1. gcd( 18,300) =

a) 4

b) 12

c) 8

d) 6

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2. ᶲ(37)=

a) 24

b) 22

c) 13

d) 36

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3. ᶲ(35)=

a) 24

b) 25

c) 22

d) 18

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4. ᶲ(21)=

a) 10

b) 12

c) 8

d) 14

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5.7^{3} mod 19 =

a) 18

b) 1

c) 14

d) 12

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^{3}mod 19 = 1.

6. 7^{(3+j)} mod 19 =

a) 7^{j} mod 19

b) 1 mod 19

c) 7^{3} + 7^{j} mod 19

d) All of the mentioned are true

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^{(3+j)}mod 19 = 7

^{3}* 7

^{j}mod 19 = 7

^{j}mod 19 ( since 7

^{3}mod 19 = 1 ).

7. What is the period of 7^{m} mod 19?

a) 2

b) 3

c) 4

d) 5

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^{m}mod 19 = 1.

8. ᶲ(19)=

a) 14

b) 13

c) 18

d) 17

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9. What is the period of 11 (mod 19)

a) 2

b) 3

c) 4

d) 5

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^{3}(mod 19) = 1.

10. What is the period of 17 (mod 19)

a) 5

b) 7

c) 9

d) 11

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^{9}( mod 19) = 1.

11. What is the period of 9 (mod 19)

a) 12

b) 10

c) 11

d) 9

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^{9}(mod 19) = 1.

12. How many primitive roots does Z<19> have?

a) 5

b) 8

c) 7

d) 6

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Consider the following Logarithmic Properties –

i) y = x^{(log_x(y))}

ii) log_x(1) = 1

iii) log_x(x) = 0

iv) log_x(yz) = log_x(y) + log_x(z)

v) log_x(y^{r}) – r x log_x(y)

13. Which of the above properties are correct ?

a) 1st 2nd and 4th

b) 2nd 3rd and 5th

c) 2nd 4th and 5th

d) 1st 4th and 5th