Question 1 |

For the below question, one or more OPTIONS are correct

The eigen vector(s) of the matrix

\begin{bmatrix} 0 &0 &\alpha\\ 0 &0 &0\\ 0 &0 &0 \end{bmatrix},\alpha \neq 0

is (are)

The eigen vector(s) of the matrix

\begin{bmatrix} 0 &0 &\alpha\\ 0 &0 &0\\ 0 &0 &0 \end{bmatrix},\alpha \neq 0

is (are)

(0,0,\alpha) | |

(\alpha,0,0) | |

(0,0,1) | |

(0,\alpha,0) |

Question 1 Explanation:

Question 2 |

The differential equation

\frac{d^2 y}{dx^2}+\frac{dy}{dx}+\sin y =0 is:

\frac{d^2 y}{dx^2}+\frac{dy}{dx}+\sin y =0 is:

linear | |

non- linear | |

homogeneous | |

of degree two |

Question 2 Explanation:

Question 3 |

Simpson's rule for integration gives exact result when f(x) is a polynomial of degree

1 | |

2 | |

3 | |

4 |

Question 3 Explanation:

Question 4 |

Which of the following is (are) valid FORTRAN 77 statement(s)?

DO 13 I = 1 | |

A = DIM ***7 | |

READ = 15.0 | |

GO TO 3 = 10 |

Question 4 Explanation:

Question 5 |

Fourier series of the periodic function (period 2 \pi ) defined by

f(x) = \begin{cases} 0, -p \lt x \lt 0\\x, 0 \lt x \lt p \end{cases} \text { is }\\ \frac{\pi}{4} + \Sigma \left [ \frac{1}{\pi n^2} \left(\cos n\pi - 1 \right) \cos nx - \frac{1}{n} \cos n\pi \sin nx \right ]

But putting x = \pi, we get the sum of the series

1 + \frac{1}{3^2} + \frac{1}{5^2} + \frac{1}{7^2} + \cdots \text { is }

f(x) = \begin{cases} 0, -p \lt x \lt 0\\x, 0 \lt x \lt p \end{cases} \text { is }\\ \frac{\pi}{4} + \Sigma \left [ \frac{1}{\pi n^2} \left(\cos n\pi - 1 \right) \cos nx - \frac{1}{n} \cos n\pi \sin nx \right ]

But putting x = \pi, we get the sum of the series

1 + \frac{1}{3^2} + \frac{1}{5^2} + \frac{1}{7^2} + \cdots \text { is }

\frac{{\pi }^2 }{4} | |

\frac{{\pi }^2 }{6} | |

\frac{{\pi }^2 }{8} | |

\frac{{\pi }^2 }{12} |

Question 5 Explanation:

Question 6 |

Which of the following improper integrals is (are) convergent?

\int ^{1} _{0} \frac{\sin x}{1-\cos x}dx | |

\int ^{\infty} _{0} \frac{\cos x}{1+x} dx | |

\int ^{\infty} _{0} \frac{x}{1+x^2} dx | |

\int ^{1} _{0} \frac{1-\cos x}{\frac{x^5}{2}} dx |

Question 6 Explanation:

Question 7 |

The function f\left(x,y\right) = x^2y - 3xy + 2y +x has

no local extremum | |

one local minimum but no local maximum | |

one local maximum but no local minimum | |

one local minimum and one local maximum |

Question 7 Explanation:

Question 8 |

Assume that each character code consists of 8 bits. The number of characters that can be transmitted per second through an asynchronous serial line at 2400 baud rate, and with two stop bits is

109 | |

216 | |

218 | |

219 |

Question 8 Explanation:

Question 9 |

Identify the logic function performed by the circuit shown in figure.

exclusive OR | |

exclusive NOR | |

NAND | |

NOR | |

None of the above |

Question 9 Explanation:

Question 10 |

Refer to the PASCAL program shown below.

The value of m, output by the program PARAM is:

```
Program PARAM (input, output);
var m, n : integer;
procedure P (var, x, y : integer);
var m : integer;
begin
m : = 1;
x : = y + 1
end;
procedure Q (x:integer; vary : integer);
begin
x:=y+1;
end;
begin
m:=0; P(m,m); write (m);
n:=0; Q(n*1,n); write (n)
end
```

The value of m, output by the program PARAM is:

1, because m is a local variable in P | |

0, because m is the actual parameter that corresponds to the formal parameter in p | |

0, because both x and y are just reference to m, and y has the value 0 | |

1, because both x and y are just references to m which gets modified in procedure P | |

none of the above |

Question 10 Explanation:

There are 10 questions to complete.