**1**. A boy took a seven digit number ending in 9 and raised it to an even power greater than 2000. He then took the number 17 and raised it to a power which leaves the remainder 1 when divided by 4. If he now multiplies both the numbers, what will be the unit’s digit of the number he so obtains?

**Answer** – **7**

**The unit’s digit of the number he so obtains is 7.**

**1**. A boy took a seven digit number ending in 9 and raised it to an even power greater than 2000. He then took the number 17 and raised it to a power which leaves the remainder 1 when divided by 4. If he now multiplies both the numbers, what will be the unit’s digit of the number he so obtains?

**Answer** – **7**

**The unit’s digit of the number he so obtains is 7.**

**2**. A hundred and twenty digit number is formed by writing the first x natural numbers in front of each other as 12345678910111213……. Find the remainder when this number is divided by 8.

**Answer** – **6**

**The remainder when this number is divided by 8 is 6.**

**2**. A hundred and twenty digit number is formed by writing the first x natural numbers in front of each other as 12345678910111213……. Find the remainder when this number is divided by 8.

**Answer** – **6**

**The remainder when this number is divided by 8 is 6.**

**3**. Which of the following number can be a number divisible by 24?

**Answer** – **13, 62, 480**

**13, 62, and 480 is divisible by 24.**

**3**. Which of the following number can be a number divisible by 24?

**Answer** – **13, 62, 480**

**13, 62, and 480 is divisible by 24.**

**4**. If A5377B is divisible by 72 then which of the following will be maximum?

**Answer** – **2AB**

**If A5377B is divisible by 72 then 2AB will be maximum.**

**4**. If A5377B is divisible by 72 then which of the following will be maximum?

**Answer** – **2AB**

**If A5377B is divisible by 72 then 2AB will be maximum.**

**5**. What is the least number which when doubled will exactly be divisible by 12, 14, 18 and 22?

**Answer** – **1386**

**1386 is the least number which when doubled will exactly be divisible by 12, 14, 18 and 22.**

**5**. What is the least number which when doubled will exactly be divisible by 12, 14, 18 and 22?

**Answer** – **1386**

**1386 is the least number which when doubled will exactly be divisible by 12, 14, 18 and 22.**

**6**. What is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder?

**Answer** – **1683**

**1683 is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder.**

**6**. What is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder?

**Answer** – **1683**

**1683 is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder.**

**7**. The least number which should be added to 28523 so that the sum is exactly divisible by 3, 5, 7 and 8 is:

**Answer** – **37**

**37 is the least number which should be added to 28523 so that the sum is exactly divisible by 3, 5, 7 and 8.**

**7**. The least number which should be added to 28523 so that the sum is exactly divisible by 3, 5, 7 and 8 is:

**Answer** – **37**

**37 is the least number which should be added to 28523 so that the sum is exactly divisible by 3, 5, 7 and 8.**

**8**. A number is such that when divided by 3,5,6 or 7 it leaves the remainder 1,3,4 or 5 respectively. Which is the largest number below 4000 that satisfies this property?

**Answer** – **3988**

**3988 is the largest number below 4000 that satisfies this property.**

**8**. A number is such that when divided by 3,5,6 or 7 it leaves the remainder 1,3,4 or 5 respectively. Which is the largest number below 4000 that satisfies this property?

**Answer** – **3988**

**3988 is the largest number below 4000 that satisfies this property.**

**9**. The sides of a pentagonal field are 1737 meters, 2160 meters, 2358 meters, 1422 meters respectively. Find the greatest length of the tape by which the five sides may be measured completely.

**Answer** – **9**

**The greatest length of the tape by which the five sides may be measured completely is 9.**

**9**. The sides of a pentagonal field are 1737 meters, 2160 meters, 2358 meters, 1422 meters respectively. Find the greatest length of the tape by which the five sides may be measured completely.

**Answer** – **9**

**The greatest length of the tape by which the five sides may be measured completely is 9.**

**10**. If x = (16^{3}+17^{3}+18^{3}+19^{3}), then x divided by 70 leaves a remainder of:

**Answer** – **0**

**If x = (16**^{3}+17^{3}+18^{3}+19^{3}), then x divided by 70 leaves a remainder of 0.

**10**. If x = (16^{3}+17^{3}+18^{3}+19^{3}), then x divided by 70 leaves a remainder of:

**Answer** – **0**

**If x = (16**^{3}+17^{3}+18^{3}+19^{3}), then x divided by 70 leaves a remainder of 0.