On selling an article for Rs 162 there is a loss of 10%.At what price it should be sell in order to gain a profit of 10%?

In the adjoining figure ∠AOC=140° where O is the centre of the circle then ∠ ABC is equal to:

Direction: In the following questions two equations numbered I and II are given. You have to solve both the equations and give answer.
(A) x>y
(B) x≥y
(C) x˂y
(D) x≤y
(E) x=y or the relations ship cannot be established

I. x² + 13x = - 42
II. y² + 16y + 63 = 0 

Fill in the blanks:
Sin A = ____ × (Cos A) 

The equidistant point from the vertices of a triangle is called its: 

The sum of square of two numbers is 68 and square of the difference of them is 36. Then multiplication value of the two is. 

If the profit on selling an article for Rs. 579 is the same as the loss on selling it for Rs. 337, then find the profit percent if its selling price is Rs. 687.

If 1³ + 2³ + .....+103 = 3025 then 4 + 32 + 108 + ..... 4000 is equal to -