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Water and turpentine oil (specific heat less than that of water) are both heated to same temperature. Equal amounts of these placed in identical calorimeters are then left in air

Find the slope of the tangent to the curve $y=x^3-3x+2$ at the point whose x- coordinate is 3.

In term of potential difference V, electric current I, permittivity ${\epsilon }_0$, permeability ${\mu }_0$ and speed of light c, the dimensionally correct relation is

The electric field in a region is given by $\overrightarrow{E}=(1200\hat{i}+1600\hat{j})\text{N/C}$. Find the flux of this field through a rectangular surface of area $0.2{\text{m}}^2$ parallel to the $y-z$ plane.

Is velocity at the highest point zero

A leakproof cylinder of length $1\text{m}$, made of a metal which has very low coefficient of expansion, is floating vertically in water at $0^{\circ }\text{C}$ such that its height above the water surface is $20\text{cm}$. When the temperature of water is increased to $4^{\circ }\text{C}$, the height of the cylinder above the water surface becomes $21\text{cm}$. The density of water at $T=4^{\circ }C$, relative to the density at $T=0^{\circ }C$ is close to:

A body, acted upon by a force of $50N$ is displaced through a distance $10$ meter in a direction making an angle of ${60}^{\circ }$ with the force. The work done by the force be

An object $2.4\text{m}$ in front of a lens forms a sharp image on a film $12\text{cm}$ behind the lens. A glass plate $1\text{cm}$ thick, of refractive index $1.5$ is inserted between lens and film with its plane faces parallel to film. At what distance (from lens) should the object shifted to be in sharp focus of film?

In the following digital circuit, what will be the output at ${}^{\prime }{Z}^{\prime }$, when the input $(A,B$) are $(1,0),\text{are}(1,0),(0,0),(1,1),(0,1)$

A bullet passes past a person at a speed $220{\text{ms}}^{-1}$. Find the fractional change in the frequency of the whistling sound heard by the person as the bullet crosses the person. Speed of sound $=330{\text{ms}}^{-1}$.

A smooth semicircular wire track of radius $R$ is fixed in a vertical plane as shown in the figure. One end of a massless spring of natural length $\frac{3}{4}R$ is attached to the lowest point $O$ of the wire track. A small ring of mass m, which can slide on the track, is attached to the other end of the spring. The spring makes an angle of ${60}^0$ with the vertical. The spring constant is $k=\frac{mg}{R}$. Consider the instant when the ring is making an angle of ${60}^0$ with the vertical. Find the tangential acceleration of the ring.

A
circular coil of 16 turns and radius 10 cm carrying a current of
0.75 A rests with its plane normal to an external field of magnitude
5.0 ×
10⁻²
T. The coil is free to turn about an axis in its plane perpendicular
to the field direction. When the coil is turned slightly and
released, it oscillates about its stable equilibrium with a frequency
of 2.0 s⁻¹.
What is the moment of inertia of the coil about its axis of rotation?

With what acceleration $a$ should the box of figure be moving upwards so that the block of mass $m$ exerts a force $\frac{7Mg}{4}$ on the floor of the box ?

River is flowing at 3 Km/h in the west direction and You can swim at a maximum speed of 5 Km/h , Given if the river is 12 km wide, How long will you take to cross the river?

A plate is moving with velocity $5\text{m/s}$ parallel to a plate that is held stationary at a distance of $10\text{mm}$ below the upper plate. If the space between the plates is filled with water having coefficient of viscosity $9\times {10}^{-4}$ Pa $s$, then the shear stress acting on the surface of the moving plate assuming linear velocity profile between plates will be

The temperature of an ideal gas is increased from ${27}^{\circ }\text{C}$ to ${127}^{\circ }\text{C}$. Then, percentage increase in $V_{rms}$ is

A body having momentum $P$ is moving in positive $x$ direction. If the direction of velocity is changed by angle ${120}^{\circ }$ from the original direction, find the magnitude of the impulse on the body when it changes its direction.

In the spectrum of hydrogen atom, the ratio of the longest wavelength in Lyman series, to the longest wavelength in the Balmer series is,

In order to establish an instantaneous displacement current of $1\text{mA}$ in the space between the plates of $2\mu F$ parallel plate capacitor, the potential difference need to apply is

A ray of light is incident at angle $i$ on a surface of a prism of small angle $A$ and emerges normally from the opposite surface. If the refractive index of the material of the prism is $\mu$, the angle of incidence $i$ is nearly equal to:

A uniformly charged ring has linear charge density $4\frac{C}{m}$. What is the electric potential at its centre?

A small block of mass 100 g is pressed against a horizontal spring fixed at one end to compress the spring through 5.0 cm (figure 8-E11). The spring constant is 100 N/m. When released, the block moves horizontally till it leaves the spring. Where will it hit the ground 2 m below the spring ?

Two points have coordinates $a(1,2)\text{and}b(x,4)$. If the line joining them has $\text{slope}=1$, the value of $x$ is

The electrons, identified by quantum numbers n and l

(i) n = 4, l = 1 (ii) n = 4, l = 0 (iii) n = 3, l = 2 (iv) n = 3, l = 1

can be placed in order of increasing energy, from the lowest to highest, as

PARAGRAPH

In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below, $\left[E\right]$ and [𝐵] stand for dimensions of electric and magnetic fields respectively, while $\left[{\epsilon }_0\right]$ and $\left[{\mu }_0\right]$ stand for dimensions of the permittivity and permeability of free space respectively. $\left[L\right]$ and $\left[T\right]$ are dimensions of length and time respectively. All the quantities are given in SI units.



The relation between $\left[{\epsilon }_0\right]$ and $\left[{\mu }_0\right]$ is

If a particle moves from point P (2,3,5) to point Q (3,4,5). Its displacement vector be