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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?
There are 40 boys in the class. They are standing in two rows facing each other in equal number. Ramu and Pankaj face each other, where Ramu is facing north and Pankaj is facing south. If they are at 10th and 8th position from their respective left in row. And if Ramu interchanges his position with Pankaj, then new position of Ramu from the right will be?
Ten boys B1, B2, B3, B4, B5, B6, B7, B8, B9, and B10 are sitting in a row facing towards the north (not necessarily in the same order). Only four boys are towards the left of B9. B6 is fourth to the right of B9. No boys are towards the left of B2. B5 is to the immediate right of B3. B4 is not towards the right of B6 and not towards the left of B9. B1 is second to the left of B7. B7 is third to the right of B2. Only two boys are sitting towards the right of B5. If B5 is to the immediate left of B6, then how many boys are sitting between B10 and B8?
In a row of boys, Punit’s position from the left end is 33rd and Ankit’s position from the right end is 25th. After interchanging their position, Punit’s position becomes 45th from the left end. How many boys are there in the row?
In a row of boys, Punits position from the left end is 33rd and Ankits position from the right end is 25th. After interchanging their position, Punits position becomes 45th from the left end. How many boys are there in the row?
In a row of boys, Rahul’s position from the right end is 39th and Pankaj’s position from the left end is 53rd . After interchanging their position, Rahul’s position becomes 64th from the right end. How many boys are there in the row?
Kamal’s position from the left end in a row of boys is 31st and Karan’s position from the right end is 29th. After interchanging their position, Kamal's position becomes 43rd from the left end. How many boys are there in the row?
In a row of boys, Punits position from the left end is 33rd and Ankits position from the right end is 25th. After interchanging their position, Punits positionbecomes 45th from the left end. How many boys are there in the row?
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