Five years ago Mathilde was six times older than her daughter. After five years, Mathilde will be 10 years more than two times the age of her daughter. Find the present age of Mathilde and her daughter.

The sum of first 8 terms of an arithmetic progression is 288. The ratio of term 5^{th} to term 25^{th} of the AP is 1:5. What is the value of the 79^{th} term of the AP?

The points ^@ A(1,-9)^@, ^@B(0,-9)^@, ^@C(3,-4)^@, and ^@D(-2,-4)^@ are the vertices of a parallelogram ^@ABCD.^@ If ^@AB^@ is the base, find the height of the parallelogram.

In the given figure, ^@ AB ^@ is a chord of length ^@ 11 \space cm ^@ of a circle with center ^@ O ^@ and radius ^@ 7 \space cm ^@. The tangents at ^@ A ^@ and ^@ B ^@ intersect at ^@ P ^@. What is the length of ^@ PA ^@?

The radii of two circles are ^@19 \space cm^@ and ^@14 \space cm^@ respectively. Find the radius of the circle having its area equal to the sum of the areas of the two circles.

A toy is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire toy is 18 mm and the diameter of the toy is 28 mm then choose its correct surface area .

Following chart shows number of students in a school who got distinction in one of three subjects. Find the number of students who got distinction in exactly two subjects.