph of the above circuit? (A) 5 (B) 6 (C) 7 (D) 8 The literal count of a Boolean expression is the sum of the number of times each literal appears in the expression. For example, the literal count of (xx + xx') is 4.

45. What are the minimum possible literal counts of the product-of-sum and sum- product representations respectively of the function given by the following Agrarian map? Here, X denotes -?don't care" (B) (9, 13) 0) Consider the ALL shown below.If the operands are in g's complement representation, which of the following operations can be performed by suitably setting the control lines K and Commonly (+ and - denote addition and subtraction respectively)? (A) A + B, and A - B, but not A + 1 (B) A + B, and A + 1, but not A- B (C) A + B, but not Ace B or A + 1 (D) A + B, and A- B, and A + 1 47. Consider the following circuit composed of XEROX gates and non-inverting buffers. The non-inverting buffers have delays 01 = 2 ins and 4 ins as shown in the figure.

Both XEROX gates and all wires have zero delay.Assume that all gate inputs, outputs ND wires are stable at logic level O at time O. If the following waveform is applied at input A, how many transition(s) (change of logic levels) occur(s) at B during the interval from O to 10 ins? The following information pertains to 48-49: Consider the following assembly language program for a hypothetical processor A, B, and C are 8 bit registers. The meanings of various instructions are shown as comments. MOVE B, ; MOVE, ; Z: CPM C, ; compare C with O E X ; jump to X if zero flag is set SUB C, #1 ; CC-I ARC A, #1 ; right rotate A through carry by one bit.Thus: ; if the initial values of A and the carry flag are ah.

. O and ; co respectively, their values after the execution of this ; instruction will be coca.. Ah and ah respectively. ; Jump to Y if carry flag is set J Y ; Jump dotcom Z Y: ADD B, #1 ; BB +1 JUMP Z ; Jump to Z X: 48.

If the initial value of register A is AH the value of register B after the program execution will (A) the number of O bits in AH (B) the number of 1 bits in AH (C) AH (D) 8 49. Which of the following instructions when inserted at location X will ensure that the value of register A after program execution is the same as its initial value? A) ARC A, #1 (B) NOPE ; no operation (C) LORD A, #1 ; left rotate A through array flag by one bit (D) ADD A, #1 Consider the following deterministic finite state automaton M. Let S denote the set of seven bit binary strings in which the first, the fourth, and the last bits are 1. The number of strings in S that are accepted by M is (A) 1 (B) 5 (C) 7 (D) 8 51 .

Let G = be a context free grammar where the rule set R is S 960 a S b I AS Which of the following statements is true? A) G is not ambiguous (B) There exist x, y L(G) such that xx L(G) (C) There is a deterministic pushdown automaton that accepts L(G) (D) We can find a deterministic finite state automaton that accepts L(G) Consider two languages Al and LA, each on the alphabet 0. Let polynomial time computable objection such that Al f (x) LA]. Further, if 52. 0 be a let f-1 be also polynomial time computable. Which of the following CANNOT be true? (A) Al Panda LA is finite (B) Al NP and LA P (C) Al is undividable and LA is decidable (D) Al is recursively enumerable and LA is recursive 53.A single tape Turing Machine M has two states co and SQL, of which co is the starting state.

The tape alphabet of M is {O, 1, B} and its input alphabet is {O, 1}. The symbol B is the blank symbol used to indicate end of an input string. The ruinations function of M is described in the following table. The table is interpreted as illustrated below.

The entry (SQL, 1, R) in row co and column 1 signifies that if M is in state co and reads 1 on the current tape square, then it writes 1 on the same tape square, moves its tape head one position to the right and transitions to state SQL .Which of the following statements is true about M? (A) M does not halt on any string in (0+1)+ (B) M does not halt on any string in (00+1)* (C) M halts on all strings ending in a O (D) M halts on all strings ending in a 1 54. Define languages LO and Al as follows: I M halts on w} Al { I M does not halt on w} Here is a triplet, whose first component, M, is an encoding of a Turing Machine, second component, w, is a string, and third component, I, is a bit. Let L = LO*IL .