Class 10 Mathematics All Chapters Test Paper Solved

1. REAL NUMBERS

1. What is the least number that is divisible by all the numbers from 1 to 10?

2. Complete the following factor tree and find the composite number x and y .

3. Write the decimal representation of the rational number 8/27.

4. If HCF of a and b is 12 and product of these numbers is 1800. Then what is LCM of these numbers?

5. 5. If a is an odd number, b is not divisible by 3 and LCM of a and b is P, what is the LCM of 3a and 2b?

6. A rational number in its decimal expansion is 1.7351. What can you say about the prime factors of q when this number is expressed in the form p/q? Give reason.

7. Find LCM of numbers whose prime factorisation are expressible as 3 × 52 and 32 × 72.

8. Find the LCM of 96 and 360 by using fundamental theorem of arithmetic.

9. The LCM of two numbers is 14 times their HCF. The sum of LCM and HCF is 600. If one number is 280, then find the other number.

10. Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers. 198 and 144.

11. If two positive integers x and y are expressible in terms of primes as x = p2q3 and y = p3q, what can you say about their LCM and HCF. Is LCM a multiple of HCF? Explain.

12. Find the largest number which divides 70 and 125 leaving remainder 5 and 8 respectively.

13. In a school, there are two Sections A and B of class X. There are 48 students in Section A and 60 students in Section B. Determine the least number of books required for the library of the school so that the books can be distributed equally among all students of each Section.

14. If n is an odd positive integer, show that (n2 – 1) is divisible by 8.

15. Prove that √7 is an irrational number

16. Find the largest number that will divide 398, 436 and 542 leaving remainders 7, 11, and 15 respectively.

17. Using prime factorisation method, find the HCF and LCM of 30, 72 and 432. Also show that HCF × LCM ≠ Product of the three numbers.

18. Amita, Sneha, and Raghav start preparing cards for all persons of an old age home. In order to complete one card, they take 10, 16 and 20 minutes respectively. If all of them started together, after what time will they start preparing a new card together?

19. Dudhnath has two vessels containing 720 ml and 405 ml of milk respectively. Milk from these containers is poured into glasses of equal capacity to their brim. Find the minimum number of glasses that can be filled.

20. There are 104 students in class X and 96 students in class IX in a school. In a house examination, the students are to be evenly seated in parallel rows such that no two adjacent rows are of the same class.