Mathematics solutions

A Complete Manual to

BASIC
MATHEMATICS
GRADE XI



Authors
Kamal Kant Marsyani
Krishan Datt Pant
Sushil Aryal




SUKUNDA PUSTAK BHAWAN
(Publishers and Distributors)
Bhotahity, Kathmandu
Telephone: 5320379, 5353537
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, CONTENTS
Units Chapters Pages

1. Logic, Sets and Real Number System 1

2. Functions 19

3. Curve Sketching 39

1. Algebra 4. Sequence and Series 52

5. Matrices and Determinants 65

6. Quadratic Equations 87

7. Complex Numbers 111
2. Trigonometry 8. Inverse Circular Functions and Trigonometric Equations 125
9. Analytic Geometry 161
3. Analytic
Geometry 10. Pair of Straight Lines 171
11. Coordinates in Space 187
4. Vectors 12. Vectors 205

5. Statistics and 13. Measures of Dispersion 215
Probability 14. Probability 233

15. Limits and Continuity 241

16. The Derivatives 279
6. Calculus
17. Application of Derivatives 331

18. Antiderivatives 343

7. Computational 19. Numerical Computation 401
Methods
20. Numerical Integration 419

OR 21. Statics 438
Mechanics 22. Dynamics 449

, 1 Algebra
Chapter 1 Logic, Sets and Real Number System


1.1 Logic.
EXERCISE 1.1 . (Textbook Page No. 15)

1. Which of the following sentences are the statements ? Find the truth values of those sentences
which are statements.
a) Kathmandu is the capital of Nepal. b) Nepal exports oil. c)3 + 5 = 8
d) Where do you live ? e) Understand logic. f)Oh! how beautiful the scene is?
Soln:a) The given sentence is declarative sentence. So, it is a statement and its truth value is true (T).
b) The given sentence is declarative sentence. So, it is a statement and its truth value is false f).
c) The given sentence is declarative sentence. So, it is a statement and truth value is true (T).
d) The given sentence is an interrogative sentence. So, it is not a statement.
e) The given sentence is an imperative sentence. So, it is not a statement.
f) The given sentence is an exclamatory sentence. So, it is not a statement.
2. Let p : demand is increasing and q : supply is decreasing.
Express each of the following statements into words.
Soln: a) ~p:demand is not increasing.
b) ~q:supply is not decreasing.
c) p  q: Demand is increasing and supply is decreasing.
d) p  q: Demand is increasing or supply is decreasing.
e) ~p  q: Demand is not increasing and supply is decreasing.
f) p  ~q: Demand is increasing or supply is not decreasing.
g) ~p  ~q: Neither demand is increasing nor supply is decreasing.
h) ~(p  q): It is false that demand is increasing and supply is decreasing.
3. Express each of the following statements into symbolic form;
a) p : temperature is increasing, q : length is expanding.
Temperature is increasing and length is expanding.
Soln: p  q
b) p : pressure is decreasing, q : Volume is increasing
Pressure is decreasing or volume is increasing.
Soln: p  q
c) p : demand is increasing, q : price is increasing
Neither demand is increasing nor price is decreasing [i.e. not increasing]
Soln: (~p  q)
d) p : Pradeep is bold, q : Sandeep is handsome
It is false that Pradeep is bold or Sandeep is handsome.
Soln: ~(p  q)

, *2* A Complete Manual to BASIC MATHEMATICS: Grade XI
4. Construct truth tables for the following compound statements;
a) (~p)  q
Soln: The truth table for (~p)  q is,
p q ~p (~p) q
T T F F
T F F F
F T T T
F F T F
b) (~p)  (~q)
Soln:The truth table for(~p)  (~q) is,
p q ~p ~q ~(p)  (~q)
T T F F F
T F F T T
F T T F T
F F T T T
c) ~(p  q)
Soln: The truth table for ~(p  q) is,
P q pq ~ (p  q)
T T T F
T F F T
F T F T
F F F T
d) ~ [p  (~ q)]
Soln: The truth table for ~ [p  (~ q)]is,
P q ~q p  (~q) ~ (p  (~q))
T T F T F
T F T T F
F T F F T
F F T T F
e) (p  q)  (q  p)
Soln: The truth table for (p  q)  (q  p) is,
P q pq qp (p  q)  (q  p)
T T T T T
T F F T F
F T T F F
F F T T T
f) (~ p  q)  p  q
Soln: The truth table for (~ p  q)  p  q is,
p q ~p (~p)  q pq (~p  q)  p  q
T T F F T T
T F F F T T
F T T T T T
F F T F F T


Chapter 1 Logic, Sets and Real Number System