Mathematics

                                                 Test Paper 1

Chapter: Real Numbers                                                                                                                                 

Max Marks: 30                                               

   Section A: Multiple Choice Questions (1 Mark Each)

1. If two positive integers a and b are written as a = x3y2 and b = xy3, where x, y are prime numbers, then HCF(a, b) is:

(a) xy                                      (b) xy2                                   (c) x3y3                          (d) x2y2

2. The largest number which divides 70 and 125, leaving remainders 5 and 8 respectively, is:

(a) 13                                      (b) 65                                   (c) 875                  (d) 1750

3. If LCM(x, 18) = 36 and HCF(x, 18) = 2, then x is:

(a) 2                                       (b) 3                                      (c) 4                        (d) 1

4. The decimal expansion of the rational number 33/22X5     will terminate after:

(a) One decimal place                                        (b) Two decimal places

          (c) Three decimal places                                    (d) More than 3

Section B: Very Short Answer Questions (2 Marks Each)

5. Explain why 7 x 11 x 13 + 13 is a composite number.

6. Find the HCF and LCM of 12, 15, and 21 by the prime factorisation method.

7. If HCF(306, 657) = 9, find LCM(306,657).

Section C: Short Answer Questions (3 Marks Each)

8. Prove that 5-√√3 is an irrational number, given that √3 is irrational.

9. Three bells toll at intervals of 9, 12, and 15 minutes respectively. If they start tolling together, after what time will they next toll together?

10. Find the smallest number which when increased by 17 is exactly divisible by both 520 and 468.

Section D: Long Answer Questions (5 Marks Each)

11.   Prove that √3 is an irrational number.

12. Case Study Based Question:
A seminar is being conducted by an Educational Organization, where the participants will be educators of different subjects. The number of participants in Hindi, English, and Mathematics are 60, 84, and 108 respectively.
   (i) In each room, the same number of participants are to be seated and all of them being in the same    

        subject. Find the maximum number of participants that can be accommodated in each room. (3 mar (ii) What is the minimum number of rooms required during the seminar? (2 marks)

 Answers Test Paper 1


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