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

Direction: Study the following information to answer the questions.

In hotel B, the ratio of female customers on Tuesday and Friday was 2 : 3. If on Friday, female customers constituted 50% of the number of customers (male + female), then what was the number of customers (male + female) in hotel B on Friday?

Simplify $$ ({Sinθ\over{1+cosθ}}+{1+cosθ\over sinθ})({1\over (tanθ+cotθ)})$$

A sum of money was invested at a certain rate of simple interest for 2 years. Had it been invested at 1% higher rate, it would have fetched Rs.192 more interest. The sum of money is-

Study  the given pie chart and answer the question that follows.
Break-up (degree-wise) of the number of students in five schools (A, B, C, D and E) in a city.
Total number of students =5200

If the ratio of the number of boys to that of girls in school B is 7:6 and the ratio of number of boys to that of girls in school D is 4 : 5, then what is the ratio of number of boys in B to that of girls in D?

If sin²a = cos³a then the value of cot⁶ a – cot²a? 

What is the value of $$ {0.55 × 4.5\over 0.81}$$ ?

What is the area ( in cm² ) of the circumcircle of a triangle whose sides are 6 cm , 8 cm and 10 cm respectively ?