The midpoints of AB and AC of a triangle ABC are X and Y respectively. If BC + XY = 12 units, then BC – XY is:

In equation $$ {x^{2}-24x+k=0}$$ the first root is x=2 then find out  the second root of equation.

If ' n ' be any natural number , then by which number ( n⁴-n ) is always divisible ? 

Directions:  In the following two equations questions numbered (I) and (II) are given. You have to solve both equations and
Give answer
(a) If x > y
(b) If x ≥ y
(c) If y > x
(d) If y ≥ x
(e) If x = y or no relation can be established

$$ {I.x^{2}-17x-84=0}$$
$$ {II.y^{2}+4y-117=0}$$

A man can swim at the rate of 3 km/hr. in still water. Then, if speed of the stream is 2 km/hr., then in what time he will cover a total distance of 5 km in with the stream and against the stream?

Tarun and Uday together can complete a piece of work in 16 days; Uday and Vivek together can complete the work in 28 4/5 days; while Tarun and Vivek together can complete the work in 18 days. In how many days can Tarun alone complete the work?

What is the discount rate of a gift whose selling price is Rs. 420 after a reduction of Rs. 60 on its marked price ?

The area of a square is 1764 cm² . The length of a rectangle is 4/7 of the side of the square and breadth of the rectangle is half its length. What is the perimeter of the rectangle?