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:
There are 5 questions to complete.