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In a situation where a country’s government exercises complete control over its territory, makes its laws, and has no foreign authority dicating its internal affairs, what term best describes the status of this country?

Option: 1

Autonomous

 

Option: 2

Independent

 

 

Option: 3

Subjugated

 

 

Option: 4

Alliance

 

A country is known to be independent when it governs itself without any interference from any foreign power.

When it is able to make its own law, control its own territory and can handle internal matters independently. Independent means full sovereignty.

Hence, the correct answer is option 2) Independent

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Posted by

Divya Sharma

In a nation where citizens elect representatives to make decisions on their behalf, and the head of state is not a hereditary monarch but a public official chosen through elections, what form of government does this nation have?

Option: 1

Monarchy

 

Option: 2

Oligarchy

 

 

Option: 3

Democracy

 

 

Option: 4

Republic

 

A republic government is a form of government where the citizens are allowed to elect representatives to make laws and decisions. This means that the head of state is not a hereditary monarch but an elected official. In such a type of government structure, the power lies with the people. This ensures the leadership through public choice rather than royal lineage.

Hence, the correct answer is option 4) Republic

 

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Posted by

Divya Sharma

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Which term from the Preamble of the Indian Constitution aligns with the idea of promoting economic equality, similar to the situation in “Harmonia”?

Option: 1

Sovereign

 

Option: 2

Socialist

 

 

Option: 3

Secular

 

 

Option: 4

Democratic

 

Socialist in the preamble of the Indian Constitution means the idea of promoting economic equality. This would mean reducing the gap between rich and poor, and making sure a fair distribution of wealth and resources. This is similar to the situation described in Harmonia.

Hence, the correct answer is option 2) Socialist

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Posted by

Divya Sharma

Situation: Imagine you are planning a community event to celebrate the founding principles of the United States. You want to include elements that reflect the Preamble. Which option best aligns with the principles outlined in the Preamble of the U.S. Constitution?

Option: 1

A charity fundraiser to support local schools and education initiatives.

 

Option: 2

A fireworks display to commemorate the nation’s history and achievements.

 

 

Option: 3

A debate competition on current political issues.

 

 

Option: 4

A military parade showcasing the strength and capabilities of the armed forces

 

The Goals of the Preamble of the US constitution are -

Promoting the general welfare

Securing the blessings of liberty

Establishment of justice

Hence, the correct answer is option 1) A charity fundraiser to support local schools and education initiatives.

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Divya Sharma

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The set of points where the function \mathrm{f(x)=|x-1| e^x}   is differentiable is

Option: 1

R


Option: 2

\mathrm{R-|1|}


Option: 3

\mathrm{R-|-1|}


Option: 4

\mathrm{R-|0|}


Since |x-1| is not differentiable at x=1. So.  \mathrm{f(x)=|x-1| c^{\prime}}  is not differentiable at x=1. Hence, the requried set is R-|1|.

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Posted by

Ritika Kankaria

A steel rod of length 400 cm is clamped at the middle. The frequency of the fundamental mode for the longitudinal vibrations of the rod is  2.5K Hz . Find the speed of sound in steel.

 

Option: 1

20km/s


Option: 2

25km/s


Option: 3

15km/s


Option: 4

26km/s


\frac{\lambda }{2}=distance between two connected antinode

\frac{\lambda }{2}=4\\ \lambda=8M

frequency of fundamental mode is 

f=\frac{v}{\lambda }\\2.5\times10^{3}=\frac{v}{8}\\v=8\times2.5\times10^{3}\\v=20km/s

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Posted by

Anam Khan

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If  \vec{A}=a y \hat{x}+b \times \hat{y}  then curl will be-

Option: 1

(a-b) \hat{z}


Option: 2

(b-a) \hat{z}


Option: 3

(a+b) \hat{z}


Option: 4

(a-b) \hat{x}


\vec{A}=a y \hat{x}+b x \hat{y}

{\nabla} \times \vec{A}= curl =\left|\begin{array}{ccc} \hat{\imath} & \hat{\jmath} & \hat{k} \\ \frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z} \\ a y & b x & 0 \end{array}\right|

\begin{aligned} & \vec{\nabla} \times \vec{A}=\hat{\imath}\left[\frac{\partial}{\partial y}(0)-\frac{\partial}{\partial z} b x\right]-\hat{j}\left[\frac{\partial}{\partial x} 0-\frac{\partial}{\partial z} a y\right] \\ &+\hat{k}\left[\frac{\partial}{\partial x} b x-\frac{\partial}{\partial y} a y\right] \end{aligned}

\\vec{\nabla} \times \vec{A}=i[0]-\hat{j}[0]+\hat{k}[b-a] \\
\vec{\nabla} \times \vec{A}=(b-a) \hat{z} \cdot

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Posted by

himanshu.meshram

If at t=0, a travelling wave pulse on a string is described by the function y=\frac{6}{x^2+3} . What will be the wave function representing the pulse at time t, if the pulse is propagating along positive x-axis with speed 4m/s?

Option: 1

y=\frac{6}{(x+4 t)^2+3}


Option: 2

y=\frac{6}{(x-4 t)^2+3}


Option: 3

y=\frac{6}{(x- t)^2}


Option: 4

y=\frac{6}{(x- t)^2+13}


y(x, 0)=\frac{6}{x^2+3}

If v is the speed of the wave, then

\\ y(x, t)=y(x-v t, 0) \\ y(x, t)=\frac{6}{(x-v t)^2+3}\\ Here, \quad v=4 \mathrm{~m} / \mathrm{s}.\\ y(x, t)=\frac{6}{(x-4 t)^2+3}

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Posted by

sudhir.kumar

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Two parallel, long wires carry current i1 and i2 with i1 > i2. When the current is in the same direction, the magnetic field at a point midway between the wire is 10\mu T. If the direction of i2 is reversed, the field becomes 30\mu T. The ratio of i1/ i2 is:

Option: 1

4


Option: 2

3


Option: 3

2


Option: 4

1


            B_{net} = \frac{\mu_{0} (i1 - i2)}{2\pi d} = 10 \mu T

\vec{B} = \frac{\mu_{0} (i1 + i2)}{2\pi d} = 30 \mu T

Solving both equations, we get:

                \frac{i1}{i2} = 2

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Posted by

shivangi.bhatnagar

An ideal gas undergoes a quasi intatic, reversible process in which ito molar heat capacity C remain constant. If during this process the relation of pressure P and volume V is given ly p^{V^N}= constant, then N in given dy (here C_p and  C_v are molar specific heat et constant pressure ad constant volume, respectively)

Option: 1

N=\frac{c_P}{c_V}


Option: 2

N=\frac{c-c_p}{c-c_v}


Option: 3

N=\frac{C_p{-c}}{c-C_v}


Option: 4

N=\frac{C-C_v}{C-C_p}


Here, \left.P V^N=K \text { (Constant }\right)

For 1mol of ideal gas, P^V=R T

\text { Dividing (1) } by\text { (2) We get, } V^N-1_T=\frac{K}{R}

\therefore\left(\frac{d V}{d T}\right)=\frac{V}{(N-1)^T}=\frac{V}{(1-N)^T}

According to the first law of thermodynamics,

\begin{aligned} d Q & =C_V d T+p^{d V} \\ \therefore \frac{d Q}{d T} & =C_V+p\left(\frac{dV}{d T}\right)=C_V+\frac{p^V}{(1-N) T}=C_V+\frac{R}{1-N} \end{aligned}

Hence, thermal capacity C=C_v+\frac{R}{1-N} \text { or, } 1-N=\frac{{R}}{C} C_v

\begin{aligned} &\text { or, } N=1-\frac{R}{c-c_v}=\frac{c-(c_v+R)}{c-c_v}=\frac{c-c_p}{C-c_v}\\ &\left[\because C_p-c_V=R\right] \end{aligned}

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Posted by

Anam Khan

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