The graphs of the equations 3x + y-5=0 and 2x- y -5=0 intersect at the point P(α,β).  What is the value of (3α + β)?

The value of $$ {(cos {\ 9°}+sin{\ 81°}})({sec {\ {9°}+cosec{\ 81°}}})\over{sin{\ 56°}sec{\ 34° }}+ {cos{\ 25°}cosec{\ 65°}}$$ is:

The ratio of investment by A to that by B in a business is 14 : 15 and the ratio of their respective profit at the end of a year is 2 : 5. If A invested the money for 3 months, then for how much time ( in months) B invested his money?

The base of right prism is a trapezium whose parallel sides are 11 cm and 15 cm and the distance between them is 9 cm. If the volume of the prism is 1731.6 cm³, then the height (in cm) of the prism will be:

If (a+b) : (b+c) : (c+a) = 7 :6 : 5 and (a+b+c)=27, then what will be the value of $$ {1\over b}:{1\over a}:{1\over c}$$.

The income of A is 25% more than that of B and the income of C is 65% less than the sum of the incomes of A and B. Income of C is what percent less than the income of A?

If x + y = 1 and xy (xy – 2) = 12,then the value of x⁴ + y⁴ is: