In Aparna Cyber ​​Commune, 10 retired R&D workers K, M, O, Q, S, U, W, Y, L and P live in two rows of flats opposite each other. One row has 5 flats facing north, and the other row has 5 flats facing south. U's flat is second to the right of P's flat, which is just opposite O's flat which faces north. Q's flat is immediately to the left of P's flat. K's flat is immediately to the left of O's flat. M's flat is to the right of O's flat. L and S's flats are at the two ends of the same row. S and Y's flats are opposite each other. Whose flat is opposite the flat which is second to the left of O's flat?

The sum of squares of all the roots of the equation:
​$$\left(x + \frac{1}{x}\right)^2 - 4 = \frac{3}{2} \left(x - \frac{1}{x}\right), x \neq 0$$ is:

One of the factors of 6x² – 24xy + 17x + 24y² – 34y + 5 is:

The cost of 2 pens and 5 pencils is ₹ 57. If the cost of a pen is increased by ₹ 1.50 and that of a pencil is decreased by ₹ 1, then the cost of 5 pens and 3 pencils is ₹ 109. What is the original cost of 3 pens and 4 pencils?

What is the remainder when the polynomial x¹⁰⁰ – 2x⁵¹ + 1 is divided by (x² – 1) ?

If x + $$\frac 1x$$​= –1, then compute: $$x^4 + \frac{1}{x^4} + 2x^2 + \frac{2}{x^2}$$​​

Let x be the greatest number which, when dividing 31, 61 and 91, leaves the same remainder. The LCM of x and 48 is:

The value of $$\frac{x}{x-y}+\frac{y}{x+y}+\frac{2xy}{y^{2}-x^{2}}$$​ is