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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
A
$${\tau _\rho } > {\tau _\omega } > {\tau _\phi }$$
B
$${\tau _\rho }
C
$${\tau _\rho } {\tau _\phi }$$
D
$${\tau _\rho } > {\tau _\omega }
Correct Answer:
$${\tau _\rho }
In a two-electron atomic system having orbital and spin angular momenta $${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}}}.$$ For the jj coupling. scheme to be applicable, the coupling strengths must satisfy the condition
A
$${\Gamma _{{l_1}{l_2}}},\,{\Gamma _{{s_1}{s_2}}} > {\Gamma _{{l_1}{s_1}}},\,{\Gamma _{{l_2}{s_2}}}$$
B
$${\Gamma _{{l_1}{s_1}}},\,{\Gamma _{{l_2}{s_2}}} > {\Gamma _{{l_1}{l_2}}},\,{\Gamma _{{s_1}{s_2}}}$$
C
$${\Gamma _{{l_1}{s_2}}},\,{\Gamma _{{l_2}{s_1}}} > {\Gamma _{{l_1}{l_2}}},\,{\Gamma _{{s_1}{s_2}}}$$
D
$${\Gamma _{{l_1}{s_2}}},\,{\Gamma _{{l_2}{s_1}}} > {\Gamma _{{l_1}{s_1}}},\,{\Gamma _{{l_2}{s_2}}}$$
S =
Training data =
=> No (negative example). How will S be represented after encountering this training data?
A
<phi, phi, phi, phi>
B
<sunny, warm, high, same>
C
<rainy, cold, normal, change>
D
<?, ?, ?, ?>
The value of $$\left( {\frac{{\sin \theta + \sin \phi }}{{\cos \theta + \cos \phi }} + \frac{{\cos \theta - \cos \phi }}{{\sin\theta - \sin\phi }}} \right)$$ is?
A
1
B
2
C
$$\frac{1}{2}$$
D
0
Two monochromatic waves having frequencies $$\omega $$ and $$\omega + \Delta \omega \left( {\Delta \omega \ll \omega } \right)$$ and corresponding wavelengths $$\lambda $$ and $$\lambda - \Delta \lambda \left( {\Delta \lambda \ll \lambda } \right)$$ of same polarization, travelling along X-axis are superimposed on each other. The phase velocity and group velocity of the resultant wave are respectively given by
A
$$\frac{{\omega \lambda }}{{2\pi }},\,\frac{{\Delta \omega {\lambda ^2}}}{{2\pi \Delta \lambda }}$$
B
$$\omega \lambda ,\,\frac{{\Delta \omega {\lambda ^2}}}{{\Delta \lambda }}$$
C
$$\frac{{\omega \Delta \lambda }}{{2\pi }},\,\frac{{\Delta \omega \Delta \lambda }}{{2\pi }}$$
D
$$\omega \Delta \lambda ,\,\omega \Delta \lambda $$
If 30Ω6 = -5, 80Ω2 = -40 and 20Ω4 = -5, then find the value of 70Ω2 = ?
A
10
B
-35
C
15
D
-20
If 7Ω6 = 84, 8Ω7 = 112 and 8Ω4 = 64, then find the value of 3Ω4 = ?
A
24 \
B
12 \
C
4 \
D
20
If 7Ω6 = 84, 8Ω7 = 112 and 8Ω4 = 64, then find the value of 3Ω4 = ?
A
24 \
B
12
C
4 \
D
20
Rho-dependent and rho-independent transcription termination mechanisms operate in prokaryotes. Rho independent termination mechanism involves
A
Binding of the rho protein upstream of the termination element
B
No protein factors and only RNA secondary structure and run of 'U's
C
Presence of UGA or UAA stop codons
D
Binding of accessory factors at termination signal
The raised cosine pulse p(t) is used for zero ISI in digital communications. The expression for p(t) with unity roll-off factor is given by $$p\left( t \right) = \frac{{\sin 4\pi \omega t}}{{4\pi \omega t\left( {1 - 16{\omega ^2}{t^2}} \right)}}.$$ The value of p(t) at $$t = \frac{1}{{4\omega }}$$ is
A
-0.5
B
0
C
0.5
D
∞
For a function g(t), it is given that
$$\int\limits_{ - \infty }^{ + \infty } {g\left( t \right){e^{ - j\omega t}}dt = \omega {e^{ - 2{\omega ^2}}}} $$ for any real value $$\omega $$ . If $$y\left( t \right) = \int\limits_{ - \infty }^t {g\left( \tau \right)} d\tau ,\,{\rm{then}}\,\int\limits_{ - \infty }^{ + \infty } {y\left( t \right)} dt$$ is. . . . . . . .
A
0
B
-j
C
$$ - {j \over 2}$$
D
$${j \over 2}$$