The cost of 2 pencils and 3 pens is ₹55 and the cost of 7 pencils and 2 pens is ₹65. What is the total price (in ₹) of one pen and one pencil?

Find the coordinates of the points where the graph of the equation $$57x - 19y = 399$$ cuts the coor...

For what value of \(m\) will the system of equations $$18x - 72y + 13 = 0$$ and $$7x - my - 17 = 0$...

If $$ (a + b\sqrt{n}) $$ is the positive square root of $$ (29 - 12\sqrt{5}) $$, where $$ a $$ and $...

The sum of all real values of $$ k $$ for which $$ \left(\frac{1}{8}\right)^k\times\left(\frac{1}{...

Let $$ x, y $$, and $$ z $$ be real numbers satisfying: $$ 4(x^2 + y^2 + z^2) = a $$ $$ 4(x - y -...

Suppose $$ x_1, x_2, x_3, \dots, x_{100} $$ are in arithmetic progression such that $$ x_5 = -4 $$ a...