If sin(α + β) = 4/5 , sin(α – β) = 5/13 , find the value of tan 2α.

If  , then the value of sin θ – cos θ is

If (49)² – (25)² = 37x, then find the value of x.

The chord of an arc of a circle is of length x, the height of the arc is y and the radius of the circle is z. Which one of the following is correct?

The area of a circle whose radius is the diagonal of a square whose area is 4 is:- 

The distance between two points A and B is 110 km. X starts running from point A at a speed of 60 km/hr and Y starts running from point B at a speed of 40 km/hr at the same time. They meet at a point C, somewhere on the line AB. What is the ratio of AC to BC?

Wheels of diameter of 7 cm and 14 cm start rolling simultaneously from A and B which are 1980 cm apart towards each other in opposite directions. Both of them make the same number of revolutions per second. If both of them meet after 10 seconds, what is the speed of the smaller wheel?

ABC is a right angled triangle in which B is a right angle. Mid points of BC and AC are respectively B' and A'. Area of ∆A'B'C is –

Two men start together to walk a certain distance, one at 4 km/h and another at 3 km/hr. The former arrives half an hour before the later. Find the distance.

The sum of digit of a two-digit number is 1/5 of the difference between the number and the number obtained by interchanging the digits. What definitely is the difference between the digits?