O 1: If n is an odd, then solve (x- 1)(x +2) = (x - 2)(x+ 7) (mod n).

Q: Find 3/(3+5 i) (d) ( 9 -15 i)/ 31 O (c) ( 9 -15 i)/ 29 (b) ( 9 -15 i) / 34 O (a) (9 +15 i) / 31 O

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Q: Q2: Find the solution of 143x³ + 22x¹ + 5x² + 3x + 1 = 0 (mod 11), if any.

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Q: What are the x² + 3x+ 2 factors of O(x-2)(x-1) O (x-2)(x+1) (x+2)(x+ 1)

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Q: Solve by Mathematical Incluction that all n2l.

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Q: 12/3÷3/4

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Q: Which of the following is equivalent to 3x²(-2x)e-x² + e-x²16x O -16xe-x²(x² - 1) O 16xe-x²(x² + 1)…

A: Given query is to simplify the expression.

Q: 15- (x + 5)lnxdx =? a) (-21/4) - 12In4 b)O (21/4) - 12ln2 (23/4) - 12ln4 d) O (-23/4) + 12ln2 e)…

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Q: n=2 n (2n — 1)!

A: The given expression is an infinite summation, where the indexing variable "n" starts from 2 and…

Q: 3 So² √(√₁² - ²√₁²³) ²³ a dt

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Q: If x2 + 9x + 14 х2 — 49 is divided by Зх + 6 x2 + x – 56 , the quotient is:

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Q: Show that (a) 8n −3n is divisible by 5 for all natural numbers n.  (b) n2 −n +41 is odd for all…

A: expansion of (a+b)n = hco an bo + nc1 an-1 b1 +.......... +ncn ao b n

Q: 00 (2n +1)" n2n n=1

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Q: given 7(x-1)=2(3x+2) prove x=11

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Q: Complete each of the following: (a) 83= 2 (mod 2) (b) 78= 2 (mod7)

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Q: If A=-1 4 -3 -7/ -1 and A¹=/? ? (22 a ? What is the value of the element a? Give your answer…

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Q: Show that whether x5 + 10x3 + x + 1 is O(x4) or not?

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Q: Solve 65x ≡ 2(mod243) by inverse method

A: Given, 65x≡2mod 243 Here gcd65,243=1 Now find the inverse of 65 mod 243.…

Q: 1. Can you reduce this expression?  (x2 + 3x)/ (2x - 1) 2. Aren't there math symbols available on…

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Q: (i) Deduce that the difference in the number of integers in the numerator and denominator of (* 2N N…

A: Properties of floor functions will be used.

Q: For non-zero denominators, which of the following is equivalent to 1 2a a a + 1 -2a3 +1 a(a + 1) 1-…

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Q: >(6k – 4)(7k + 3) - k=1 Enter your answer as a number without any arithmetic symbols. Sum =

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Q: X+ 2)(x+ 3)(x+ 4) = 990 X = ?

A: Given that the equation x+2x+3x+4=990  .

Q: 1. A force F=100 N is acting on an object of mass m-10 kg. The force makes an angle of 10° with the…

A: Given that  Force on the object is 100N Mass of the object =10kg  Force making an angle of 10  To…

Q: 2 (a) Work out 14 x 4 – 24 ÷ 2. (b) Find a number between 80 and 90 that is a multiple of both 3 and…

A: We have to solve two subparts in the given problem.                        (a) We need to work out…

Q: What is the coefficent of 5 in (x + 1)7 - x²(x+3) 5

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Q: 2 A= find For 3 -2 r B= 7 -1 O A +2B ®(A+2B) (AB)" 3)

A: NOTE: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: 7 [3-(2-5x)] + X= 4 (9x+2} +1+x/²

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Q: (d) an 10"+1 +3 x 4"-1+5 is divisible by 9 for all n2 1,

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Q: rel= = 0A 15, x² = 4(4x² - 1) If, 2 Prove that, x = √√5 +√√3

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Q: 3x-11 mang má O a. Inkx+6Xx-17+c O b. In x-1)(x+67+c Ocinkx+1Xx-6+c Od. Inx-6)(x+1)+c

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Q: Prove (n + 6)² – (n + 2)² is always a multiple of 8. (Use direct proof.)

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Q: (4) 3√27  -   (3) 3√216

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.