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IIT JEE MAIN 2026

LTL QT24 - Number system, Test 1

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1.HCF of 1007 and 1273 is :

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2.The product of two numbers is 84 and their HCF is 2. Find the numbers of such pairs.

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3.The product of two numbers is 15120 and their HCF is 6, find the number of such pairs

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4.The number of pairs of two numbers whose product is 300 and their HCF is 5:

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5.The largest possible number by which when 76, 132 and 160 are divided the remainders obtained are the same is :

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6.Find the number of pairs of two numbers whose HCF is 5 and their sum is 50.

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7.The largest possible length of a tape which can measure 525 cm, 1050 cm and 1155 cm length of cloths in a minimum number of attempts without measuring the length of a cloth in a fraction of the tape's length

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8.Minimum how many similar tiles of square shape are required to furnish the floor of a room with the length of 462 cm and breadth of 360 cm?

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9.The ratio of two numbers is 15: 11. If their HCF be 13 then these numbers will be :

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10.The three numbers are in the ratio 1:2:3 and their HCF is 12. These numbers are

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11.Two pencils are of 24 cm and 42 cm. If we want to make them of equal size then minimum no. of similar pencils is

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12.The unit digit of the following expression (1!)^99 + (2!)^98 + (3!)^97 + (4!)^96 + ... (99!)^1 is:

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13.The sum of all four digit numbers which are divisible by 7 is:

 

 

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14.What are the values of the digits a and b, respectively, in the number a 5523879 b, if it is divisible by both a and b :

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15.(2^19 + 1) is divisible by:

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16.The unit digit of (12345k) ^ 72 is 6. The value of k is:

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17.What is the least number which must be subtracted from 369 to make it a perfect cube?

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18.The quotient when 12.5 is divided by 1/6 is:

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19.Three bells, toll at interval of 36 sec, 40 sec and 48 sec respectively. They start ringing together at particular time. They will toll together next time after :

 

 

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20.The greatest integer that divides 358, 376, 232 leaving the same remainder in each case is:

 

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21.For a journey the cost of a child ticket is 1/3rd of the cost of an adult ticket. If the cost of the tickets for 4 adults and 5 children is Rs.85, the cost of a child ticket is:

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22.The least number which is a perfect square and has 540 as a factor is:

 

 

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23.A fraction becomes 4 when 1 is added to both the numerator and denominator and it becomes 7 when 1 is subtracted from both the numerator and denominator. The numerator of the given fraction is :

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24.The largest sum of money which is contained in both Rs.49.56 and Rs.38.94 an exact number of times is:

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25.Tanya gives away to each of four girls 1/12,5/18,7/30,7/48 of the apples in a basket and has only just enough apples to be able to do so without dividing an apple. The minimum number of apples she has in her basket :

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