A logic circuit provides the output $Y$ as per the following truth table:
| A | B | Y |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
The expression for the output $Y$ is:
$Y = 1$ exactly when $B = 0$, so $Y = \overline{B}$.
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A logic circuit provides the output $Y$ as per the following truth table:
| A | B | Y |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
The expression for the output $Y$ is:
$Y = 1$ exactly when $B = 0$, so $Y = \overline{B}$.
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: The potential ($V$) at any axial point, at 2 m distance($r$) from the centre of the dipole of dipole moment vector $\vec{P}$ of magnitude, $4 \times 10^{-6}\ \text{C m}$, is $\pm 9\times 10^3\ V$.
(Take $\dfrac{1}{4\pi\epsilon_0} = 9\times 10^9$ SI units)
Reason R: $V = \pm \dfrac{2P}{4\pi\epsilon_0 r^2}$, where $r$ is the distance of any axial point, situated at 2 m from the centre of the dipole.
In the light of the above statements, choose the correct answer from the options given below:
Correct axial potential: $V = p/(4\pi\epsilon_0 r^2) = 9\times 10^3$ V (A correct). R's formula has extra factor 2 (that is for field, not potential) — R false.
The terminal voltage of the battery, whose emf is $10V$ and internal resistance $1\ \Omega$, when connected through an external resistance of $4\ \Omega$ as shown in the figure is:
$I = 10/5 = 2$ A; $V_\text{term} = 2 \times 4 = 8$ V.
In the above diagram, a strong bar magnet is moving towards solenoid-2 from solenoid-1. The direction of induced current in solenoid-1 and that in solenoid-2, respectively, are through the directions:
Lenz's law: solenoid-1 sees N-flux decreasing (current $A \to B$); solenoid-2 sees S-flux increasing (current $D \to C$).
In an ideal transformer, the turns ratio is $\dfrac{N_p}{N_s} = \dfrac{1}{2}$. The ratio $V_s : V_p$ is equal to (the symbols carry their usual meaning):
$V_s/V_p = N_s/N_p = 2:1$.
A tightly wound 100 turns coil of radius 10 cm carries a current of 7 A. The magnitude of the magnetic field at the centre of the coil is (Take permeability of free space as $4\pi \times 10^{-7}$ SI units):
$B = \mu_0 N I/(2R) = 14\pi \times 10^{-4} \approx 4.4$ mT.
Given below are two statements:
Statement I: Atoms are electrically neutral as they contain equal number of positive and negative charges.
Statement II: Atoms of each element are stable and emit their characteristic spectrum.
In the light of the above statements, choose the most appropriate answer from the options given below:
Both statements are standard textbook facts.
The quantities which have the same dimensions as those of solid angle are:
Solid angle, strain and plane angle are all dimensionless.
If $c$ is the velocity of light in free space, the correct statements about photon among the following are:
A. The energy of a photon is $E = h\nu$.
B. The velocity of a photon is $c$.
C. The momentum of a photon, $p = \dfrac{h\nu}{c}$.
D. In a photon-electron collision, both total energy and total momentum are conserved.
E. Photon possesses positive charge.
Choose the correct answer from the options given below:
A–D true; E false (photons have zero charge).
A bob is whirled in a horizontal plane by means of a string with an initial speed of $\omega$ rpm. The tension in the string is $T$. If speed becomes $2\omega$ while keeping the same radius, the tension in the string becomes:
$T \propto \omega^2$, so tension becomes $4T$.
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