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In the circuit shown in figure, the heat produced in the $5\Omega$ resistor due to the current flowing through it is $10\text{calories per second}$. The heat generated in the $4\Omega$ , resistor is

The $K_{\alpha }$ X- rays arising from a cobalt ($Z=27$) target have a wavelength of 179 $pm$. The $K_{\alpha }$ X rays arising from a nickle target (Z=28) is

Find the angular separation between th econsecutive bright fringes in a young's doubel slit experiment with blue- green light of wavelength 500 nm. The separation between the slits is $2.0\times {10}^{-3}m$

Two rods having same length and cross-sectional area are connected individually between temperature $T_1$ and $T_2$. If the rate of loss of heat due to condution is equal and specific heat of two rods are in the ratio $1:2$, then the ratio of their thermal conductivity will be

How to solve problems related to centre of mass and centre of gravity

A square loop $\text{OABCO}$ of side length $l$ carries a current $i$. It is placed as shown in the figure. The magnetic moment of the loop will be :

The additional kinetic energy to be provided to a satellite of mass $m$, revolving around a planet of mass $M$, to transfer it from a circular orbit of radius $2R$ to another orbit of radius $3R$ is:

A whistle giving out 450 Hz approaches a stationary observer at a speed of 33 m/s. The frequency heard by the observer (in Hz) is :

The vertices of a quadrialteral are $A(1,2,-1),B(-4,2,-2),C(4,1,-5)$ and $D(2,-1,3)$. Forces of magnitudes $2N,3N,2N$ are acting at point $A$ along the lines $AB,AC$ and $AD$ respectively. Their resultant is:

Condition for which the terminal potential difference of a cell exceed its a emf ??

The electron in a hydrogen atom makes a transition $n_1\to n_2$ where $n_1$ and $n_2$ are the principal quantum numbers of the two states. Assume the Bohr model to be valid. The time period of the electron in the initial state is 8 times that in the final state. The possible values of $n_1$ and $n_2$ are

At what temperature root mean square velocity of hydrogen becomes double of its value at $\text{S.T.P}$, keeping pressure constant?

A body of mass m is moving in a circle of radius r with a constant speed v. The force on the body is $\frac{m{v}^2}{r}$ and is directed towards the centre. What is the work done by this force in moving the body over half the circumference of the circle

In the equation $x=A\sin (\omega t+\frac{\pi }{4})$. Match the following, when $x=\frac{A}{2}$



$\begin{array}{cc}\text{Column I}& \text{Column II}\\ \text{(A) Kinetic energy}& \text{(p) Half the maximum value}\\ \text{(B) Potential energy}& \text{(q) 3/4 times the maximum value}\\ \text{(C) Acceleration}& \text{(r) 1/4 times the maximum value}\\ & \text{(s) Cannot say anything}\end{array}$

Find the magnitude of the electric field $\left(|\overrightarrow{E_{ind}}|\right)$ at the center of the sphere due to the induced charges on the sphere.

A wooden block of mass $20g$ is dropped from the top of the cliff $50m$ high. Simultaneously a bullet of mass $20g$ is fired from the foot of the cliff upwards with a velocity $25m{s}^{-1}$. The bullet and the wooden block will meet each other after time : ($g=10m{s}^{-2}$)

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The average kinetic energy of one $\text{mole}$ of gas per degree of freedom (on the basis of theory of gases)

A lawn roller is displaced through 1km using a force of 200N in a direction making an angle of ${60}^0$ with the lawn. The work done is

A metallic rod completes the circuit as shown in the figure. The circuit is normal to a magnetic field of $B=0.15\text{T}$. If the resistance of the circuit is $3\Omega$, the force required to move the rod, with a constant velocity of $2\text{m/s}$, is

A convex mirror is used to form the image of an object. Then which of the

following statements is wrong

[CPMT 1973]

If radius of a hollow metallic sphere is $R$. If the potential difference between it's surface and a point at a distance $3R$ from it's centre is $V$ then the electric field intensity at a distance $3R$ from it's centre will be

In the series LCR circuit at resonance the applied ac voltage is 220V. The potential drop across the inductance is 110 V. what is the potential drop across the resistance?

A long straight wire is parallel to one edge of the loop as shown in the figure. If the current in the long wire varies with time as $I=I_0{e}^{-\frac{t}{\tau }}$, what will be the induced emf in the loop ?

Two indentical blocks each of mass $M=9\text{kg}$ are placed on a rough horizontal surface of coefficient of static friction $\mu =0.1$, assume static and kinetic coefficient of friction to be equal. The two blocks are joined by a light spring and block $B$ is in contact with a vertical fixed wall as shown in figure. A bullet of mass $m=1\text{kg}$ and velocity $V_o=10\text{m/s}$ hit the block $A$ and gets embedded in it.
Find the maximum compression of spring (Take spring constant $k=240\text{N/m}$ and $g=10{\text{m/s}}^2$.

What is de Broglie wavelength associated with an electron, accelerated through a potential difference of $64\text{V}$?

If a train travelling at $72\text{kmph}$ is to be brought to rest in a distance of $200\text{metres}$, then its retardation should be

A conducting rod of length $l$ and mass $m$ is moving down a smooth inclined plane of inclination $\theta$ with constant velocity $v$. A current $I$ is flowing in the conductor in a direction perpendicular to the paper inwards. A vertically upward magnetic field $\overrightarrow{B}$ exists in space. Then, magnitude of magnetic field $\overrightarrow{B}$ is

The position of the particle is given by $x=2t^3-4t^2+5$ in $\text{m}$. The acceleration of the particle at $5\text{sec}$ is

Magnetic flux $\varphi$ in weber in a closed circuit of resistance $10\Omega$ varies with time $t$ (in seconds) as $\varphi =6t^2-5t+1$. The magnitude of induced current at $t=0.25\text{s}$ is



​​​​​​​$[$1 Mark$]$

Capacitance of the capacitor shown in the figure is