If $$ {x^{4}+x^{2}y^{2}+y^{4}={21\over256}}$$ and $$ {x^{2}+xy+y^{2}={3\over16}}$$ then $$ {2(x^{2}+y^{2})}=?$$

A wire is in the shape of a rectangle. Its length is 42.7m and breadth is 21.8m. If the same wire is re-bent in the shape of a square, what will be the measure of the side of the square?

₹12,000 is lent for one year t the rate of 15% per annum, the interest being compounded annually. If the compounding of the interest is done half- yearly, then how much more interest will be obtained at the end of the one-year period on the same initial sum?

If 2sinθ+cosθ= $${7\over3}$$ then the value of (tan²θ-sec²θ) is

Direction: The following table shows the number of students of 7 colleges A, B, C, D, E, F, G participating in extra-curricular activities :

The ratio of total number of students in activity II and I is ?

At what rate per annum will Rs. 32000 yield a compound interest of Rs. 5044 in 9 months interest being compounded quarterly?

Find two such numbers whose middle proportional is 18 and third proportional is 144.

Ramiya got married 8 years ago. Her present age is 6/5 times her age at the time of her marriage. Ramiya’s brother was 10 years younger than her at the time of her marriage. What is the ratio of Ramiya’s present age and her brother’s age at the time of her marriage?