Content
S.No. Chapter Name Page No.
1. Real Numbers 01–15
2. Polynomials 16–26
3. Pair of Linear Equations in Two Variables 27–36
4. Quadratic Equations 37–55
5. Arithmetic Progression 56–73
6. Similar Triangles 74–103
7. Co-ordinate Geometry 104–116
8. Introduction to Trigonometry 117–128
9. Some Applications of Trigonometry 129–138
(Heights and Distances)
10. Circles 139–158
11. Constructions 159–166
12. Areas Related to Circles 167–188
13. Surface Areas and Volumes 189–211
14. Statistics 212–228
15. Probability 229–247
Case Study Based Questions 248–275
Practice Question Paper 276–339
,CHAPTER
1 Real Numbers
KEY POINTS
PROPERTIES OF REAL NUMBERS
Mathematics-X 1
, VERY SHORT ANSWER TYPE QUESTIONS
1. A number N when divided by 16 gives the remainder 5 ______ is the remainder
when the same number is divided by 8.
2. HCF of 33 × 54 and 34 × 52 is ________ .
3. If a = xy2 and b = x3y5 where x and y are prime numbers then LCM of (a, b) is
_____ .
4. In the given factor tree find x and y
y
2 x
5 7
5. If n is a natural number, then 252n – 92n is always divisible by :
(i) 16 (ii) 34
(iii) both 16 or 34 (iv) None of these
327
6. The decimal expansion of the rational number will terminate after
23 5
(a) One decimal place (b) Two decimal place
(c) Three decimal place (d) More than three decimal place
7. Which of the following rational numbers have terminating decimal?
18 5 2 7
(i) (ii) (iii) (iv)
225 18 21 250
(a) (i) and (ii) (b) (ii) and (iii)
(c) (i) and (iii) (d) (i) and (iv)
8. Euclid’s division Lemma states that for two positive integers a and b, there
exist unique integers q and r such that a = bq + r, where r must satisfy.
(a) 1 < r < b (b) 0 < r b
(c) 0 r < b (d) 0 < r < b
n n n
9. p = (a × 5) For p to end with the digit zero a = _____ for natural number n.
(a) any natural number (b) even number
(b) odd number (d) none of these
2 Mathematics-X
, 10. HCF is always
(a) multiple of LCM (b) Factor of LCM
(c) divisible by LCM (d) (a) and (c) both
11. All decimal numbers are
(a) rational number (b) irrational numbers
(c) real numbers (d) integers
12. Which of these numbers always end with the digits 6.
(a) 4n (b) 2n (c) 6n (d) 8n
13. Write the prime factof of 2 × 7 × 11 × 13 × 17 + 21
14. Write the form in which every odd integer can be written taking t as variable.
15. What would be the value of n for which n2–1 is divisible by 8.
16. What can you say about the product of a non-zero rational and irrational number?
13497
17. After how many places the decimal expansion of will terminate?
1250
18. Find the least number which is divisible by all numbers from 1 to 10 (both
inclusive).
19. The numbers 525 and 3000 are divisible by 3, 5, 15, 25 and 75. What is the
HCF of 525 and 3000?
20. What is x : y in the factor-tree?
x
2 210
2 105
3 35
5 y
SHORT ANSWER TYPE QUESTIONS-I
21. If n is an odd integer then show that n2 – 1 is divisible by 8.
22. Use Euclid’s division algorithm to find the HCF of 16 and 28.
23. Show that 12n cannot end with the digit 0 or 5 for any natural number n.
(NCERT Exemplar)
Mathematics-X 3
S.No. Chapter Name Page No.
1. Real Numbers 01–15
2. Polynomials 16–26
3. Pair of Linear Equations in Two Variables 27–36
4. Quadratic Equations 37–55
5. Arithmetic Progression 56–73
6. Similar Triangles 74–103
7. Co-ordinate Geometry 104–116
8. Introduction to Trigonometry 117–128
9. Some Applications of Trigonometry 129–138
(Heights and Distances)
10. Circles 139–158
11. Constructions 159–166
12. Areas Related to Circles 167–188
13. Surface Areas and Volumes 189–211
14. Statistics 212–228
15. Probability 229–247
Case Study Based Questions 248–275
Practice Question Paper 276–339
,CHAPTER
1 Real Numbers
KEY POINTS
PROPERTIES OF REAL NUMBERS
Mathematics-X 1
, VERY SHORT ANSWER TYPE QUESTIONS
1. A number N when divided by 16 gives the remainder 5 ______ is the remainder
when the same number is divided by 8.
2. HCF of 33 × 54 and 34 × 52 is ________ .
3. If a = xy2 and b = x3y5 where x and y are prime numbers then LCM of (a, b) is
_____ .
4. In the given factor tree find x and y
y
2 x
5 7
5. If n is a natural number, then 252n – 92n is always divisible by :
(i) 16 (ii) 34
(iii) both 16 or 34 (iv) None of these
327
6. The decimal expansion of the rational number will terminate after
23 5
(a) One decimal place (b) Two decimal place
(c) Three decimal place (d) More than three decimal place
7. Which of the following rational numbers have terminating decimal?
18 5 2 7
(i) (ii) (iii) (iv)
225 18 21 250
(a) (i) and (ii) (b) (ii) and (iii)
(c) (i) and (iii) (d) (i) and (iv)
8. Euclid’s division Lemma states that for two positive integers a and b, there
exist unique integers q and r such that a = bq + r, where r must satisfy.
(a) 1 < r < b (b) 0 < r b
(c) 0 r < b (d) 0 < r < b
n n n
9. p = (a × 5) For p to end with the digit zero a = _____ for natural number n.
(a) any natural number (b) even number
(b) odd number (d) none of these
2 Mathematics-X
, 10. HCF is always
(a) multiple of LCM (b) Factor of LCM
(c) divisible by LCM (d) (a) and (c) both
11. All decimal numbers are
(a) rational number (b) irrational numbers
(c) real numbers (d) integers
12. Which of these numbers always end with the digits 6.
(a) 4n (b) 2n (c) 6n (d) 8n
13. Write the prime factof of 2 × 7 × 11 × 13 × 17 + 21
14. Write the form in which every odd integer can be written taking t as variable.
15. What would be the value of n for which n2–1 is divisible by 8.
16. What can you say about the product of a non-zero rational and irrational number?
13497
17. After how many places the decimal expansion of will terminate?
1250
18. Find the least number which is divisible by all numbers from 1 to 10 (both
inclusive).
19. The numbers 525 and 3000 are divisible by 3, 5, 15, 25 and 75. What is the
HCF of 525 and 3000?
20. What is x : y in the factor-tree?
x
2 210
2 105
3 35
5 y
SHORT ANSWER TYPE QUESTIONS-I
21. If n is an odd integer then show that n2 – 1 is divisible by 8.
22. Use Euclid’s division algorithm to find the HCF of 16 and 28.
23. Show that 12n cannot end with the digit 0 or 5 for any natural number n.
(NCERT Exemplar)
Mathematics-X 3
