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There are five persons sitting on a bench. Blue eyed lady sitting in the middle is my mother. At the extreme left, the man with grey hair is my maternal uncle. Lady sitting at the extreme right is having a pimple on her nose and is the wife of person who is sitting between blue eyed lady and grey haired man and has a pointed nose. A lady having marks on her face is the younger sister of the blue eyed lady and sitting on the remaining fifth place. The person having a pointed nose is the son of the blue eyed lady. What is the lady having marks on her face to the man sitting at extreme left ?

Correct Answer: Sister
The man sitting at the extreme left is my maternal uncle and the lady having marks on her face is my mother's sister. Hence, the lady having marks on her face is the sister of the man sitting at the extreme left.

Two boys are playing on a ground. Both the boys are less than 10 years old. Age of the younger boy is equal to the cube root of the product of the age of the two boys. If we place the digit representing the age of the younger boy to the left of the digit representing the age of the elder boy, we get the age of the father of the younger boy. Similarly, we place the digit representing the age of the elder boy to the left of the digit representing the age of the younger boy and divide the figure by 2, we get the age of the mother of the younger boy. The mother of the younger boy is younger than his father by 3 years. Then, what are the ages of elder and younger boys ?

A' promises to provide maintenance allowance to her maternal uncle in consideration of certain properties gifted to her by her mother. 'A' refuses to pay maintenance amount and maternal uncle institutes suit against 'A' to enforce the promise. Which one of the following is the correct statement? Maternal uncle:

If a + b + c + d = 4, then find the value of $$\frac{1}{{\left( {1 - a} \right)\left( {1 - b} \right)\left( {1 - c} \right)}}$$     + $$\frac{1}{{\left( {1 - b} \right)\left( {1 - c} \right)\left( {1 - d} \right)}}$$     + $$\frac{1}{{\left( {1 - c} \right)\left( {1 - d} \right)\left( {1 - a} \right)}}$$     + $$\frac{1}{{\left( {1 - d} \right)\left( {1 - a} \right)\left( {1 - b} \right)}}$$     is?

If a + b + c + d = 4, then the value of $$\frac{1}{{\left( {1 - a} \right)\left( {1 - b} \right)\left( {1 - c} \right)}}$$     + $$\frac{1}{{\left( {1 - b} \right)\left( {1 - c} \right)\left( {1 - d} \right)}}$$     + $$\frac{1}{{\left( {1 - c} \right)\left( {1 - d} \right)\left( {1 - a} \right)}}$$     + $$\frac{1}{{\left( {1 - d} \right)\left( {1 - a} \right)\left( {1 - b} \right)}}$$     is?

The film director wants an actress for the lead role of Lucy who perfectly fits the description that appears in the original screenplay. He is not willing to consider actresses who do not resemble the character as she is described in the screenplay, no matter how talented they are. The screenplay describes Lucy as an average-sized, forty something redhead, with deep brown eyes, very fair skin, and a brilliant smile. The casting agent has four actresses in mind.

Actress #1 : is a stunning red-haired beauty who is 5'9" and in her mid-twenties. Her eyes are brown and she has an olive complexion.
Actress #2 : has red hair, big brown eyes, and a fair complexion. She is in her mid-forties and is 5'5".
Actress #3 : is 5'4" and of medium build. She has red hair, brown eyes, and is in her early forties.
Actress #4 : is a blue-eyed redhead in her early thirties. She's of very slight build and stands at 5'.

Five friends are sitting on a bench facing the north. Ankit is sitting to the immediate right of Anjum. Amit is sitting to the left of Priya and to theimmediate right of Ram. Ram is sitting to the right of Ankit. Who is sitting at the extreme right end?

A man goes to the fair with his son and dog. Unfortunately man misses his son which he realizes 20 minutes later. The son comes back towards his home at the speed of 20 m/min and man follows him at 40 m/min. The dog runs to son and comes back to the man to show him the direction of his son. He keeps moving to and fro at 60 m/min between son and father, till the man meets the son. What is the distance traveled by the dog in the direction of the son?

A woman going with a boy is asked by another woman about their relationship between them. The woman replied, "My maternal Uncle and the uncle of his maternal uncle is the same". How is the lady related with that boy?

There are five girls - R, S, T, P and Q sitting in a row facing north. T is sitting exactly in the middle of the row. Q is sitting to the immediate right and immediate left of Pand T respectively. S is not sitting at the extreme end. Who is sitting third to the left of R?

The Hamiltonian of a particle is given by $$H = \frac{{{p^2}}}{{2m}} + V\left( {\left| {\overrightarrow {\bf{r}} } \right|} \right) + \phi \left( { + \left| {\overrightarrow {\bf{r}} } \right|} \right)\overrightarrow {\bf{L}} .\overrightarrow {\bf{S}} ,$$        where $$\overrightarrow {\bf{S}} $$ is the spin, $$V\left( {\left| {\overrightarrow {\bf{r}} } \right|} \right)$$  and $$\phi \left( {\left| {\overrightarrow {\bf{r}} } \right|} \right)$$  are potential functions and $$\overrightarrow {\bf{L}} \left( { = \overrightarrow {\bf{r}} \times \overrightarrow {\bf{p}} } \right)$$   is the angular momentum. The Hamiltonian does not commute with