VTU Programming in C and Data Structures - May 2016 Exam Question Paper

VTU First Year Engineering (C Cycle) (Semester 1)
Programming in C and Data Structures
May 2016

Total marks: --
Total time: --

INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

1(a) What is psecudo-code? Compare it with an algorithm.

5 M

1(a) Find the Laplace transform of te^3t sin 4t.

5 M

1(b) Convert the following into ' C ' expression ;

i) x^{y}^{z} i i) e^{| \sqrt{x} |} i i i) \frac{a \cdot b}{\sqrt{c} \cdot d} i v) \sqrt{s (s - a) (s - b) (s - c)} .

$i) x^{y}{^z}\ \ ii) e^{|\sqrt{x}|}\ \ iii) \dfrac{a\cdot b}{\sqrt{c}\cdot d}\ \ iv) \sqrt{s(s-a)(s-b)(s-c)}.$

4 M

1(b) Find half-range cosine series for f(x)=e^x,
0

5 M

1(c) Write a C program to find largest among three integers using ternary operators.

6 M

1(c) Is

f (z) = \frac{z}{z}

$f(z)=\frac{z}{z}$ / analytic?

5 M

1(d) Explain formatted input and output statement with examples.

5 M

1(d) Prove that

\nabla x (\bar{a} x \nabla \log r) = 2 \frac{(\bar{a} . \bar{r}) \bar{r}}{r^{4}}

$\nabla x\left ( \bar{a}x \nabla \log r\right )=2\frac{(\bar{a}.\bar{r})\bar{r}}{r^4}$ /, where \bar{a} is a constant vector.

5 M

2(a) Write structure of C program. List primitive data types with size and range.

10 M

2(a) Find the Z- transform of

\frac{1}{{(z - 5)}^{3}}

$\frac{1}{\left ( z-5 \right )^3}$ / if |z|<5.

6 M

2(b) Define type casting. Explain with an example.

4 M

2(b) If V=3x²y+6xy-y³, show that V is harmonic & find the corresponding analytic function.

6 M

2(c) Evaluate following (where i = 2, j = 3, k = 4 and a = 5) :
i) a = i*( j/=k/i)
ii) a>>i%j
iii) * = a / i % i.

6 M

2(c) Obtain Fourier series for the function

f (x) = {\begin{matrix} 1 + \frac{2 x}{π}, - π \leq x \leq 0 \\ 1 - \frac{2 x}{π}, 0 \leq x \leq π \end{matrix}

$f(x)=\left\{\begin{matrix} 1+\frac{2x}{\pi }, -\pi\leq x\leq 0 & \\ \\ 1-\frac{2x}{\pi },0\leq x\leq \pi & \end{matrix}\right.$ / hence deduce that

\frac{π^{2}}{8} = \frac{1}{1^{2}} + \frac{1}{3^{2}} + \frac{1}{5^{2}} + . . . . . . . . .

$\frac{\pi ^2}{8}=\frac{1}{1^2}+\frac{1}{3^2}+\frac{1}{5^2}+.........$ /

8 M

3(a) Write a C program to grade student result based on following conditions ;
i) Marks <35 grade "Fail"
ii) 35≥ Marks <60 grade "Second class"
iii)60≥ marks <70 grade "First class"
iv) 70≥ marks ≤ 100 grade "First class with distinction".

8 M

3(a) Find

L^{- 1} [\frac{(s + 2)^{2}}{(s^{2} + 4 s + 8)^{2}}]

$L^{-1}\left [ \frac{(s+2)^2}{(s^2+4s+8)^2} \right ]$ / using convolution theorem.

6 M

3(b) Explain switch statement with an example.

7 M

3(b) Show that the set of functions

1, \sin (\frac{π x}{L}), \cos (\frac{π x}{L}), \sin (\frac{2 π x}{L}), \cos (\frac{2 π x}{L}), . . . . . . . . . .

$1,\sin \left ( \frac{\pi x}{L} \right ),\cos\left ( \frac{\pi x}{L} \right ),\sin \left ( \frac{2\pi x}{L} \right ),\cos \left ( \frac{2\pi x}{L} \right ),..........$ / Form an orthogonal set in (-L,
L) and construct an orthonormal set.

6 M

3(c) Write a note on goto statement.

5 M

3(c) Verify Green's theorem for

\int (e^{2 x} - x y^{2}) d x + (y e^{x} + y^{2}) d y

$\int \left ( e^{2x}-xy^2 \right )dx+\left ( ye^x+y^2 \right )dy$ / Where C is the closed curve bounded by y²=x&x²=y.

8 M

4((c) What is dangling else problem? Explain how to handle this in C programming.

4 M

4(a) Explain cascade if-else and nested if-else satements.

6 M

4(a) Find Laplace transform of \( f(t)=K\frac{t}{T}for 0/

6 M

4(b) Write a C program to implement simple calculator using operators +, - , * and /. Also handle divide by zero error. Use switch statement .

10 M

4(b) Show that the vector,

\bar{F} = (x^{2} - y z) i + (y^{2} - z x) j + (z^{2} - x y) k

$\bar{F}=\left ( x^2-yz \right )i+\left ( y^2-zx \right )j+\left ( z^2-xy \right )k$ / is irrotational and hence, find φ such that \bar{F}=∇φ

6 M

4(c) Find Found series for f(x) in (0,
2π),

f (x) {\begin{matrix} x, & 0 \leq x \leq π \\ 2 π - x, & π \leq x \leq 2 π \end{matrix}

$f(x)\left\{\begin{matrix} x,& 0\leq x\leq \pi \\ 2\pi -x, & \pi \leq x\leq 2\pi \end{matrix}\right.$ / hence deduce that

\frac{π^{4}}{96} = \frac{1}{1^{4}} + \frac{1}{3^{4}} + \frac{1}{5^{4}} + . . . . . . . . . .

$\frac{\pi ^4}{96}=\frac{1}{1^4}+\frac{1}{3^4}+\frac{1}{5^4}+..........$ /

8 M

5(a) Define array? How two dimension arrays are declared and initialized ?

6 M

5(a) Use Gauss's Divergence theorem to evaluate

\iint_{s} \bar{N} . \bar{F} d s

$\iint_{s}\bar{N}.\bar{F} ds$ / where

\bar{F} = 2 x i + x y j + z k

$\bar{F}=2xi+xyj+zk$ over the region bounded by the cylinder x^{2<\sup>+y²=4,
z=0,
z=6.}

6 M

5(b) Write C program to genrate Fibonacci numbers using arrays.

6 M

5(b) Find inverse Z- transform of

f (x) = \frac{z}{(z - 1) (z - 2)}, | z | > 2

$f(x)=\frac{z}{\left ( z-1 \right )\left ( z-2 \right )}, |z|>2$ /

6 M

5(c) Explain following string function:
i) strlen
ii) strcpy
iii) strcmp
iv) strcat.

8 M

5(c) i) Find

L^{- 1} [l o g (\frac{s + 1}{s - 1})]

$L^{-1}\left [ log\left ( \frac{s+1}{s-1} \right ) \right ]$ /
ii)

L^{- 1} [\frac{s + 2}{s^{2} - 4 s + 13}]

$L^{-1}\left [ \frac{s+2}{s^2-4s+13} \right ]$ /

8 M

6(a) Explain various ways of passing parameters to the functions.

6 M

6(a) Solve (D²+3D+2)y=2(t²+t+1) with y(0)=2 & y'(0)=0.

6 M

6(b) Write a C program to find factorial of an integer using recursive function.

8 M

6(b) Find the bilinear transformation which maps the points 0,
i,
-2i of z-plane onto the points -4i,
∞,
0 respectively of W-plane. Also obtain fixed points oft he transformation.

6 M

6(c) Write a C program to find length of string without using strlcn ( ) recursive function.

6 M

6(c) Find Fourier sine integral of $\left\{\begin{matrix} x, &02 \end{matrix}\right. $/

8 M

7(a) Compare arrays with structures.

6 M

7(b) Define structure. Explain it with an example.

5 M

7(c) Explain the following :
i) typedef to define structure
ii) Accessing structure members
iii) Initialization of structure.

9 M

8(a) Explain following file handling functions:
i) fopen ( )
ii) fclose ( )
iii) fscanf ( ) iv) fprinff ( )
v) fseek ( )

10 M

8(b) Write a C program to create a integer data file and then segregate odd and even integers into two different files.

10 M

9(a) What is pointer ? Explain with program.

6 M

9(b) Explain the following :
i) #define
ii) #include
iii) nesting of macro
iv) argumented macro.

10 M

9(c) Explain malloc and calloc functions.

4 M

10(a) What is sack? Explain Write its applications.

8 M

10(b) Explain queue and write its applications.

8 M

10(c) Write a note on trees.

4 M

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