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Question

The value of $T\left(\frac{1}{2}\right)$ is :

The correct answer is
$\sqrt{\pi}$

Identify T(x) Function

The question asks for the value of $T\left(\frac{1}{2}\right)$. Given the options and the common mathematical context where such questions appear, $T(x)$ typically represents the Gamma function, denoted as $\Gamma(x)$.

Evaluate T(1/2) Using Gamma Function Property

The Gamma function $\Gamma(x)$ is a generalization of the factorial function to complex and real numbers. A fundamental property of the Gamma function is its value at $x = \frac{1}{2}$:

$ \Gamma\left(\frac{1}{2}\right) = \sqrt{\pi} $

Assuming $T(x) = \Gamma(x)$, we can directly apply this property:

$ T\left(\frac{1}{2}\right) = \Gamma\left(\frac{1}{2}\right) = \sqrt{\pi} $

Conclusion

Therefore, the value of $T\left(\frac{1}{2}\right)$ is $\sqrt{\pi}$.

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Important Questions from Miscellaneous

  1. Which of the following relationships is/are not true?
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    (B). PV = $\frac{3}{2}kT$
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    Choose the correct answer from the options given below
  2. Match List-I with List-II
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    (A). ns$^2$(I). 2100
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    (D). ns$^2$np$^6$(IV). 900

    Choose the correct answer from the options given below:
  3. The shielding constant of a 2p electron (calculated using Slater's rules) is
  4. Match List-I with List-II
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    SpectroscopyProperty
    (A). Raman(I). Polarizability
    (B). FTIR(II). Dipole Moment
    (C). UV-Visible(III). Absorbance
    (D). NMR(IV). Spin

    Choose the correct answer from the options given below:
  5. The structure of protein comprises of:
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