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Two plates of the same area and the same thickness having thermal conductivities $k_1$ and $k_2$ are placed one on top of the other. The top and bottom faces of the composite plate are maintained at different constant temperatures. The thermal conductivity of the composite plate will be

A cyclist riding the bicycle at a speed of $14\sqrt{3}\text{m/s}$ takes a turn around a circular road of radius $20\sqrt{3}\text{m}$ without skidding. What is his inclination to the vertical?

[Take $g=9.8{\text{m/s}}^2$]

A trolley of mass M is attached to a block of mass m by a string passing over a frictionless pulley as shown in the figure. If the coefficient of friction between the trolley and the surface below is $\mu ,$ what is the acceleration of the trolley and the block system when they are released?

A block of mass $m$ is lying on a wedge having inclination of $\alpha ={\tan }^{-1}\left(\frac{1}{5}\right)$. Wedge is moving with a constant acceleration of $2{\text{m/s}}^2$. Find the minimum value of coefficient of friction so that $m$ remains stationary with respect to wedge. Take $g=10{\text{m/s}}^2$.

A co-axial cable which carrying equal current $I$ in opposite direction have cross section as shown in diagram. If $B_1$ and $B_2$ are the magnetic field at inner and outer point of cable, then which of the following relation is correct

An eye specialist prescribes spectacles having a combination of convex lens of focal length $40\text{cm}$ in contact with a concave lens of focal length $25\text{cm}$. The power of this lens combination in diopter is

If a planet revolves around the sun which of the following doesn't remain constant ?

1. 295.5

A body rolling on ice with vel. 8m/s comes to rest after traveling 4 m.Compute the co efficient of friction

Dimensional formula of mechanical equivalent of heat is

Hubble telescope uses light of wavelength $550\text{nm}$ through a $2.44\text{m}$ aperture. The height of Hubble telescope above the surface of Earth is given to be $600\text{km}.$ Find the least distance between two objects on the surface of Earth to be visible to the telescope sufficiently resolved.

The inverse Fourier transform of $X\left(\omega \right)=e^{-\omega }u\left(\omega \right)$is

A smooth inclined plane of length L having inclination θ with the horizontal is inside a lift which is
moving down with retardation a. The time taken by a body to slide down the inclined plane, from rest, will be

The
work function of caesium metal is 2.14 eV. When light of frequency 6
×10¹⁴ Hz
is incident on the metal surface, photoemission of electrons occurs.
What is the

(a) maximum
kinetic energy of the emitted electrons,

(b)
Stopping potential, and

(c)
maximum speed of the emitted
photoelectrons?

The resistances of the four arms $\text{P, Q, R}$ and $\text{S}$ , in a Wheatstone's bridge, are $10\Omega ,30\Omega ,30\Omega \text{and}90\Omega$ respectively. The e.m.f. and internal resistance of the cell are $7\text{V}\text{and}5\Omega$ respectively. If the galvanometer resistance is $50\Omega ,$ the current drawn from the cell will be -

A point mass $\left(m_o\right)$ is at the surface of a planet of density $\rho$ and radius $r$. Gravitational force experienced by $m_o$ is proportional to

A satellite is moving around the with speed v in a circular orbit of radius r. If the orbit radius is decreased by $1\%$, its speed will

A line AB is making an angle of ${30}^{\circ }$ from +ve x-axis, the line is in xy plane, what is the velocity of a car moving with speed 36 $km/hr$ along AB?

A sample consisting of 1 mol of mono-atomic gas $(C_V=\frac{3}{2}R)$is taken through the cycle as shown.

$\Delta U$ for the process $(1\to 2)$ is

For the given equation representing position, $y=\text{A sin}\omega t+A\sin (\omega t+\frac{2\pi }{3})$, match the column.
$\begin{array}{cc}\text{Column I}& \text{Column II}\\ \text{(A) Motion}& \text{(p) Is periodic but not SHM}\\ \text{(B) Amplitude}& \text{(q) Is SHM}\\ \text{(C) Initial phase}& \text{(r) A}\\ \text{(D) Maximum velocity}& \text{(s)}\frac{\pi }{3}\\ & \text{(t)}\frac{\omega }{3}\\ & \text{(u) None}\end{array}$

Temperature of a body $\theta$ is slightly more than the temperature of the surrounding ${\theta }_0$ . Its rate of cooling $\left(R\right)$ versus temperature of body $\left(\theta \right)$ is plotted. Its shape would be

A body is moving in a circle with a speed of $1\text{m/s}$. This speed increases at a constant rate of $2\text{m/s}$ every second. Assume that the radius of the circle described is $25\text{m}$. The total acceleration of the body after $2\text{s}$ is

The central fringe in a Young’s double slit experiment with the wavelength $\lambda =500$ nm has intensity $I_0$. If one of the slits is covered by a $5\mu m$ thick film of glass $(\mu =1.5)$, the intensity at centre of the screen becomes $I_1$. The ratio of $\frac{I_1}{I_0}$ is

Motion described by an object is shown in the figure given below, the acceleration of the object is

The kinetic energy $k$ of a particle moving along a circle of radius $R$ depends on the distance covered $s$ as $k=a{s}^2$ where $a$ is a constant. The force acting on the particle is

The magnitude of the displacement of a particle moving in a circle of radius $a$ with constant angular speed $\omega$ varies with time $t$ as

Two charged conducting
spheres of radii a and b are connected to each other by
a wire. What is the ratio of electric fields at the surfaces of the
two spheres? Use the result obtained to explain why charge density on
the sharp and pointed ends of a conductor is higher than on its
flatter portions.

1. 2.5

In
a certain region of space, electric field is along the z-direction
throughout. The magnitude of electric field is, however, not constant
but increases uniformly along the positive z-direction,
at the rate of 10⁵
NC⁻¹
per metre. What are the force and torque experienced by a system
having a total dipole moment equal to 10⁻⁷
Cm in the negative z-direction?

A quarter circular conducting ring of radius $r$ is rotating at angular velocity $\omega$ in uniform magnetic field as shown in figure.
EMF induced across the ring is