Aman and Raman can complete a work separately in 30 days and 20 days respectively. They start work together. After 10 days Raman leaves the work. The remaining work is done by Aman. How many extra days will Aman take to complete the work?

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