Subject: Higher Mathematics (Theoretical)

Full Marks: 75 Subject: Code: 126 Time: 3 Hours

[NB: The Figures in the right margin indicate full marks]Algebra: 35

1. Answer any one from two questions. 4

Exercise: 1.1= 4**,5**,6**,8

Example: 5**

Exercise: 1.2= 1(i)***,5**,7**, Proposition: 9 (i), (ii), 10 (i), (ii), 11 (i)**, (ii)***, 12***, 13

Example: 1.3= 9**, 10**

2. Algebraic Expression: Answer any two from three questions. 3×2=6

(a) Resolve in to factors:

Exercise: 2.1= 11 (iii), (vii), (ix), (x)***

Example: 10, 12**

Exercise: 2.2= 1 (v), (vii), (xv)**

(b) Simplify/Partial fractions:

Exercise: 2.3= 3**, 4**, 5**, 7**, 8***, 12

Example: 6**, 11***

(c) Prove that/show that

Exercise: 2.1= 7**

Example: 6**

Exercise: 2.2 = 2**, 3**, 4**, 5***

Corollary- 1, 5

3. Method Mathematical Induction: Answer any one from two questions. 4

Exercise: 3= 4 (iii)**, 5 (ii), (iv)**, (v)**, (vi)**, (vii), (viii)

Example: 3**

4. Indices and logarithms: Answer any one from two questions. 5

Exercise: 4.2= 5 (b), (f), 6 (c)**, 7(a)**, (b)***, (c)*, (d)**, (e)

Example: 10**, 11***, 12, 14***

Exercise: 4.3= 2 (a)**, (c)**, (d)***, (e)***, (f)*

Example: 10**, 11**, 12**

5. Relation Function and graph: Answer any one from two questions. 4

Exercise: 5.1= 1 (b), (d), 2 (a), (b), (d), 5 (a)**, (b)**, (c)**, (d)**, 9**, 10**

Example: 2**

Exercise: 5.2= 4 (a), (b)**, (c)**, (d)**, 6 (a)

6. Equation in on variable and inequalities: Answer any one from two questions. 4

Exercise: 6.1= 6, 7, 8, 9**, 10**

Example: 5

Exercise: 6.2= 8**, 9**, 10**, 11**, 12**

Example: 5**, 7**, 8**

Exercise: 6.3= 5, 6

Example: 2***, 3**

Exercise: 6.4= 4, 5**, 6**, 7, 8

Example: 2

7. System of linear equations with two or three variables and Inequalities of two variables: Answer any one from two questions. 4

Exercise: 7.1= 5, 6, 7, 10*, 11

Example: 5

Exercise: 7.2= 5**, 7**, 8**, 9**

Example: 3, 6**

Exercise: 7.3= 6*, 8*, 9*

Example: 3***

8. Infinite series: Answer one from one question. 4

Exercise: 8= 3, 4 (a), (b), (c)**, 5**, 6

Example: 1 (a), (b), 2

9. Answer any one from two questions. 6

Theorem: 2.3**, 3.3, 3.4, 3.7***

Theorem: 4.4***, 4.6***, 4.7**, 4.8

10. Answer any one from two questions. 6

Exercise: 2= 5**, 6**, 7**, 8**, 9. 10***

Exercise: 3.1= 6**, 8**, 13***

Exercise: 3.2= 6**, 8**

Exercise: 4= 6*, 7**, 9, 11**, 18**, 22, 23**

11. Answer any one from two questions. 5×1=5

Problem: 1*, 2**, 4, 5, 6, 7, 8, 9**, 10**

12. Answer any one from two questions. 4×1=4

Exercise: 6= 1 (c), 5 (b), 6, 7**, 9**, 10**

Example: 3***, 4***, 5**, 6

Solid Geometry-4

13. Answer any one from two questions. 5×1=5

Exercise: 7.2= 6**, 7*, 11, 12, 13, 14, 15**, 18**, 19**, 20**, 21**, 25**

Example: 8**

Trigonometry-12

14. Answer any three from five questions. 4×3=12

Exercise: 8.1= 2, 3, 4, 5, 6**, 7, 8, 10, 15**, 16**, 17**, 18**

What is radian? Prove that radian is a constant angel

Exercise: 8.2= 3**, 4, 10**, 11**, 12**, 13, 14**, 15**, 16**, 19**, 20**, 21**, 22

Example: 4***

Exercise: 8.3= 1 (iv), (v), (vi), 4 (i), (iv), 5 (iii), 6 (i), (ii)**, 7 (i), (ii), (iii), (iv), 9***, {(i) to (xi)}, 11, 13, 14, 15

Example: 4, 5

Statistics-5

15. Answer any one from two questions. 5×1=5

Exercise: 9.2= 3, 4, 5, 6

Example: 2, 3

Exercise: 9.3= 2, 3, 5, 6

Example: 3**, 4**

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