Find the ratio between the fourth proportional of 12, 16, 6 and the third proportional of 4, 6.

The value of   $${sin23^0cos67^0+sec52^0sin38^0+cos23^0sin67^0+cosec52^0cos38^0}\over cosec^220^0-tan^270^0$$ is

What should come in place of the question mark '?' in the following number series?

7, 13, ?, 49, 97, 193

If $$ A = {1\over 2}+{1\over 3}×{1\over 4}÷{1\over 5}-{1\over 6}$$ and $$B={1\over 2}÷{1\over 3}×{1\over 4}+{1\over 5} $$ , then what is the value of A - B?

Each side of a square is 12 cm long. The perimeter of this square is equal to the perimeter of a rectangle whose length is 16 cm. What will be the area of this rectangle?

If the arcs of square length in two circles subtend angles of 60° and 75° at their centres, the ratio of their radii is 

The HCF of x⁸ – 1 and x⁴ + 2x³ – 2x – 1 is :

△ABC ∼ △DEF. If the areas of △ABC and △DEF are 100 cm² and 81 cm², respectively and the altitude of △DEF is 6.3 cm, then the corresponding altitude of △ABC is: