If $$a = 28 - 5\sqrt{12}$$ and $$b = 2 + \sqrt{3}$$​, find the value of $$(a\sqrt{3} + b)$$​​

Solve the following system of 3 equations in 3 unknowns.
x - 3z = -5
2x - y + 2z = 16
7x - 3y - 5z = 19

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

The cost of 2 pens and 19 pencils is ₹118. If the cost of a pen decreases by ₹5 and the cost of a pencil increases by ₹4, then the cost of 5 pens and 8 pencils is ₹144. What is the original cost of 14 pens and 6 pencils?

The polynomial $$ax^3 + bx^2 + x - 6$$​ has (x + 2) as a factor and leaves remainder 4 when divided by (x - 2). Find the value of a and b.

Find the value of K for which equation x – Ky = 2, 3x + 2y = 5 has unique solution.

If $$2352 = 2^x \times 3^y \times 7^z \\$$​, then the value of $$x + y + z$$​ is

For the equation y = 7x − 2, which of the following statements is true?

15 chairs and 19 tables cost ₹5,300 and 19 chairs and 19 tables cost ₹5,700. What is the cost of 12 chairs and 13 tables?

The total number of students in class A and class B is 120 . If 15 students from class A are taken and added to class B , the number in class B becomes twice that of A. Find out the number of students in class A in the beginning.