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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?
Which of the following could provide an example of exceptional demand curves?
1. Demand for "Giffen goods"
2. Demand based on fears of a future rise in prices
3. Demand for second-hand clothes
4. Demand for daily newspapers
Select the right answer:
The Central Information Commission (CIC) on Monday brought Indian cricket governing body BCCI under Right to Information Act.  Now, this will enable BCCI to accept all the queries. Which of the following substantiates the given statement? I: The cricket governing body BCCI is the part of the Central Information Commission.  II: Under Right to Information Act, BCCI has to answer the queries. III: The cricket governing body BCCI was brought under the Right to Information Act to bring transparency in their administration.
When demand for a factory's products is high, more money is spent at the factory for safety precautions and machinery maintenance than demand is low. Thus the average number of on-the-job accidents per employee each month should be bower during periods when demand is high than when demand is low and less money is available for safety precautions and machinery maintenance. Which of the following,if true about a factory when demand for its product is high casts the most serious doubt on the conclusion drawn above?
when demand for factory's products is high . more money is spent at the factory for safety precautions and machinery maintenance than when demand is low. thus the average number of on -the-job accidents per employee each month should be lower during perids when demand is high than when demand is low and less money is available for safety precautions and machinery maintenance .when demand for its products is high, casts the most serious doubt on the conclusion drawn above?
The value of the expression $$\frac{{{{\left( {a - b} \right)}^2}}}{{\left( {b - c} \right)\left( {c - a} \right)}} + $$   $$\frac{{{{\left( {b - c} \right)}^2}}}{{\left( {a - b} \right)\left( {c - a} \right)}} + $$    $$\frac{{{{\left( {c - a} \right)}^2}}}{{\left( {a - b} \right)\left( {b - c} \right)}}$$   = ?
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
$$\frac{{{{\left( {4.53 - 3.07} \right)}^2}}}{{\left( {3.07 - 2.15} \right)\left( {2.15 - 4.53} \right)}} + \, $$     $$\frac{{{{\left( {3.07 - 2.15} \right)}^2}}}{{\left( {2.15 - 4.53} \right)\left( {4.53 - 3.07} \right)}} + \,\, $$     $$\frac{{{{\left( {2.15 - 4.53} \right)}^2}}}{{\left( {4.53 - 3.07} \right)\left( {3.07 - 2.15} \right)}}$$     is simplified to :
In a six-digit number, the digit of thousands place is 4. The digit at ten's place is double that of digit at thousand's place and digit at hundreds places is half of the digit at thousand’s place. The digit at unit's place is half of the digit at hundred's place. Digit at Ten thousand's place is sum of the digits at thousands and hundreds place and digit at lakh's place is half the digit at ten thousands place. What will be the number?