Thursday, September 16, 2010


1. Define Divisibility relation in N and Z.
2. State Division algorithem.
3. Define GCD of two integers
4. Define prime and composite numbers. Are 0 and 1 prime numbers? Composite
5. Define the congruence relation in Z and express in terms of divisibility

1. Define transpose of a matrix with example.
2. Define equality of matrices
3. Define multiplication of matrices
4. Define symmetric and skew symmetric matrices and give examples.
5. If A is a matrix of order mxn and B is a matrix of order nxp. Do AB and BA exist? If
so what are their orders?
6. Define the minor and cofactor of an element of a determinant of a matrix (aij)
7. Define Adjoint of a square matrix.
8. Define singular and nonsingular matrices .
9. Deine Inverse of a square matrix.
10. Define a)Characteristic matrix b)Characteristic polynomial c)characteristic
equation d) characteristic matrix of a square matrix (each carries 1M)
11. Stae Cayley Hamilton theorem.

1. Define a binary operation * on a non empty set S.
2. Define associative axiom for an algebraic structure (S, *)
3. Define a group.
4. Define an abelian group and give an example of non abelian group
5. Define a semi group with example.
6. Define a subgroup of a group and give an example.
7. Give an example of finite subgroup of a finite group.
8. Is union of two subgroups a subgroup? Give reasons.

1. Define coplanar vector
2. Define position vector of a point.
3. Define collinear vector.
4. Define scalar product of two vectors.
5. Define Vector product of two vectors.
6. Define scalar triple product of three vectors
7. Define vector triple product of three vectors.

1. Define the power of the point w.r.t circle
2. What is the condition for any line to be tangent to a circle?
3. Define Radical axis of two circles and find its equation.
4. Define Radical centre of three circles
5. Define Orthogonal circles.

1. Define parabola , ellipse, Hyperbola in terms of locus of point (Each carries 1M)
2. Define Latus rectum.
3. Define auxiliary circle for a)an ellipse b) a hyperbola (each carries 1M)
4. Define directrix of the parabola as a locus.
5. Define the director circle for an ellipse/Hyperbola

1. Define modulus of complex number
2. Define the conjugate of complex number
3. State Demoivre’s theorem

1. Define Differential coefficient of a continuous function
2. What is the formula for finding the derivative of a function at a particular point from
the first principles?
3. Define a)right hand derivative b) left hand derivative of f(x) at x=a.
4. State Chain Rule of differentiation.
5. Define the length of the sub tangent and subnormal of a curve at any point.
6. Define Increasing and Decreasing function
7. Define maximum and minimum points of a function.
8. State Fundamental theorem of Integral calculus.
9. Define Differential equation.
10. Define order and degree of a differential equation


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