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The Taj Mahal Palace opened in Mumbai, in 1903. Alpha, Beta and Gamma three friends had a dinner at one of its famous restaurant. When the bill was received, Alpha paid 4/3 as much as Beta paid and Beta paid 1/4 as much as Gamma paid. What fraction of the bill did Beta pay?
Alpha, Beta and Gama went for a picnic at Jurassic Park, when they feel hungry they took out the stuff they brought. Alpha bought 6 sandwiches while Beta bought 4 and Gamma bought none. Both Alpha and Beta shared their sandwiches with Gamma such that each got the same amount. If Gamma paid a total amount of Rs. 10 to Alpha and Beta, how much of Rs. 10 should Alpha get ? (Assume that sandwiches and rupees can be split.)
Which of the following statement regarding radioactive decay is correct?  Average life equals to 1.44 of half-life. Half-life is directly proportional to decay constant. The decay of element is proportional to no of atoms or moles.
Alpha, Beta and Gama are three masons appointed in a construction company. They got a task and all of them began the work together. Alpha can finish the task in 12 days, Beta in 10 days and Gama in 15 days. Due to fracture in his hand, Alpha had to leave his job after 4 days of his appointment. Five days before the completion of the task Beta leave. How long did the work last?   
Three boys Alpha, Beta and Gama planned to make a sports car. Alpha and Beta can finish the task in 18 days; Beta and Gama can do it in 24 days while Gama and Alpha can finish it in 36 days. In how many days will each one of them finish it?
Alpha and Beta sold their Fridge at Rs. 75000 each, in which Alpha got a profit of 30% and Beta incurred loss of 30%. Find the ratio of the C.P of the Fridge sold by Alpha to that of Beta.
If the equation x2 + kx + 1 = 0 has the roots α and β, then what will be the equation with the roots \(-\left(\frac{\alpha \beta + 1}{\beta}\right)\) and \(-\left(\frac{\alpha \beta + 1}{\alpha}\right)\) ?
If α + β = 90° and α:β = 2:1, then the ratio ofcosα to cosβ is
If α and β are the roots of equation x2– 2x + 4 = 0, then what is the equation whose roots are α3/β2and β3/α2?
If $$\frac{{{\text{cos }}\alpha }}{{{\text{cos }}\beta }} = a$$   and $$\frac{{{\text{sin }}\alpha }}{{{\text{sin }}\beta }} = b{\text{,}}$$   then the value of $${\sin ^2}\beta $$  in terms of a and b is?