Some students (only boys and girls) from different schools appeared for an Olympiad exam. 20% of the boys and 15% of the girls failed the exam. The number of boys who passed the exam was 70 more than that of the girls who passed the exam'. A total of 90 students failed. Find the number of students that appeared for the exam.

A sphere of radius 5 cm is melted to form a cone with base of same radius. The height (in cm) of the cone is

If x = z = 225 and y = 226 then the value of : x³ + y³ + z³ – 3xyz is

If x² + x = 5 then the value of   $${(x+3)^3}+{1\over (x+3)^3}$$ is

In an isosceles triangle, if the unequal angle is twice the sum of the equal angles, then each equal angle is

One acute angle of a right-angled triangle is double the other. If the length of its hypotenuse is 10 cm, then its area is

If m = – 4, n = – 2, then the value of m³ – 3m² + 3m + 3n + 3n² + n³ is

If   $$x+{1\over x}=2 $$ then the value of    $$x^{12}-{1\over x^{12}} $$ is