GATE CSE 2016 SET-2

Consider the following expressions:
(i) false
(ii) Q
(iii) true
(iv) P\vee Q
(v) \neg Q \vee P
The number of expressions given above that are logically implied by P \wedge (P \Rightarrow Q) is ________.

Let f(x) be a polynomial and g(x) = f'(x) be its derivative. If the degree of (f(x)+ f(-x)) is 10, then the degree of (g(x)-g(-x)) is ________.

The minimum number of colours that is sufficient to vertex-colour any planar graph is _________.

Consider the systems,each consisting of m linear equations in n variables.
I. If m \lt n, then all such systems have a solution
II. If m \gt n, then none of these systems has a solution
III. If m = n, then there exists a system which has a solution
Which one of the following is CORRECT?

Suppose that a shop has an equal number of LED bulbs of two different types. The probability of an LED bulb lasting more than 100 hours given that it is of Type 1 is 0.7, and given that it is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more than 100 hours is _________.

Suppose that the eigen values of matrix A are 1, 2, 4. The determinant of (A^{-1})^{T} is _________.

Consider an eight-bit ripple-carry Combinational Circuit for computing the sum of A and B, where A and B are integers represented in 2's complement form. If the decimal value of A is one, the decimal value of B that leads to the longest latency for the sum to stabilize is ________.

Let, x_{1} \oplus x_{2} \oplus x_{3} \oplus x_{4}=0 where x_{1}, x_{2} , x_{3} , x_{4} are Boolean variables, and \oplus is the XOR operator. Which one of the following must always be TRUE?

Let X be the number of distinct 16-bit integers in 2's complement representation. Let Y be the number of distinct 16 bit integers in sign magnitude representation. Then X-Y is ________.

A processor has 40 distinct instructions and 24 general purpose registers. A 32-bit instruction word has an opcode, two register operands and an immediate operand. The number of bits available for the immediate operand field is _______ .