The function for exchanging American dollars for Singapore Dollar on a given day is f(x) = 1.23x, where x represents the number of American dollars. On the same day function for exchanging Singapore dollar to Indian Rupee is g(y) = 50.50y, 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

Find the domain of \(\frac { 1 }{ 1-2sinx } \)

Check whether the following for one-to-oneness and ontoness.
(i) \(f:R\rightarrow R\) defined by f(x) \(f(x)={1\over x}.\)
(ii) \(f: \mathbb{R}-\{0\} \rightarrow \mathbb{R}\) defined by \(f(x)=\frac{1}{x}\)

Compute log₃5 log₂₅27

For each given Angle, find a coterminal angle with a measure of \(\theta\) such that \(0^o\le \theta \le 360°\) 
395⁰ 

In a circular of diameter 40 cm, a chord is of length 20 cm. FInd the length of the minor arc of the chord?

In a \(\triangle\)ABC, prove that (b + c) cos A +(c + a) cos B + (a + b) cos C = a + b + c

Count the number of three-digit numbers which can be formed from the digits 2, 4, 6, 8 if
(i) repetitions of digits is allowed.
(ii) repetitions of digits is not allowed

Prove that ¹⁵C₃ + 2 x ¹⁵C₄ + ¹⁵C₄ + ¹⁵C₅ = ¹⁷C₅.

Find the number of ways of arranging the letters of the word RAMANUJAN so that the relative positions of vowels and consonants are not changed.

A man repays an amount of Rs. 3250 by paying Rs. 20 in the first month and then increases the payment by Rs.15 per month. How long will it take him to clear the amount?

If the 5^th and 9^th terms of a harmonic progression are \({1\over 19}\) and \({1 \over 35},\) find the 12^th term of the sequence.

Prove that the product of the 2^nd and 3^rd terms of an arithmetic progression exceeds the product of the first and fourth by twice the square of the difference between the 1^st and 2^nd.

Prove that \(\left| \begin{matrix} 1 & a & { a }^{ 3 } \\ 1 & b & { b }^{ 3 } \\ 1 & c & { c }^{ 3 } \end{matrix} \right| =\left( a-b \right) \left( b-c \right) \left( c-a \right) \left( a+b+c \right) \) 

Find the unit vectors parallel to the sum of \(3\vec { i } -5\vec { j } +8\vec { k } \) and \(-2\vec { i } -2\vec { k } \) 

Evaluate \(\lim _{ x\rightarrow a }{ \frac { { (x+2) }^{ \frac { 3 }{ 2 } }-{ (a+2) }^{ \frac { 3 }{ 2 } } }{ x-a } } \)

If f(x) = 2x² + 3x - 5, then prove that f' (0) + 3 f' (-1) = 0

Evaluate \(\int { \frac { \left( { a }^{ x }+{ b }^{ x } \right) ^{ 2 } }{ { a }^{ x }{ b }^{ x } } } \)dx

Integrate the function with respect to x : \(\sqrt { { x }^{ 2 }-3x+10 } \)

One card is drawn from a well shuffled pack of 52 cards. If E is the event, "the card drawn is a king or queen" and F is the event "the card drawn is a queen or an ace", then find P(E/F).