<p>The expression 2x³ + ax² + bx + 3, where a and b are constants, has a factor of x-1 and leaves a remainder of 15 when divided by x + 2. Then, (a, b) =</p>

Given below are two statements:

Statement (I): The difference, the sum, and the product of two numbers are in the ratio 1: 5: 12. The product of the two numbers is 18.

Statement (II): The last digit in the decimal representation of 2⁹¹ is 6.

In light of the above statements, choose the most appropriate answer from the options given below.

Amicable numbers are a pair of distinct natural numbers (a, b) such that the sum of the proper divisors of a equals b and the sum of the proper divisors of b equals a. Given that (220, y) is a pair of amicable numbers, y equals:

Given below are two statements:

Statement I : The sum of exponents of prime factors in the prime factorization of 392 is 5.

Statement II : The decimal representation $\frac{13}{2^3 \times 5}$ will terminate after 2 decimal places.

In the light of the above statements, choose the correct answer from the options given below:

Arrange the following fractions in descending order.

(A) $\frac{5}{9}$

(B) $\frac{7}{11}$

(C) $\frac{8}{15}$

(D) $\frac{11}{17}$

After adding 5 to both numerator and denominator of the following fractions, arrange them in ascending order of the magnitude of change in their values.

A. $\frac{2}{3}$

B. $\frac{3}{4}$

C. $\frac{4}{5}$

D. $\frac{5}{6}$