Category: COURSE DESCRIPTION:

• Relations and Functions
• Inverse Trigonometric Fucntions
• Matrices
• Determinants
• Continuity and Differentiability
• Application of Derivatives
• Integrals
• Applications of Integrals
• Differential Equations
• Vector Algebra
• Three Dimensional Geometry
• Linear Programming
• Probability

### Relations and Functions

1
Equivalence Relation
2
Equivalence Relation – Problems
3
Types of Functions
4
Composite Functions, Exercise.1.3 [3(ii), 4]
5
Invertible Function, How to find the Value of Inverse, Exercise.1.3 
6
Exercise.1.3 [8,11,13]
7
Exercise.1.3 , Binary Operations; Exercise.1.4 [1(i,iii),2,9(ii)]
8
Exercise.1.4 [9(i,v),11]; Identity Element
9
Exercise 1.1 (2, 3, 4 & 5)
10
Exercise 1.1 ( 6, 7, 9 i, 9 ii)
11
Exercise 1.1 [10( i, ii, iii, iv, v), 15, 16]
12
Exercise1.4 [6(i,ii,iii,iv,v),7,8,12(i,ii),13]

### Inverse Trigonometric Functions

1
Introduction, Properties; Exercise.2.1 [2, 3, 4]
2
Exercise.2.2 [1, 2, 3, 4, 5]
3
Exercise.2.2 [6, 7, 8, 9, 10]
4
Exercise.2.2 [11, 12, 13, 14, 15, 16]
5
Exercise.2.2 [17, 18, 19, 20, 21]
6
Miscellaneous Exercise. [3, 4, 5, 8]
7
Exercise 2.1 (1,5,6,7,8,9,10,11,12,13)

### Matrices - Part 1

1
Introduction, Types of Matrices, Operations on Matrices.
2
Transpose of a Matrix, Results of Transpose of a Matrix, Exercise. 3.1 [ 1, 2]
3
Exercise. 3.1 [ 4, 5]
4
Exercise 3.1 [6, 7, 9]

### Matrices - Part 2

1
Exercise 3.2 [1(i, ii, iii, iv, v), 2(i, ii, iii, iv), 3(i, ii, iii)
2
Exercise.3.2 [3 (iv, v, vi), 4, 5]
3
Exercise.3.2 [6, 7 (i, ii), 8, 9]
4
Exercise.3.2 [10, 11, 12 & 13]
5
Exercise.3.2 [14(i, ii)]
6
Exercise. 3.2 [15, 16]
7
Exercise. 3.2 [17, 18]
8
Exercise. 3.3 [ 1(i, ii, iii), 2(i, ii), 3(i, ii) , 4]
9
Exercise 3.3 [5(i, ii), 6(i, ii)]; Concept of Symmetric and Skew Symmetric Matrix
10
Exercise 3.3 [8(i, ii), 9, 12, 10(i)]
11
Exercise 3.3 [10 (iv)]; Ex 3.4 
12
Exercise 3.4 [2, 3, 4, 5, 6]
13
Exercise 3.4 [7, 8, 9, 10, 11]
14
Exercise. 3.4 [12, 13, 14, 15]

### Determinants - Part 1

1
Introduction To Determinants; Exercise 4.1 [1, 2(i, ii), 3, 4]
2
Exercise 4.1 [5 (i,ii,iii,iv) , 6, 7 (i,ii), 8]
3
Properties of Determinants ; Exercise 4.2(1)
4
Exercise 4.2( 2 TO 5)
5
Exercise 4.2[ 6,7,8 (i,ii)]
6
Exercise 4.2[9,10(i,ii),11(i)]
7
Exercise 4.2[11(ii),12,13,14]
8
Area of triangle and Collinearity; Exercise 4.3 [ 1-(i,ii,iii),2,3(i,ii) ] ; Equation of line joining given two points
9
Exercise 4.3 [ 4(i,ii),5];Minors and Cofactors; Exercise 4.4 [1(i,ii),2(i),3,4]
10
Adjoint of Matrix; Exercise 4.5 (1,2,3,4)
11
Exercise 4.5 (5 to 10)

### Determinants - Part 2

1
Exercise 4.5 (11 to 14)
2
Exercise 4.5 (15,16)
3
Consistency of system of equations ; Exercise 4.6 (1,2,3,4,5,6)
4
Exercise 4.6 (7,8,9,10,11)
5
Exercise 4.6 (12,13,14)
6
Exercise 4.6 (15);Miscellaneous Exercise (16)

### Continuity and Differentiability

1
Introduction; Properties of Continuity
2
Exercise 5.1 (3-d,4,5,6,7)
3
Exercise 5.1 (8 to 13)
4
Exercise 5.1 (14 to 18, 20)
5
Exercise 5.1 (21 a,b,c)
6
Exercise 5.1 (22,23,24)
7
Differentiability; Exercise 5.3 (1 to 10)
8
Exercise 5.3 (11,13,14,15);Exercise 5.4 (1 to 10)
9
Exercise 5.5 (1 to 4)
10
Exercise 5.5 (5 to 8)
11
Exercise 5.5 (9 to 13)
12
Exercise 5.5 (14,15,16,17a)
13
Exercise 5.6 (1 to 7)
14
Exercise 5.6 (8 to 11); Exercise 5.7 (1 to 5)
15
Exercise 5.7 (6 to 11)
16
Exercise 5.7 (13 to 17)
17
Rolle’s theorem; Exercise 5.8 (1 to 4)
18
Exercise 5.1 (26 to 30)
19
Exercise 5.2 (1 to 9)

### Application of Derivatives - Part 1

1
Application of Derivatives; Rate of Change of Quatities ;Exercise 6.1 (1 to 4)
2
Exercise 6.1 (5 to 9)
3
Exercise 6.1 (10 to 18)
4
Increasing and Decreasing Functions; Theorem 1; Exercise 6.2 (1 to 5)
5
Exercise 6.2 (7,6)
6
Exercise 6.2 (9,10 ,13 to 16)(17 to 19)
7
Tangents
8
Exercise 6.3 (7 to 11)
9
Exercise 6.3 (13,14)
10
Exercise 6.3 (15 to 17)

### Application of Derivatives - Part 2

1
Exercise 6.3 (18 to 21)
2
Exercise 6.3 (22 to 26)
3
Exercise 6.4 [1 – (i to v)]
4
Exercise 6.4 [1 – (vi to xii)]
5
Exercise 6.4 [1 – (vi to xii),2,3]
6
Exercise 6.4 (4,5,6,7,8)
7
Exercise 6.4 (9) ;Exercise 6.5 [1-(a,b,c,d)]
8
Exercise 6.5 [2 – (i to v)]
9
Exercise 6.5 [3 – (i to iv)]
10
Exercise 6.5 [3 – (v to viii)]
11
Exercise 6.5 [4- (a,b,c),5-(a,b,c)]
12
Exercise 6.5 (5,6,7)
13
Exercise 6.5 (8,9,11)
14
Exercise 6.5 (12 to 14)
15
Exercise 6.5 (15 to 17)
16
Exercise 6.5 (19 to 20)
17
Exercise 6.5 (21,22)
18
Exercise 6.5 (23)
19
Exercise 6.5 (24,25)
20
Exercise 6.5 (27,28,29)

### Integrals - Part 1

1
Integrals ; Exercise 7.1 (1 to 7)
2
Exercise 7.1 (8,9,12,13,14,15)
3
Exercise 7.1 (16 to 21)
4
Exercise 7.1 (22) ;Exercise 7.2 (1 to 5)
5
Exercise 7.2 (6 to 10)
6
Exercise 7.2 (11 to 17)
7
Exercise 7.2 (18,21 to 26)
8
Exercise 7.2 (27 to 33)
9
Exercise 7.2 (34 to 39); Exercise 7.3 (1,2)
10
Exercise 7.3 (3,5,6)
11
Exercise 7.3 (7 to 10)
12
Exercise 7.3 (11 to 13)
13
Exercise 7.3 (14 to 18)
14
Exercise 7.3 (20,21)
15
Exercise 7.3 (22 to 24); Exercise 7.4(1)
16
Exercise 7.4 (2,4,5,6)
17
Exercise 7.4 (7 to 11)
18
Exercise 7.4 (12 to 14)
19
Exercise 7.4 (15 to 17)
20
Exercise 7.4 (18)
21
Exercise 7.4 (19,20)
22
Exercise 7.4 (21,22)
23
Exercise 7.4(23 to 25)
24
Exercise 7.5 (1 to 3)
25
Exercise 7.5 (4,5)

### Integrals - Part 2

1
Exercise 7.5 (9,10)
2
Exercise 7.5 (11,12)
3
Exercise 7.5 (13 to 15)
4
Exercise 7.5 (16 to 18)
5
Exercise 7.5 (20 to 23)
6
Exercise 7.6 (1 to 5)
7
Exercise 7.6 (6 to 9)
8
Exercise 7.6 (10 to 14)
9
Exercise 7.6 (15 to 21)
10
Exercise 7.6 (22 to 24); Exercise 7.7 (1,2)
11
Exercise 7.7 (3,4,5,6)
12
Exercise 7.7 (7 to 11)
13
Definite Integrals ; Exercise 7.8(1,2)
14
Exercise 7.8(4)
15
Exercise 7.8(5.6)
16
Exercise 7.9(1 to 8)
17
Exercise 7.9(15 to 18)
18
Exercise 7.9(19,21,22); Exercise 7.10(1)
19
Exercise 7.10(2,3)
20
Exercise 7.10(4,5,7,8)
21
Exercise 7.11(2,3,4,5)
22
Exercise 7.11(7,8,9,10)
23
Exercise 7.11(15,17,18,19,20,21)

### Applications of Integrals

1
Introduction
2
Exercise 8.1(1,2,3)
3
Exercise 8.1(8,9,10)
4
Exercise 8.1(11,12,13); Exercise 8.2(1)
5
Exercise 8.2(2,3)
6
Exercise 8.2(4,6,7)

### Differential Equations

1
Introduction
2
Exercise 9.4(11)
3
Exercise 9.4(12,13,14,16)
4
Exercise 9.2(1,2,3,4,5,6)
5
Exercise 9.2(7,8,9,10,11,12)
6
Exercise 9.3(1,2,5,10,11,12)
7
Exercise 9.4(1,2,3,4,5,6,7,9)
8
Exercise 9.4(17,18,19)
9
Exercise 9.4(22,23);Exercise 9.5(1)
10
Exercise 9.5(2,3,4)
11
Exercise 9.5(5,6,7)
12
Exercise 9.5(8,9,10)
13
Exercise 9.5(12,17)
14
Exercise 9.6(1,2,3,5)
15
Exercise 9.6(6,7,8,10)
16
Exercise 9.6(11,12,13,14,15)
17
Exercise 9.6(16,17,18,19)

### Vector Algebra

1
Introduction
2
Exercise 10.2 (2,3,4,6,7,9,10)
3
Exercise 10.2 (12 to 18)
4
Exercise 10.3 (1 to 7)
5
Exercise 10.3 (8 to 15)
6
Exercise 10.3 (18); Exercise 10.4 (1,2,3,5)
7
Exercise 10.4 (6,7,9,10,11,12)

### Three Dimensional Geometry

1
Introduction
2
Exercise 11.1(1,2,3,4)
3
Exercise 11.1(5);Exercises 11.2(1,2,3,4)
4
Exercise 11.2(6,7,12)
5
Exercise 11.2(13,14,15)
6
Exercise 11.2(16,17);Exercise 11.3(1)
7
Exercise 11.3(3,4,7)
8
Exercise 11.3(8,9,10)
9
Exercise 11.3(11,12,13)
10
Exercise 11.3 [14(a,b,c,d)]

### Linear Programming

1
Introduction
2
Exercise 12.1(4,5)
3
Exercise 12.1(6,7)
4
Exercise 12.2(1,2)
5
Exercise 12.2(3,4)
6
Exercise 12.2(5)
7
Exercise 12.2(6,7)
8
Exercise 12.2(8)
9
Exercise 12.2(9,11)

### Probability

1
Introduction
2
Exercise 13.1(1 to 5)
3
Exercise 13.1[6(i,ii)]
4
Exercise 13.1[6(iii),8,9]
5
Exercise 13.1(10,11)
6
Exercise 13.1(12,14,15); Exercise 13.2(1,2)
7
Exercise 13.2(3,5,8,11)
8
Exercise 13.2(10,16)
9
Exercise 13.2(6,7,9,12,15)
10
Exercise 13.3(1,3,4)
11
Exercise 13.3(5,6,7)
12
Exercise 13.3(8,9,10,11)
13
Exercise 13.3(12,13); Exercise 13.4(1,2,3)
14
Exercise 13.4(4,6)
15
Exercise 13.4(9,11,14)
16
Exercise 13.5(1,9,12,13)