1. Find all r E Z satisfying each of the following equations. (a) 3r = 2 (mod 7) (d) 9r = 3 (mod 5) (b) 5x +1 = 13 (mod 23) (c) 5x +1 = 13 (mod 26) (e) 5x = 1 (mod 6) (f) 3r =1 (mod 6)

Q: [ (ax + b) c+b) dx = ○ / (ax + b) ² + C O O4a ¹ª (ax + b) ² + C O4a (ax + b)² + C O4 (ax + b) + C 7a

A: You must have basic idea about indefinite integral in order to understand this better.

Q: s9-3x then y If y O 89-3x)4 25 O 819-3x)4 25 O 8(0-3x)4 O -24(9-3x)4 O 24(9-3x)4

A: The function is given by,

Q: 1. If x=27-3k and y = i +5j -4k, express each of the following in terms of i, j, k b) 2(3x+y)-3(4y…

A: Given x→=2i→-3k→ & y→=i→+5j→-4k→To write expression in terms of i→,j→,k→:

Q: et x, y E Z. We have (x+y)³ = (x+y)² (x+y) = (x² +2xy+y?)(x+y) = (x³+3x?y+3xy² + y³) = x³ + y3 od 3.

A:

Q: 16) If v = 9i + 3j, what is || 8v ||?

A: Recall: If v→ =v1i +v2j then , v→ =v12+v22

Q: 13 - What is the Lagrange interpolation polynomial which passes through (2,2) and (4,6)

A: We use the Lagrange interpolation formula

Q: :: Find L-1 5+7 \s+7/

A:

Q: 4. Prove that x*+2x²+5 + x²+2x*+6 =0 x-1 x-7 has a solution between 1 and 7.

A: We need to solve the polynomial.

Q: If n = 12 m (me N), prove that "C₂ (2+√√3)² "Co- - + "C4 (2+√√3)4 "C6 (2+√3)6 ·+···=(−1)| 2√2 1+√3 n

A:

Q: 0.78125ab²1 9 112, 15 ² q. (3/8c²d¹²e" 2 -2 S. (6; ²K³) ²x 20K 1³ X 3₁1-3 (3) = P. (4a² b ²) ²³² × 3…

A: According to guideline given to us, in multiple question we are only allowed to answer only first…

Q: 2 5 A ^^ - [ ²7 ] and -7 6 Given : Find the following 1. (24)¹ 2. (AB)-¹ 3. (4¹) ¹ B 7 -[? -37] 2 0

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: 7. I) Find, if possible, AB ond BA A= 3212/ 2.

A:

Q: Prove that 5n²+3n+2 € O(n²).

A:

Q: 5) Find CD 2x +21 C D x + 21 10

A: Given the line segments

Q: 18) If a and b are negative and c is positive, determine whether the following are positive or…

A:

Q: [-1 2 Q5/ Let A = |-2 5 -3] 3 4 ,then the C33 is 0 1 -1 -10 -2

A:

Q: Find x and y 24 -2 22 [2x-2y 2 -2 20 21 o -10: [4 : 25 24y 25 2x+y -4

A: Given:

Q: Solve the systems of linear congruence equations.

A:

Q: 1. Let -1 3 [1 2 3] A = 2 1 4 [1 2 3] 0 1 2 -4 1 and C 2 1 -3 Find the following: (a) 24 (b) 2АB (c)…

A: Solve by matrix operations

Q: (1 2 43) 32 1. IF A = THEN (A) (B) (X Y) Z W

A:

Q: Choose all the equivalent expressions for f(x) = (2x +7x² + 2x + 9) ÷ (2x + 3) O f(¤) = (2x + 3) (x²…

A:

Q: Evaluate O √x(1+x²) dx 2 x1/2 1 2x¹/2 O O 2,2/3 3 O 3x²/3 2 + 2x¹/2 + C x1/2 + +C 2 2x5/2 5 5x5/2 -…

A: Note: Every options given by the question are incorrect. I am 100% sure about it.  The correct…

Q: Find the value of S in (3A +4Si)(6-7i) = 3+5i

A:

Q: 6 4 3 5 9 7 10 ^ - :: ³ - 1 - - [H] A = 1 3 C B 6 4 2 0 8 11 5 2 if D=C-A, then the element d13 is:…

A:

Q: 3). B = (2 1 (5 1 and C = -3 :), find (a) Given that A = 7 3 -1. ЗА + 2B — С

A:

Q: The postfix search of the expression 8 (3- 1) +2 x 5 is O a. None O b. 31 - 8 : 25 x + Oc8:3-1 + 2 x…

A:

Q: Show that (6+c) ba са (c+a) cb =2abc(a+b+c) ab 3 (a+b) ас bc

A:

Q: 2. (a) Show that (z − 1)(26 + 25 + 24 + z³ + z²+z+1) = z7 - 1. (b) Show that if ¢ is a 7th root if…

A:

Q: Prove that Σ=1(3i2 - 2t) = 2n3 +n2 - n 2

A:

Q: 1.] For the given differential equation, X=U is a/an: A. Regular point B. Ordinary point C. Regular…

A: As per the company rule, we are supposed to solve the first three sub-parts of a multi-parts…