Q−2: [2+3+3 marks] Find integers and such that .

Find the GCD and LCM for the numbers 2772 and 37800.

Encrypt the message “I NEED HELP” by translating the letters into numbers, applying the encryption function

,and then translating the numbers back into letters. Q−3: [4×2] Let and be the functions from to .Find .

Is onto? Is g one-to-one? Explain you answer.

Check whether exists. If it is so, define . Otherwise, provide a reason for not existence of .

Check whether exists. If it is so, define . Otherwise, provide a reason for not existence of .

Q−4: [4+4 marks] Of 32 people who save paper or bottles (or both) for recycling, 30 save paper and 14 save bottles. Find the number of people who

Students need to answer 8 out of 10 questions in biology exam.

save both

save only paper, and

save only bottles.

Find the number of the ways a student can choose the 8 questions.

In how many ways can a student choose 8 questions if the first three questions are mandatory?

In how many ways can a student choose 8 questions if at least 4 of the first 5 questions must be answered?

Q−5: [2+3+3 marks] Consider an experiment of rolling two dice, and assume that each simple event in the sample space is as likely as any other find the probability that:A sum of 7 turns up;

A sum of 7 or 11 turns up;

A sum is greater than

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