## CBSE PRACTICE PAPER MATHS FOR CLASS 10 REAL NUMBERS CHAPTER 1

**Q 1 – The prime factorisation of 13915 is (1 Marks)**

**a) 5 × 11 ^{3} × 13^{2}**

b) 5 × 11^{3} × 23^{2}

c) 5 × 11^{2} × 23

d) 5 × 11^{2} × 13^{2}

**Q 2 – A Mathematics Exhibition is being conducted in your School and one of your friends is making a model of a factor tree. He has some difficulty and asks for your help in completing a quiz for the audience.**

**Observe the following factor tree and answer the following:**

**1. What will be the value of x? (1 Marks) **

**a) 15005**

b) 13915

c) 56920

d) 17429

b) 13915

c) 56920

d) 17429

**2. What will be the value of y? (1 Marks) **

**a) 23**

b) 22

c) 11

d) 19

b) 22

c) 11

d) 19

**3. What will be the value of z? (1 Marks) **

**a) 22**

b) 23

c) 17

d) 19

b) 23

c) 17

d) 19

**Q 3 – The product of HCF and LCM of 60, 84 and 108 is (1 Marks) a) 55360 b) 35360 c) 45500 d) 45360**

**Q 4 – A seminar is being conducted by an Educational Organisation, where the participants will be educators of different subjects. The number of participants in Hindi, English and Mathematics are 60, 84 and 108 respectively.**

**In each room the same number of participants are to be seated and all of them being in the same subject, hence maximum number participants that can accommodated in each room are(1 Marks)**

a) 14

b) 12

c) 16

d) 18

**2. What is the minimum number of rooms required during the event? (1 Marks)**

**a) 11**

**b) 31c) 41d) 21**

**Q 5 – For any two positive integers a and b, there exist (unique) whole numbers q and r such that(1 Marks) (a) q = ar + b , 0 **

**⩽**

**r < b.**

(b) a = bq + r , 0

(b) a = bq + r , 0

**⩽**

**r < b.**

(c) b = aq + r , 0

(c) b = aq + r , 0

**⩽**

**r < b.**

(d) none of these

(d) none of these

**Q 6 – The least number that is divisible by all the numbers from 1 to 8 (both inclusive) is (1 Marks)**

**(a) 840(b) 2520**

**(c) 8(d) 420**

**Q 7 – The decimal expansion of the rational number ** **will terminate after how many places of decimals? (1 Marks)**

**Q 8 – If the HCF of 408 and 1032 is expressible in the form 1032 ** ** 2 + 408 ** ** p, then find the value of p. (1 Marks)**

**Q 9 – ****The decimal expansion of π is:****(1 Marks)**

**Terminating****Non-terminating and Non-recurring****Non-terminating and recurring****Doesn’t exist**

**Q 10 – Find the largest number that will divide 398, 436 and 542 leaving remainders 7, 11, and 15 respectively. (1 Marks)**

**Q 11 – Which of the following rational numbers have a terminating decimal expansion and what no of terminating decimal digits are present (1 Marks)**

**Q 12 – HCF and LCM of two numbers is 9 and 459 respectively. If one of the numbers is 27, find the other number. (1 Marks)**

**Q 13 – Find LCM of numbers whose prime factorisation is expressible as 3 × 5 ^{2} and 3^{2} × 7^{2}.(1 Marks)**

**Q 14 – Find the HCF (865, 255) using Euclid’s division lemma. (2 Marks)**

**Q 16 – Check whether 4 ^{n} can end with the digit 0 for any natural number n. (2 Marks)**

**Q 18 – Two tankers contain 850 liters and 680 liters of petrol. Find the maximum capacity of a container which can measure the petrol of each tanker in the exact number of times. (2 marks)**

**Q 19 – By using Euclid’s algorithm, find the largest number which divides 650 and 1170. (2 Marks)**

**Q 20 – The length, breadth, and height of a room are 8 m 50 cm, 6 m 25 cm and 4 m 75 cm respectively. Find the length of the longest rod that can measure the dimensions of the room exactly. (2 Marks)**

**Q 21 – If two positive integers x and y are expressible in terms of primes as x = p ^{2} q^{3} and y = p^{3}q,**

**what can you say about their LCM and HCF. Is LCM a multiple of HCF? (2 Marks)**

**Q 22 – Find the HCF and LCM of 306 and 657 and verify that LCM × HCF = Product of the two numbers. (2 Marks)**

**Q 23 – Find whether decimal expansion of 13/64 is a terminating or non-terminating decimal. If it terminates, find the number of decimal places its decimal expansion has. (3 Marks)**

**Q 24 – Floor of a room is to be fitted with square marble tiles of the largest possible size. The size of the room is 10 m ** ** 7 m. What should be the size of tiles required that has to be cut and how many such tiles are required? (3 Marks)**