A, B, C, D and E are standing in a line facing North. E is standing 40 metres left to B. A is standing 20 metres left to C. D is standing 20 metres right to Eand 50 metres right to C. Where is B standing from D?

Use the following passage for the questions based on it. There are 6 flats on a floor in two rows. Out of these, three are north facing and the other three are south facing flats. The flats are to be allotted amongst Arun, Biswajyot, Chitra, Derek, Evan, and Fatima. Biswajyot gets a north facing flat and is not next to Derek. Derek and Fatima get diagonally opposite flats. Chitra is next to Fatima, and gets a south facing flat.Evan gets a north facing flat. Which of the following combination gets south facing flats?

A

Arun, Chitra and Fatima

B

Chitra, Biswajyot and Derek

C

Evan, Arun and Fatima

D

Derek, Arun and Biswajyot

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?

A

0

B

5

C

1

D

4

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?

A

0

B

1

C

4

D

1 + abcd

Use the following passage for the questions based on it. There are 6 flats on a floor in two rows. Out of these, three are north facing and the other three are south facing flats. The flats are to be allotted amongst Arun, Biswajyot, Chitra, Derek, Evan, and Fatima. Biswajyot gets a north facing flat and is not next to Derek. Derek and Fatima get diagonally opposite flats. Chitra is next to Fatima, and gets a south facing flat.Evan gets a north facing flat. Except Derek and Fatima, which other pair is diagonally opposite to each other?

A

Arun and Biswajyot

B

Arun and Chitra

C

Evan and Derek

D

Evan and Chitra

Use the following passage for the questions based on it. There are 6 flats on a floor in two rows. Out of these, three are north facing and the other three are south facing flats. The flats are to be allotted amongst Arun, Biswajyot, Chitra, Derek, Evan, and Fatima. Biswajyot gets a north facing flat and is not next to Derek. Derek and Fatima get diagonally opposite flats. Chitra is next to Fatima, and gets a south facing flat.Evan gets a north facing flat. Which of the following pairs is exactly opposite to each other?

A

Derek and Evan

B

Fatima and Chitra

C

Evan and Chitra

D

Evan and Arun

A, B, C and X, Y, Z were sitting facing each other. A, B and C were facing south and X, Y and Z were facing north. X was left of Y but in front of A; Zwas not at the left end and was not facing C. Who were at the left and right positions respectively?

A

B and Y

B

C and X

C

B and Z

D

A and X

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

A

$$\overrightarrow {\bf{L}} + \overrightarrow {\bf{S}} $$

B

$$\overrightarrow {{{\bf{S}}^2}} $$

C

$${L_z}$$

D

$$\overrightarrow {{{\bf{L}}^2}} $$

The value of the expression $$\frac{{{{\left( {a - b} \right)}^2}}}{{\left( {b - c} \right)\left( {c - a} \right)}} + $$ $$\frac{{{{\left( {b - c} \right)}^2}}}{{\left( {a - b} \right)\left( {c - a} \right)}} + $$ $$\frac{{{{\left( {c - a} \right)}^2}}}{{\left( {a - b} \right)\left( {b - c} \right)}}$$ = ?

A

0

B

3

C

$$\frac{1}{3}$$

D

2

$$\frac{{{{\left( {4.53 - 3.07} \right)}^2}}}{{\left( {3.07 - 2.15} \right)\left( {2.15 - 4.53} \right)}} + \, $$ $$\frac{{{{\left( {3.07 - 2.15} \right)}^2}}}{{\left( {2.15 - 4.53} \right)\left( {4.53 - 3.07} \right)}} + \,\, $$ $$\frac{{{{\left( {2.15 - 4.53} \right)}^2}}}{{\left( {4.53 - 3.07} \right)\left( {3.07 - 2.15} \right)}}$$ is simplified to :

A

0

B

1

C

2

D

3

Question : Which direction is Sunny facing now ?

Statements :
I. If Sunny turns to his right and again turns to his right, he will be facing North.
II. If Sunny walks some distance and turns left and again walks some distance, then his face will be towards left of Dinesh who is facing South.

A

I alone is sufficient while II alone is not sufficient

B

II alone is sufficient while I alone is not sufficient

C

Either I or II is sufficient

D

Neither I nor II is sufficient

E

Both I and II are sufficient