The function for exchanging American dollars for Singapore Dollar on a given day is f(x) = 1.23 x, where x represents the number of American dollars. On the same day the function for exchanging Singapore Dollar to Indian Rupee is g(y) = 50.50 y , where y represents the number of Singapore dollars. Write a function which will give the exchange rate of American dollars in terms of Indian rupee.

Given x + sin y = 2009 and x + 2009 cos y = 2008, where y in[0,(pi)/(2)] , then [x+y] equals, where [.] represents the greatest integer function,

If alpha is an integer satisfying |alpha|lt=4-|[x]|, where x is a real number for which 2xtan^(-1)x is greater than or equal to ln(1+x^2), then the number of maximum possible values of alpha (where [.] represents the greatest integer function) is_____

A salesperson whose annual earnings can be represented by the function A (x) = 30,000+0.04x, where x is the rupee value of the merchandise he sells. His son is also in sales and his earnings are represented by the function S(x) = 25,000 +0.05 x. Find (A+S) (x) and determine the total family income if they each sell Rs 1,50,00,000 worth of merchandise.

A curve is given by the equations x=sec^2theta,y=cotthetadot If the tangent at Pw h e r etheta=pi/4 meets the curve again at Q ,t h e n[P Q] is, where [.] represents the greatest integer function, _________.

Let f(x) = ([x]+1)/({x}+1) for f: [0, (5)/(2) ) to ((1)/(2) , 3] , where [*] represents the greatest integer function and {*} represents the fractional part of x. Draw the graph of y= f(x) . Prove that y=f(x) is bijective. Also find the range of the function.

Let G(x)=(1/(a^x-1)+1/2)F(x), where a is a positive real number not equal to 1 and f(x) is an odd function. Which of the following statements is true? (a) G(x) is an odd function (b) G(x)i s an even function (c) G(x) is neither even nor odd function. (d)Whether G(x) is an odd or even function depends on the value of a

Each question has four choices, a,b,c and d,out of which only one is correct. Each question contains STATEMENT 1 and STATEMENT 2. if both the statements are true and statement 2 is the correct explanation of statement 1. If both the statements are true but statement 2 is not the correct explanation of statement 1. If statement is True and statement2 is false. If statement1 is false and statement2 is true. Consider the function f(x)=sin(k x)+{x}, where (x) represents the fractional part function. Statement 1 : f(x) is periodic for k=mpi, where m is a rational number Statement 2 : The sum of two periodic functions is always periodic.

Tangents PA and PB are drawn to the circle (x-4)^(2)+(y-5)^(2)=4 from the point P on the curve y=sin x , where A and B lie on the circle. Consider the function y= f(x) represented by the locus of the center of the circumcircle of triangle PAB. Then answer the following questions. Which of the following is true ?