Question 1 |
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 ________.
(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 ________.
2 | |
3 | |
4 | |
5 |
Question 1 Explanation:
Question 2 |
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 ________.
10 | |
9 | |
11 | |
8 |
Question 2 Explanation:
Question 3 |
The minimum number of colours that is sufficient to vertex-colour any planar graph is _________.
2 | |
3 | |
4 | |
5 |
Question 3 Explanation:
Question 4 |
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?
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?
I, II and III are true | |
Only II and III are true | |
Only III is true | |
None of them is true |
Question 4 Explanation:
Question 5 |
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 _________.
0.25 | |
0.55 | |
0.65 | |
0.75 |
Question 5 Explanation:
Question 6 |
Suppose that the eigen values of matrix A are 1, 2, 4. The determinant of (A^{-1})^{T} is _________.
0 | |
0.125 | |
0.25 | |
0.75 |
Question 6 Explanation:
Question 7 |
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 ________.
0 | |
1 | |
-1 | |
2 |
Question 7 Explanation:
Question 8 |
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?
x_{1} x_{2} x_{3} x_{4}=0 | |
x_{1} x_{3}+ x_{2}=0 | |
\bar{x}_{1}\oplus \bar{x}_{3}=\bar{x}_{2}\oplus \bar{x}_{4} | |
x_{1} +x_{2}+ x_{3}+ x_{4}=0 |
Question 8 Explanation:
Question 9 |
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 ________.
0 | |
1 | |
2 | |
16 |
Question 9 Explanation:
Question 10 |
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 _______ .
14 | |
16 | |
18 | |
20 |
Question 10 Explanation:
There are 10 questions to complete.