PYQs

1) Draw a flow chart and write a basic algorithm (in FORTRAN/C/C++) for evaluating $y={\int }_0^6{\displaystyle \frac{dx}{1+x^2}}$ using Trapezoidal rule.

[2019, 10M]

2) Write down the basic algorithm for solving the equation: $x{e}^x-1=0$ by bisection method, correct to 4 decimal places.

[2018, 10M]

3) In a certain examination, a candidate has to appear for one major & two major subjects. The rules for declaration of results are marks for major are denoted by $M_1$ and for minors by $M_2$ and $M_3$. If the candidate obtains 75% and above marks in each of the three subjects, the candidate is declared to have passed the examination in first class with distinction. If the candidate obtains 60% and above marks in each of the three subjects, the candidate is declared to have passed the examination in first class. If the candidate obtains 50% or above in major, 40% or above in each of the two minors and an average of 50% or above in all the three subjects put together, the candidate is declared to have passed the examination in second class. All those candidates, who have obtained 50% and above in major and 40% or above in minor, are declared to have passed the examination. If the candidate obtains less than 50% in major or less than 40% in anyone of the two minors, the candidate is declared to have failed in the examinations. Draw a flow chart to declare the results for the above.

[2012, 20M]

4) Draw a flow chart for Lagrange’s interpolation formula.

[2011, 20M]

5) Given $3\times 3$ matrices

$A=(a_{ij})$, $B=(b_{ij})$. Draw programme outline, flow chart and also write a programme in BASIC to enable evaluation of $F$, given $F=5\ast (A+B)\ast (A-B)$.

[2007, 30M]

6) Draw a programme outline and a flow chart and also write a programme in BASIC to enable solving the following system of 3 linear equations in 3 unknowns $x_1$, $x_2$ and $x_3$: $C\ast X=D$ with $C={\left(c_{ij}\right)}_{i,j=1}^3$, $X={\left(x_j\right)}_{j=1}^3$, $D={\left(d_i\right)}_{i=1}^3$.

[2006, 30M]

7) In a certain exam, candidates have to take 2 papers under part $A$ and 2 papers under part $B$. A candidate has to obtain minimum of 40% in each paper under part $A$, with an average of 50%, together with a minimum of 35% in each paper under part $B$, with an aveage of $40$. For a complete PASS, an overall minimum of 50% is required. Write a BASIC program to declare the result of 100 candidates.

[2004, 15M]

8) Write a BASIC program for solving the differential equation:

to get $y(x)$, for $0.2\le x\le 5$ at an equal interval of 0.2, by Runge-Kutta fourth order method.

[2004, 15M]

9) Draw a flow chart and also write a program in BASIC to find one real root of the non linear equation $x=\varphi (x)$ by the fixed point iteration method. Illustrate it to find one real root, correct up to four places of decimals, of $x^3-2x-5=0$.

[2005, 30M]

10) A teacher conducts three tests TEST 1, TEST 2 and FINAL for 50 marks each. Out of the marks scored in the two tests, TEST 1 and TEST 2, he takes the better one and adds to the marks scored in FINAL, so that the total marks scored will be for a maximum 100.

The letter grades will be assigned depending on the amrks scored as per the following norm:

0-39: $E$
40-49: $D$
50-59: $C$ 60-74: $B$ 70-100: $A$

For each student data consisting of name, scores in TEST 1, TEST 2 and FINAL are given. Write a program in BASIC which will print out the names, total marks scored and grade obtained for all 20 students in a class.

[2002, 20M]

11) Draw a flow chart to examine whether a given number is a prime.

[2002, 10M]

12) Write a computer program in BASIC to evaluate the polynomial

for values of $x=1.2$ $(0.2)$ $2.0$.

[2001, 15M]

13) In an examination students are awarded letter grades according to the following scheme:

|   Score Range          |  Letter Grade |
|:------------------------|:-------------|  
|     Score$\geq$90    |       A       |
| $80\geq$Score$<$90 |       B       |
|$70\geq$Score$<$80  |       C       |
|$60\geq$Score$<$70  |       D       |
|     Score$<$60       |       F       |

For each score print a message identifying the letter grade. For grade $F$ an additional message ‘This is a falling case’ may be mentioned. Prepare the flowchart for this scheme and write the program in BASIC.

[20M]