Question

Therefore, Vani's birthday must be on Weuleu)
Exercise 2.3
1. Find the least positive value of x such that
(iii) 89 =
(x + 3) (mod 4)
Sli) 71 = x (mod 8) (ii) 78 += 3 (mod 5)
(iv) 96= (mod 5) (6.50 = 4 (mod 6)
2. If x is congruent to 13 modulo 17 then 7x - 3 is congruent to which number modulo
3. Solve 5x = 4 (mod 6)
4. Solve 3x - 2 = 0 (mod 11)
5. What is the time 100 hours after 7 a.m.?
6. What is the time 15 hours before 11 p.m.?
7. Today is Tuesday. My uncle will come after 45 days. In which day my uncle wi
coming?
8. Prove that 2" + 6x9" is always divisible by 7 for any positive integer n.
9. Find the remainder when 281 is divided by 17.
5210th Standard Mathematics
X Std_EM Final.indb 52
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Answer 1

Answer:

Step-by-step explanation:

What is the time 100 hours after 7 a.m.?

It is the same time after 24 hrs

100 hrs = 96 hrs + 4 hrs

=> 100 Hrs = 24 * 4 +  4  hrs

=> Time after 100 hrs will be equal to time after 4 hrs

4 hrs after 7 am =  7 + 4 = 11 a.m.

What is the time 15 hours before 11 p.m.?

12 hrs before p.m. would be a.m

15 = 12 + 3

=>  15 hours before 11 p.m. = 3 hrs before 11 a.m.

3 hrs before 11 a.m. = 11 -3  = 8 a.m

Today is Tuesday. My uncle will come after 45 days. In which day my uncle wi ll be coming?

Today is Tuesday

after 7 days same day come

45 = 7 * 6 + 3

after 45 days same day will be as after 3 days

3 days after Tuesday is  Friday

281 = 272 + 9  = 17*16  + 9

=>281/17 =  (17*16  + 9)/17

=> 281/17 =  16   + 9/17

remainder = 9