2004

1) Convert:
(i) The decimal number \(412\) to octal, to binary & finally to hexadecimal number
(ii) The hexadecimal number \(F9A.BC3\) to a decimal number.

2) Write a BASIC program to evaluate \(\int_{2}^{5} \dfrac{d x}{1+x^{2}}\) using Simpson’s \(\frac{1}{3}\) rule with 20 subintervals.

2003

1.(i) Convert \(ABCD\) hex and \(76543\) octal to decimal. 1.(ii) Convert \(39870\) decimal to octal and hexadecimal.

2) Write a programme in BASIC to integrate \(\int_{0}^{10}\left(1-e^{-\frac{x}{2}}\right) d x\) by trapezoidal rule for 20 equal sub-divisions of the interval \((0,10) .\) Indicate which lines are to be changed for different integral.

3) Draw a flow chart and write a program in BASIC for an algorithm to determine the greatest common divisor of two given +ve integers.

2002

• Convert \((135.34)_{8}\) to decimal number and then convert the resulting decimal number to binary number.

• Write a BASIC Program to find:
  (i) the sum of first N natural numbers
  (ii) the factorial of a given number

2001

1) Convert the decimal number \((1479.25)_{10}\) to the binary and the hexadecimal numbers.

2) Write an algorithm for generating even integers \(\leq100\). Also draw the flow chart which executes this algorithm.

2000

1) Draw a flow chart for finding the roots of the equation \(a x^{2}+b x+c=0\).