Assume any number x, add 7 to it, multiply by 2, add 2, divide by 2, finally subtract x. The number we get after all the operations is A 6 B 7 C 8 D 9

Geeta planned to floor her living room of size 520×300 cm with the least number of square tiles of equal areas. If the cost for the first 100 tiles is ₹64.00 per tile, ₹50.00 per tile for the next 100 tiles, and ₹40.00 for any number of tiles after the first 200, find the total cost incurred on tiling.

A. Suppose the demand and supply curve of commodity X in a perfectly competitive market are given by:

$q^D = 700 – p$

$q^S = 500 + 3p for p ≥ 15$

$= 0$ for $0 ≤ p < 15$

Assume that the market consists of identical firms. Identify the reason behind the market supply of commodity X being zero at any price less than Rs 15.What will be the equilibrium price for this commodity? At equilibrium, what quantity of X will be produced?

B. Considering the same demand curve as in exercise A, now let us allow for free entry and exit of the firms producing commodity X. Also assume the market consists of identical firms producing commodity X. Let the supply curve of a single firm be explained as

$q^s_f = 8 + 3p for p ≥ 20$

$= 0$ for $0 ≤ p < 20$

(a) What is the significance of p = 20?

(b) At what price will the market for X be in equilibrium? State the reason for your answer.

(c) Calculate the equilibrium quantity and number of firms.

Total number of integral solutions of $|x| + |y| + |z| = 15$ is $k$, then $\frac{k}{41} =$.

Which one of the following options is true, and why? $y=3 x+5$ has

(i) a unique solution,

(ii) only two solutions,

(iii) infinitely many solutions

Consider a, b, c as real numbers.

$$ X = \frac{a + b}{a - b} \quad Y = \frac{b + c}{b - c} \quad Z = \frac{c + a}{c - a} $$

What is the value of $XY + YZ + ZX$?

A) 1

B) 2

C) None of these