A teacher brought a certain number of friendship bands for the students in the classroom for Friendship Day celebrations. Each student gives a friendship band to every other student. On the Friendship Day at 10 am 2 students were absent, so 102 friendship bands were not utilised. But at 11 am one of the absent students came to the classroom. Find the number of friendship bands unutilised.

If f(x) = max (x2– 4, x, –1), then what is the minimum value of f(x)

Two circles of radius 2 and centers O and P touch each other as shown in the figure. If AD and BD are tangents, then the length of BD is

The number of real roots of the equation x6 + 4×2 – 30 = 0

I have some clocks in the room. Alarm is set in different clocks at different time intervals in integral multiple of a minute. Incidentally, all the alarms ring togetherafter 4 hrs. Find the maximum number of clocks inside the room.

How many positive numbers are there which satisfy the equation:

How many ordered triplets of real numbers (x, y, z) are there which satisfy the following equations:(x + y)(x + y + z)= 120(y + z)(x + y + z)= 96(x + z)(x + y + z)= 72

A question paper consists of three sections consisting of 2,3 and 4 questions respectively. Attempting one question from each section is compulsory but a candidateneed not attempt all the questions. In how many ways can a candidate attempt the questions?

The work done by 2 men in a day is equal to the work done by 3 children in a day. The work done by 3 men in a day is equal to the work done by 5 women in a day.It takes 10 days for a man, a woman and a child to complete a job working together. How many days will 2 children working together take to complete the same job?

A series N has terms in the following order 1, 4, 18, 96, 600,………What is the remainder when sum of first 12 terms of the given series is divided by 13?