Consider the following logic circuit. The output is Y = 0 when :

$$\text{ Choose the correct logic circuit for the given truth table having inputs }A\text{ and }B\text{. }$$ .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-c3ow{border-color:inherit;text-align:center;vertical-align:top} Inputs Output A B Y 0 0 0 0 1 0 1 0 1 1 1 1

Consider a n-type semiconductor in which ${\mathrm{n}}_{\mathrm{e}}$ and ${\mathrm{n}}_{\mathrm{h}}$ are number of electrons and holes, respectively. (A) Holes are minority carriers (B) The dopant is a pentavalent atom (C) ${\mathrm{n}}_{\mathrm{e}}{\mathrm{n}}_{\mathrm{h}}\ne {\mathrm{n}}_i^2$ (where ${\mathrm{n}}_i$ is number of electrons or holes in semiconductor when it is intrinsic form) (D) ${\mathrm{n}}_{\mathrm{e}}{\mathrm{n}}_{\mathrm{h}}⩾{\mathrm{n}}_i^2$ (E) The holes are not generated due to the donors Choose the correct answer from the options given below :

The Boolean expression $\mathrm{Y}=A\bar{B}C+\bar{A}\bar{C}$ can be realised with which of the following gate configurations. A. One 3-input AND gate, 3 NOT gates and one 2-input OR gate, One 2-input AND gate, B. One 3 -input AND gate, 1 NOT gate, One 2 -input NOR gate and one 2 -input OR gate C. 3 -input OR gate, 3 NOT gates and one 2 -input AND gate Choose the correct answer from the options given below:

Two bodies A and B of equal mass are suspended from two massless springs of spring constant k1 and k2, respectively. If the bodies oscillate vertically such that their amplitudes are equal, the ratio of the maximum velocity of A to the maximum velocity of B is

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Time period of a simple pendulum is longer at the top of a mountain than that at the base of the mountain. Reason (R) : Time period of a simple pendulum decreases with increasing value of acceleration due to gravity and vice-versa. In the light of the above statements, choose the most appropriate answer from the options given below :

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : A simple pendulum is taken to a planet of mass and radius, 4 times and 2 times, respectively, than the Earth. The time period of the pendulum remains same on earth and the planet. Reason (R) : The mass of the pendulum remains unchanged at Earth and the other planet. In the light of the above statements, choose the correct answer from the options given below :

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Knowing initial position ${\mathrm{x}}_0$ and initial momentum $p_0$ is enough to determine the position and momentum at any time $t$ for a simple harmonic motion with a given angular frequency $\omega$. Reason (R) : The amplitude and phase can be expressed in terms of ${\mathrm{X}}_0$ an ${\mathrm{p}}_0$. In the light of the above statements, choose the correct answer from the options given below :

A light hollow cube of side length 10 cm and mass 10 g , is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is $y\pi \times 10^{-2}\mathrm{s}$, where the value of $y$ is (Acceleration due to gravity, $g=10\mathrm{m}/{\mathrm{s}}^2$, density of water $=10^3\mathrm{kg}/{\mathrm{m}}^3$ )

A particle is executing simple harmonic motion with time period 2 s and amplitude 1 cm . If D and d are the total distance and displacement covered by the particle in 12.5 s , then $\frac{\mathrm{D}}{\mathrm{d}}$ is

A particle oscillates along the $x$-axis according to the law, $x(\mathrm{t})=x_0{\sin }^2\left(\frac{\mathrm{t}}{2}\right)$ where $x_0=1\mathrm{m}$. The kinetic energy $(\mathrm{K})$ of the particle as a function of $x$ is correctly represented by the graph

A block of mass 2 kg is attached to one end of a massless spring whose other end is fixed at a wall. The spring-mass system moves on a frictionless horizontal table. The spring's natural length is 2 m and spring constant is 200 N/m. The block is pushed such that the length of the spring becomes 1 m and then released. At distance x m (x < 2) from the wall, the speed of the block will be

A particle is subjected to two simple harmonic motions as : $$x_1=\sqrt{7}\sin 5\mathrm{tcm}$$ and $x_2=2\sqrt{7}\sin \left(5t+\frac{\pi }{3}\right)\mathrm{cm}$ where $x$ is displacement and $t$ is time in seconds. The maximum acceleration of the particle is $x\times 10^{-2}{\mathrm{ms}}^{-2}$. The value of $x$ is :

Two blocks of masses $m$ and $M,(M>m)$, are placed on a frictionless table as shown in figure. A massless spring with spring constant k is attached with the lower block. If the system is slightly displaced and released, then ( $\mu =$ coefficient of friction between the two blocks) A. The time period of small oscillation of the two blocks is $T=2\pi \sqrt{\frac{(m+M)}{k}}$ B. The acceleration of the blocks is $a=-\frac{kx}{M+m}$ ( $x=$ displacement of the blocks from the mean position) C. The magnitude of the frictional force on the upper block is $\frac{m\mu |x|}{M+m}$ D. The maximum amplitude of the upper block, if it does not slip, is $\frac{\mu (M+m)g}{k}$ E. Maximum frictional force can be $\mu (\mathrm{M}+\mathrm{m})\mathrm{g}$. Choose the correct answer from the options given below :

Two simple pendulums having lengths $l_1$ and $l_2$ with negligible string mass undergo angular displacements ${\theta }_1$ and ${\theta }_2$, from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct?

A plane electromagnetic wave propagates along the + x direction in free space. The components of the electric field, $\vec{E}$ and magnetic field, $\vec{B}$ vectors associated with the wave in Cartesian frame are

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Electromagnetic waves carry energy but not momentum.Reason (R) : Mass of a photon is zero. In the light of the above statements, choose the most appropriate answer from the options given below :

The magnetic field of an E.M. wave is given by $\vec{B}=\left(\frac{\sqrt{3}}{2}\hat{i}+\frac{1}{2}\hat{j}\right)30\sin \left[\omega \left(t-\frac{z}{c}\right)\right]$ (S.I. Units).The corresponding electric field in S.I. units is:

The electric field of an electromagnetic wave in free space is $\overrightarrow{\mathrm{E}}=57\cos \left[7.5\times 10^6\mathrm{t}-5\times 10^{-3}(3x+4y)\right](4\hat{i}-3\hat{j})N/C$. The associated magnetic field in Tesla is