Q1. A regular heptagon (= 7-sided polygon with all angles equal and all sides equal) is randomly placed in the plane. What is the probability that an observer can see 4 sides?

Direction for Q2 to Q3

Three mountaineers A, V and N are climbing up a mountain with their respective probabilities of reaching the summit being 1/3, 1/5 and 1/4 respectively.
What is the probability that

Q2.  All of them reach the summit.
a. 3/60
b. 1/60
c. 1
d. 0

Q3. At least one of them reaches the summit ?
a. 59/60
b. 36/60
c. 17/60
d. 1/60

Q4. Exactly one of them reaches the Summit?
a. 13/30
b. 17/30
c. 19/30
d. 11/30

Q5. There are 7 boys and 8 girls in a class. A teacher has 3 items viz a pen, a pencil and an eraser, each 5 in number. He distributes the items, one to each student. What is the probability that a boy selected at random has either a pencil or an eraser?
a. 2/3
b. 2/21
c. 14/45
d. None of these

Q6. Fifteen coupons are numbered 1, 2, 3. . . . . . . 15 respectively. Seven Coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupon is 9, is
a. (9/10)^6
b. (8/15)^7
c. (3/5)^7
d. None of these

Q7.If two smallest squares are chosen at random on a chessboard, the probability that they have a side in common is
a. 9/14
b. 26/64
c. 5/7
d. 1/18