Question 1 |

Consider the statement

"Not all that glitters is gold"

Predicate glitters(x) is true if x glitters and predicate gold(x) is true if x is gold. Which one of the following logical formulae represents the above statement?

"Not all that glitters is gold"

Predicate glitters(x) is true if x glitters and predicate gold(x) is true if x is gold. Which one of the following logical formulae represents the above statement?

\forall x:glitters(x)\Rightarrow \neg gold(x) | |

\forall x:gold(x)\Rightarrow glitters(x) | |

\exists x:gold(x)\wedge \neg glitters(x) | |

\exists x:glitters(x)\wedge \neg gold(x) |

Question 1 Explanation:

Question 2 |

Suppose you break a stick of unit length at a point chosen uniformly at random. Then the expected length of the shorter stick is

0.25 | |

0.5 | |

0.75 | |

1 |

Question 2 Explanation:

Question 3 |

Let G=(V,E) be a directed graph where V is the set of vertices and E the set of edges. Then which one of the following graphs has the same strongly connected components as G ?

G_{1}=(V,E_{1}) where E_{1}\equiv \{(u,v)|(u,v)\notin E\} | |

G_{2}=(V,E_{2}) where E_{2}\equiv \{(u,v)|(u,v)\in E\} | |

G_{3}=(V,E_{3}) where E_{3}\equiv \{(u,v)| there is a path of lenth \leq 2 from u to v in E} | |

G_{4}=(V_{4},E) where V_{4} is the set of vertices in G which are not isolated |

Question 3 Explanation:

Question 4 |

Consider the following system of equations:

3x + 2y = 1

4x + 7z = 1

x + y + z = 3

x - 2y + 7z = 0

The number of solutions for this system is

3x + 2y = 1

4x + 7z = 1

x + y + z = 3

x - 2y + 7z = 0

The number of solutions for this system is

0 | |

1 | |

2 | |

3 |

Question 4 Explanation:

Question 5 |

The value of the dot product of the eigenvectors corresponding to any pair of different eigenvalues of a 4-by-4 symmetric positive definite matrix is

0 | |

1 | |

2 | |

3 |

Question 5 Explanation:

Question 6 |

Let the function

f(\theta)=\begin{vmatrix} sin\theta & cos\theta & tan\theta \\ sin(\frac{\pi}{6}) & cos(\frac{\pi}{6}) & tan(\frac{\pi}{6})\\ sin(\frac{\pi}{3})& cos(\frac{\pi}{3}) & tan(\frac{\pi}{3}) \end{vmatrix}

where \theta \in [\frac{\pi}{6},\frac{\pi}{3}] and f'(\theta ) denote the derivative of f with respect to \theta . Which of the following statements is/are TRUE?

(I) There existrs \theta \in (\frac{\pi}{6},\frac{\pi}{3}) such that f'(\theta )=0

(I) There existrs \theta \in (\frac{\pi}{6},\frac{\pi}{3}) such that f'(\theta )\neq 0

f(\theta)=\begin{vmatrix} sin\theta & cos\theta & tan\theta \\ sin(\frac{\pi}{6}) & cos(\frac{\pi}{6}) & tan(\frac{\pi}{6})\\ sin(\frac{\pi}{3})& cos(\frac{\pi}{3}) & tan(\frac{\pi}{3}) \end{vmatrix}

where \theta \in [\frac{\pi}{6},\frac{\pi}{3}] and f'(\theta ) denote the derivative of f with respect to \theta . Which of the following statements is/are TRUE?

(I) There existrs \theta \in (\frac{\pi}{6},\frac{\pi}{3}) such that f'(\theta )=0

(I) There existrs \theta \in (\frac{\pi}{6},\frac{\pi}{3}) such that f'(\theta )\neq 0

I only | |

II only | |

Both I and II | |

Neither I nor II |

Question 6 Explanation:

Question 7 |

Consider the following Boolean Algebra for F:

F(P,Q,R,S)=PQ+\bar{P}QR+\bar{P}Q\bar{R}S

The minimal sum-of products form of F is

F(P,Q,R,S)=PQ+\bar{P}QR+\bar{P}Q\bar{R}S

The minimal sum-of products form of F is

PQ+QR+QS | |

P+Q+R+S | |

\bar{P}+\bar{Q}+\bar{R}+\bar{S} | |

\bar{P}R+\bar{PRS}+P |

Question 7 Explanation:

Question 8 |

The base (or radix) of the number system such that the following equation holds is_______.

\frac{312}{20}=13.1

\frac{312}{20}=13.1

4 | |

5 | |

6 | |

7 |

Question 8 Explanation:

Question 9 |

A machine has a 32-bit architecture, with 1-word long instructions. It has 64 registers, each of which is 32 bits long. It needs to support 45 instructions, which have an immediate operand in addition to two register operands. Assuming that the immediate operand is an unsigned integer, the maximum value of the immediate operand is ____________.

16383 | |

8191 | |

32767 | |

4097 |

Question 9 Explanation:

Question 10 |

Consider the following program in C language:

```
# include < stdio.h >
main()
{
int i;
int * pi = &i;
scanf( "%d", pi) ;
printf ("%d \ n", i+5) ;
}
```

Which one of the following statements is TRUE?Compilation fails. | |

Execution results in a run-time error. | |

On execution, the value printed is 5 more than the address of variable i. | |

On execution, the value printed is 5 more than the integer value entered |

Question 10 Explanation:

There are 10 questions to complete.