Real number CBSE TEST PAPER-06

Math Adda


CBSE TEST PAPER-06

MATHEMATICS (Class-10)

Chapter 1. Real Numbers
1. Express each number as a product of its prime factors:

(i) 140 (ii) 156 (iii) 3825 (iv) 5005 (v) 7429

2. Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers.

(i) 26 and 91 (ii) 510 and 92 (iii) 336 and 54

3. Find the LCM and HCF of the following integers by applying the prime factorization method.

(i) 12, 15 and 21 (ii) 17, 23 and 29 (iii) 8, 9 and 25

4. Given that HCF (306, 657) = 9, find LCM (306, 657).

5. Check whether 6n can end with the digit 0 for any natural number n.

6. Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.

7. There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?

12. Use Euclid’s division lemma to show that the square of any positive integer is of the form 5q, 5q+1,5q+4 for some integer q.

13. Show that any one of the numbers (n + 2), n and (n + 4) is divisible by 3.

14. If 793800 = 2 3 x 3 m x 5 n x 7 2, find the value of m and n. 15. If the HCF of 210 and 55 is expressible in the form 210 × 5 + 55y then find y

Real number

Math Adda

                    CBSE TEST PAPER-05

                            MATHEMATICS (Class-10)

                               Chapter 1. Real Numbers

1. Use Euclid’s division algorithm to find the HCF of : (i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255
2. Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.
3. An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march? Sol. Hints: Find the HCF of 616 and 32
4. Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m. [Hint : Let x be any positive integer then it is of the form 3q, 3q + 1 or 3q + 2. Now square each of these and show that they can be rewritten in the form 3m or 3m + 1.]
5. Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m, 9m+ 1 or 9m + 8.
6. Consider the numbers 4n, where n is a natural number. Check whether there is any value of nfor which 4n ends with the digit zero.
7. Find the LCM and HCF of 6 and 20 by the prime factorization method.
8. Find the HCF of 96 and 404 by the prime factorization method. Hence, find their LCM.
9. Find the HCF and LCM of 6, 72 and 120, using the prime factorization method.
10. Find the value of y if the HCF of 210 and 55 is expressible in the form 210 x 5 + 55y
11. Prove that no number of the type 4K + 2 can be a perfect square.

Real Number

Math Adda

                 CBSE TEST PAPER-04

                         MATHEMATICS (Class-10)

                        Chapter 1. Real Numbers

1.    Express 5005 as a product of its prime factors.

2.    Find the LCM and HCF of 24, 36 and 72 by the prime factorization method.

3.    Find the LCM and HCF of 96 and 404 by the prime factorization method

4.    State whether 64/455  will have a terminating decimal expansion or a non-terminating repeating decimal

5.     State whether15/ 1600   will have a terminating decimal expansion or a non-terminating repeating decimal.

6.    Find the LCM and HCF of 510 and 92 and verify that LCM × HCF = product of the two numbers.

7.    Use Euclid’s division algorithm to find the HCF of 196 and 38220 (3 marks)

8.    Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m,9m + 1 or 9m + 8

9.     Show that every positive odd integer is of the form 2q, and that every positive odd integer is of the form 2q + 1, where q is some integer

10.  10. Show that 3√ 2 is irrational.

11.  11. Prove that 3 + 2 √5 is irrational.

12.  A sweet seller has 420 kaju barfis and 130 badam barfis. She wants to stack them in such a way that each stack has the same number, and they take up the least area of the tray. What is the maximum number of barfis that can be placed in each stack for this purpose?