**ELEMENTS OF NUMBER THEORY:**

**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**

**numbers?**

**5. Define the congruence relation in Z and express in terms of divisibility**

**MATRICES AND DETERMINANTS:**

**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.**

**GROUPS**

**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.**

**VECTORS**

**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.**

**CIRLCES:**

**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.**

**CONIC SECTION**

**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**

**COMPLEX NUMBERS**

**1. Define modulus of complex number**

**2. Define the conjugate of complex number**

**3. State Demoivre’s theorem**

**CALCULUS:**

**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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