Problem 1

Anjali generates a cryptogram where is plain text which is encrypted and is encryption algorithm requiring the key and sends it to Anil. Anil will decrypt the message to recover the plain text as:

( Hint : The decryption will be the inverse function of the original function .)

Problem 2

An analyst makes the following forecast about the stock of a company ABC. He says that the stock price of the company ABC which is currently trading at $100 has a 20% probability of hitting $80, 45% probability of hitting $65 and 35% probability of touching $53 in a year's time. The same analyst also makes the following forecast about the stock of another company XYZ. He says that the stock price of the company XYZ which is currently trading at $110 has a 12% probability of hitting $120, 25% probability of hitting $178 and 63% probability of touching $150 in a year's time.

Which of the above two stocks had higher information content?

1. stock of the company ABC;
2. stock of the company XYZ;
3. both the stocks of companies ABC and XYZ had equal information content;
4. the information content of the stocks cannot be determined from the given data;

( Hint : If is a random variable which has value with a probability of then the information content of , given by , is defined as . This is also known as the entropy. Entropy and its application is relatively new in the field of finance though its applications are growing. The above problem can also be analyzed intuitively without the application of information theory math though it may not be obvious at the first reading. )

Problem 3

A matrix equation is given by

Where A is a n x n square matrix, B is a n x 1 column vector and X, is a n x 1 solutions vector. The solutions vector X is given by:

( Hint : Remember that in matrix algebra , where is an identity matrix .)

Problem 4

The first term in a sequence is 3. Each even numbered term is 4 more than the previous term and each odd numbered term (excluding the first term) is -1 times the previous term. What is the 150 th term of the sequence?

1. 7
2. -7
3. -3
4. 3

( Hint : Find the sequence of terms for a few terms, say, 6 terms and you will see a repetitive pattern. If the term repeats after say, 6 terms, then divide 150 by 6 and find the remainder. The remainder will give the term which will be the same as the 150 th term. This is a property of repetitive sequence .)

Problem 5

A developer is writing a code in Excel? using VBA (visual basic for applications). While executing the code he gets a message " Run Time Error __". A possible reason could be:

1. he may have misspelled the keywords;
2. the code refers to an object that does not exist;
3. there is faulty programming by the developer;
4. None of the above.

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