Only ONE fresh egg can be there.

Had there been at least TWO fresh eggs in the container, it is possible that the two fresh eggs may be picked when we pick randomly.  However, it is stated that if we “pick two eggs randomly from the container, at least one of them will be rotten.”. For this condition to hold good, there should not be two or more fresh ones,  Hence, only one of them can be fresh. (Since it is also known that ‘there is at least one fresh egg’, the fresh eggs count can’t be zero.)

186

21 + 11 = 32
32 + 22 = 54
54 + 33 = 87
87 + 44 = 131
131 + 55 = 186

Based on the wording of the question, there is no solution. The condition is that the pieces should be arranged “… such that no piece is under any threat“. Note the clause “no piece” – that covers both white AND black pieces. Since all files (a – h) are occupied by at least one white piece, the black Queen can’t be placed on ANY square because the white piece(s) occupying the corresponding file will be under threat by the black Queen.

(It seems that the ‘not under threat’ condition is meant to cover black pieces only.)

Edit: Assuming that the ‘no threat’ condition is for black pieces only AND standard chess moves rules apply, one possible solution is as shown in the figure. 

Ground Floor

The building could be a 20-storey one, but the window from which the baby fell may be on the ground floor. 

PS: Since the question mentions “fall out“, the possibility of the baby falling into the room is ruled out.

Harish stole the monkey, Manoj stole the cat and Tarun, the dog.

Explanation: The statements and known facts are:

Harish: Tarun stole the cat.                                 — S1
Manoj: Tarun stole the dog.                                — S2
Tarun: I didn’t steal the cat or the  dog.        — S3

Facts:
The one who stole the monkey told a lie  — F1
The one who stole the cat told a truth       — F2

Statement 3 (by Tarun) says that he didn’t steal the cat or the dog. If we assume that this statement was true, it implies that he stole the monkey. However, as per the known fact F1, (person who stole the monkey lied), the statement S3 must be false, contradicting our assumption. This, in turn, implies that Tarun stole either the cat or the dog. However, had he stolen the cat, he would have told the truth (as per the known fact F2). Thus, the only possibility is that Tarun stole the Dog.

Now, what remains is to identify who stole the cat and the monkey. We know that one of the remaining suspects (who took the monkey) told a lie and the other (who took the cat) told the truth. Had Harish told the truth (S1), Tarun should have taken the cat. However, we know that Tarun did not take the cat. (He took the dog.) So, what Harsh told was a lie, whereas Manoj had said that Tarun stole the dog, which turned out true. This implies that Harish stole the Monkey (and lied, as per fact F1) and Manoj stole the cat (and told the truth that Tarun stole the dog.).

Youngest is Katrina  and oldest is Bipasha.

Katrina, the youngest, is younger than Kareena (statement 1) & Isabelle (who are of same age) (Stmt 4), who are younger than Karishma (stmt 1), who, in turn, is younger than Bipasha (stmt 3), who turns out the eldest.

I (eye)

1

Till the middle of the field. Thereafter, the goose will be running outwards.