Generic selectors
Exact matches only
Search in title
Search in content
Search in posts
Search in pages
Filter by Categories
nmims post
Objective Type Set
Online MCQ Assignment
Question Solution
Solved Question
Uncategorized

1. “An Equations has either no solution or exactly three incongruent solutions”
a) True
b) False

View Answer

Answer: b [Reason:] “An Equations has either no solution or exactly two incongruent solutions”.

2. Find the solution of x2≡ 3 mod 11
a) x ≡ -9 mod 11 and x≡ 9 mod 11
b) x ≡ 9 mod 11
c) No Solution
d) x ≡ 5 mod 11 and x ≡ 6 mod 11

View Answer

Answer: d [Reason:] On finding the quadratic congruencies we get x ≡ 5 mod 11 and x ≡ -5 mod 11.

3. Find the solution of x2≡ 2 mod 11
a) No Solution
b) x ≡ 9 mod 11
c) x ≡ 4 mod 11
d) x ≡ 4 mod 11 and x ≡ 7 mod 11

View Answer

Answer: a [Reason:] There is no solution possible on solving the congruency.

4. Find the set of quadratic residues in the set –
Z11* = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
a) QR set = {1, 2, 4, 5, 9} of Z11*
b) QR set = {1, 3, 6, 5, 9} of Z11*
c) QR set = {1, 3, 4, 9,10} of Z11*
d) QR set = {1, 3, 4, 5, 9} of Z11*

View Answer

Answer: d [Reason:] QR set = {1, 3, 4, 5, 9} of Z11* is the set of quadratic residues. The values which have solutions fall under the QR set.

5. In Zp* with (p-1) elements exactly:
(p – 1)/2 elements are QR and
(p – 1)/2 elements are QNR.
a) True
b) False

View Answer

Answer: a [Reason:] The statement is true concerning elements of Zp* with (p-1) elements.

6. Find the set of quadratic residues in the set –
Z13* = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,11,12}
a) QR { 1, 2, 4,5, 10, 12}
b) QR { 2, 4, 5, 9, 11, 12}
c) QR { 1, 2, 4,5,10, 11}
d) QR { 1, 3, 4, 9, 10, 12}

View Answer

Answer: d [Reason:] QR { 1, 3, 4, 9, 10, 12}of Z13* is the set of quadratic residues. The values which have solutions fall under the QR set.

7. Euler’s Criterion can find the solution to x2 ≡ a (mod n).
a) True
b) False

View Answer

Answer: b [Reason:] Euler’s Criterion cannot find the solution to x2 ≡ a (mod n).

8. Find the solution of x2≡ 15 mod 23 has a solution.
a) True
b) False

View Answer

Answer: b [Reason:] a=15 (15)((23-1)/2)≡(15)11≡-1 (QNR and no solution).

9. Find the solution of x2≡ 16 mod 23
a) x = 6 and 17
b) x = 4 and 19
c) x = 11 and 12
d) x = 7 and 16

View Answer

Answer: b [Reason:] a=16 (16)((23+1)/4) ≡ (16)6≡1 (QR and there is solution). x ≡ ±16(23 + 1)/4 (mod 23) ≡±4 i.e. x = 4 and 19.

10. Find the solution of x^2≡3 mod 23
a) x≡±16 mod 23
b) x≡±13 mod 23
c) x≡±22 mod 23
d) x≡±7 mod 23

View Answer

Answer: a [Reason:] a=3 3((23+1)/4)≡36≡1 (QR and there is solution). x ≡ ±3(23 + 1)/4 (mod 23) ≡±16 i.e. x = 7 and 16.

11. Find the solution of x2≡ 2 mod 11 has a solution.
a) True
b) False

View Answer

Answer: b [Reason:] 2 is a QNR.

12. Find the solution of x2≡7 mod 19
a) x≡±16 mod 23
b) x≡±11 mod 23
c) x≡±14 mod 23
d) x≡±7 mod 23

View Answer

Answer: b [Reason:] a=7 7((19+1)/4)≡75≡1 (QR and there is solution) x ≡ ±7(19 + 1)/4 (mod 19) ≡±11 i.e. x = 11 and 12.

13. “If we use exponentiation to encrypt/decrypt, the adversary can use logarithm to attack and this method is very efficient. “
a) True
b) False

View Answer

Answer: b [Reason:] The first part of the statement is true. But this method is very inefficient as it uses the exhaustive search method.