. Highlight various fields of case work practice with suitable examples in Indian context.
See Answer →Describe various types of correctional institutions set up under the Juvenile Justice (Care & Protection of Children) Act 2000.
See Answer →Explain philosophical base of correctional system with the help of suitable examples.
See Answer →Let M and T be a metro city and a nearby district town, respectively. Our government is trying to develop infrastructure in T so that people shift to T. Each year 15% of T’s population moves to M and 10% of M’s population moves to T. What is the long term effect of on the population of M and T? Are they likely to stabilise?
See Answer →Can A be similar to A+I? Give reasons for your answer.
See Answer →If C and D are nxn matrices such that CD = −DC and D^{-1} exists, then show that C is similar to -D. Hence show that the eigenvalues of C must come in plus-minus pairs.
See Answer →Which of the following statements are true and which are false? Give reasons for your answer.
i) If v is a finite dimensional vector space and T:v→ v is a diagonalisable linear operator, then there is a basis, unique up to order of the elements, with respect to which the matrix of T is diagonal.
ii) Up to similarity, there is a unique 3 x 3 matrix with minimal polynomial (x- 1)^2
(x-2).
iii) If λ is the eigenvalue of a matrix A with characteristic polynomial f(x), (x-λ)(x-λ)^k
if (x) and (x-λ)k+1 + f(x), then the geometric multiplicity of λ is at most k.
iv) If p(A) = 1, then Ak → ∞ as k → ∞.
v) If N is nilpotent, eN is also nilpotent.
vi) The sum of two normal matrices of the order n is normal.
vii) If P and Q are positive definite operators, P+Q is a positive definite operator.
viii) Generalised inverse of a nxn matrix need not be unique.
ix) All the entries of a positive definite matrix are non-negative.
x) The SVD of any 2 × 3 matrix is unique.
What do you understand by file organisation? Explain the methods of file organisation.
See Answer →Explain the meaning of the terms garbage collection, fragmentation, relocation and compaction
See Answer →Write a function that evaluates an expression in RPN that is given as a string.
See Answer →Based on Example 5 in Unit 12, write functions to add and multiply polynomials of real variables.
See Answer →How will you store the following sparse matrix in vector and linked list representation so that only nonzero elements are stored?
Write the inorder, preorder and postorder traversals of the following binary search tree.
A
/
B H
/ /
C E I
/ F
D / J
G
See Answer →Write statements to accomplish each of the following. Assume the structure
struct person
{
char lastName [10];
char City [20];
int Age;
};
has been defined and that the file is already open for writing.
i. Initialize the file ”personaldata.dat” so that there are 100 records with
lastName=””, City=” ” and Age = 0.
ii. Input 10 last names. first names and ages and write them to the file
What does the following C function compute? Discover.
int some fun(int n)
{
if(n%2 == 0)
return 2;
int d, s = sqrt(n);
for(d = 3; d <= s; d = d+2)
if(n%d == 0)
return d;
return n;
}
See Answer →
Write a C program that uses pointers and a single function to compute the two
roots of a quadratic equation, given its coefficients. Your function must be able to cope with the four cases:
i. non-existent roots
ii. real and different roots
iii. real and equal roots
iv. complex roots
Write a macro to compute the surface area of a cone.
See Answer →What do you understand by an automatic variable? How does it differ from a static variable? Explain.
See Answer →