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In a two-electron atomic system having orbital and spin angular momenta $${l_1}{l_2}$$  and $${s_1}{s_2}$$  respectively, the coupling strengths are defined as $${\Gamma _{{l_1}{l_2}}},\,{\Gamma _{{s_1}{s_2}}},\,{\Gamma _{{l_1}{s_1}}},\,{\Gamma _{{l_2}{s_2}}},\,{\Gamma _{{l_1}{l_2}}}$$      and $${\Gamma _{{l_2}{s_1}}}.$$  For the jj coupling. scheme to be applicable, the coupling strengths must satisfy the condition
The resonance widths $$\Gamma $$ of $$\rho ,\,\omega $$  and $$\phi $$ particle resonances satisfy the relation $${\Gamma _\rho } > {\Gamma _\omega } > {\Gamma _\phi }$$   . Their lifetimes r satisfy the relation
Which two of the following statements are true?  a) Skewness studies the flatness or peakedness of the distribution  b) A positively skewed distribution curve is stretched more to the right than to the left  c) On the basis of empirical relationship between mean, mode and median for moderately asymmetrical distribution, Karl Pearson's coefficient of skewness can be measured by 3 (Mean -Median) divided by Standard Deviation  d) If mean < mode, the distribution is positively skewed  Choose the correct option from those below: 
Alpha, Beta and Gama went for a picnic at Jurassic Park, when they feel hungry they took out the stuff they brought. Alpha bought 6 sandwiches while Beta bought 4 and Gamma bought none. Both Alpha and Beta shared their sandwiches with Gamma such that each got the same amount. If Gamma paid a total amount of Rs. 10 to Alpha and Beta, how much of Rs. 10 should Alpha get ? (Assume that sandwiches and rupees can be split.)
The value of $$\oint {\Gamma \frac{{3{\text{z}} - 5}}{{\left( {{\text{z}} - 1} \right)\left( {{\text{z}} - 2} \right)}}{\text{dz}}} $$     along a closed path $$\Gamma $$ is is equal to (4πi), where z = x + iy and $${\text{i}} = \sqrt { - 1} .$$   The correct path $$\Gamma $$ is
If the shape parameter of the gamma distribution is twice the scale parameter, what will be the value of the mean of the distribution?
Statement I Exponential probability distribution has the mean = $$\frac{1}{\mu }$$ and variance = $$\frac{1}{{{\mu ^2}}}$$
Statement II The mean, median and mode do not coincide in the normal distribution.
Statement III The binomial distribution is symmetrical for any value of p (probability of success).
The following question consists of six sentences of a passage. The first and the sixth sentences are given in the beginning as S1 and S6. The middle four sentences in each have been jumbled up and labelled P, Q, R and S. You are required to find the proper sequence of the four sentences and mark your response accordingly. S1 : One of the many young scientists who chose to throw in their lot with Rutherford was an Oxford physical chemist, Frederick Soddy. S6 : We now know that Gamma rays are a particularly fierce form of X-rays. P : His association with Rutherford lasted only two years, but that was long enough to change the whole face of physics. Q : He was just 23. R : They found that thorium changed into a new element , thorium X, and in the process gave off what was apparently a gas and at the same time a third type of ray, which they named after the Greek letter ‘Gamma’. S : When he teamed up with Rutherford, they investigated thorium which, as Marie Curie had shown, was radioactive. The proper sequence should be
In the following items, each passage consists of six sentences. The first and the sixth sentence are given in the beginning as S1 and S6. The middle four sentences in each have been removed and jumbled up. These are labeled P, Q, R and S. You are required to find out the proper sequence of the four sentences and mark your response accordingly on the Answer Sheet. S1 :One of the many young scientists who chose to throw in their lot with Rutherford was an Oxford physical chemist, Frederick Soddy.
S6:We now know that Gamma rays are a particularly fierce form of X-rays.
P:His association with Rutherford lasted only two years, but that was long enough to change the whole face of physics.
Q:He was just 23.
R:They found that thorium changed into a new element, thorium X, and in the process gave off what was apparently a gas and at the same time a third type of ray, which they named after the Greek letter Gamma.
S:When he teamed up with Rutherford,they investigated thorium which, as Marie Curie had shown, was radioactive. The proper sequence should be
Consider a Poisson distribution for the tossing of a biased coin. The mean for this distribution is μ. The standard deviation for this distribution is given by