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In a diffraction pattern due to a single slit of width a, the first minimum is observed at an angle ${30}^{\circ }$ when light of wavelength $5000\stackrel{\circ }{A}$ is incident on the slit. The first secondary maximum is observed at an angle of

A
plane is in level flight at constant speed and each of its two wings
has an area of 25 m².
If the speed of the air is 180 km/h over the lower wing and 234 km/h
over the upper wing surface, determine the plane’s mass. (Take
air density to be 1 kg m^–3).

Assuming that light of wavelength $6000\mathring{\text{A}}$ is coming from a star. What is the limit of resolution of a telescope whose objective has diameter of $122\text{cm}?$

If surface area of a cube is changing at a rate of $5m^2/s$ , find the rate at which length of the body diagonal changes, at a moment when side length is $1m$.

The free end of a cantilever beam is supported by the free end of another cantilever beam using a roller as shown in the figure given below. What is the deflection at the roller support B?

The extra charge flowing through the cell on closing the key $k$ is equal to

Four charges $q_1=1\mu \text{C},q_2=2\mu \text{C},q_3=-3\mu \text{C}$ and $q_4=4\mu \text{C}$ are kept on the vertices of a square of side $1\text{m}$. Find the electric potential energy of this system of charges.

A massless spring $(K=800{\text{Nm}}^{-1}),$ attached with a mass $\left(500\text{g}\right)$ is completely immersed in $1\text{kg}$ of water. The spring is stretched by $2\text{cm}$ and released so that it starts vibrating. What would be the order of magnitude of the change in the temperature of water when the vibrations stop completely?

(Assume that the water container and spring receive negligible heat and specific heat of mass $=400{\text{J kg}}^{-1}{\text{K}}^{-1},$ specific heat of water $=4184{\text{J kg}}^{-1}{\text{K}}^{-1})$

The speed at which the image of a luminous point object is moving, if the luminous point object is moving at speed $v_0$ towards a spherical mirror, along its axis is:

(Given, $R=$ radius of curvature & $u=$ object distance)

The middle point of conductor is earthed and its ends are maintained at a potential difference of 220 V . What is the potential at the two ends and at the mid point??

An object $O$ is moving with velocity of $(\hat{i}+2\hat{j}+3\hat{k})\text{m/s}$ and a plane mirror in $yz$ plane facing the object is moving with velocity of $\left(2\hat{i}\right)\text{m/s}$. The velocity of the image with respect to ground (in SI units) will be

x logx

Match Column - $\text{I}$ with Column -$\text{II}$
$\begin{array}{cc}\text{Column - I}& \text{Column - II}\\ \text{i.Velocity of a particle following}& \text{(p)}\alpha \\ \text{equation}x=u(t-8)+\alpha (t-2{)}^2& \\ \text{at}t=0& \\ \text{ii.Acceleration of a particle moving according to equation}& \text{(q)}2\alpha \\ x=u(t-8)+\alpha (t-2{)}^2\text{at}t=0& \\ \text{iii.Velocity of the particle moving}& \text{(r) u}\\ \text{according to equation}x=ut+& \\ 5\alpha t^2\ln (1+\frac{t}{2})+\alpha t^2\text{at}t=0& \\ \text{iv.Acceleration of the particle moving}& \text{(s)}u-4\alpha \\ \text{according to the equation}x=ut+& \\ 5\alpha t^2(1+\frac{t}{2})+\alpha t^2\text{at}t=0& \end{array}$

Figure shows two conducting thin concentric shells of radii $r$ and $3r$. The outer shell carries a charge $q$ and the inner shell is neutral. The charge that will flow from inner shell to earth after the switch $S$ is closed is

The equation of projectile is $y=16x-\frac{5x^2}{4}$. The horizontal range is-

Is
it necessary for a transmitting antenna to be at the same height
as that of the receiving antenna for line-of-sight communication? A
TV transmitting antenna is 81m tall. How much service area can it
cover if the receiving antenna is at the ground level?

Find the workdone by the battery when switch ${\text{S}}_n$ is closed as shown in figure.

What is the average translational kinetic energy of a gas molecule at $500\text{K}$?

In the ideal inductor circuit shown, $\text{X}$ is joined to $\text{Y}$ for a long time, and then $\text{X}$ is joined to $\text{Z}$. The total heat produced in $R_2$ is:

A hollow sphere of radius $2\text{m}$ is projected horizontally along a rough surface with velocity $v_0$ and angular velocity ${\omega }_0$. Find out their ratio so that the sphere stops moving after some time.

Difference in heights between the liquid columns in the vertical limbs of an accelerated $U$-tube as shown in the figure is:

[Take $g=10{\text{m/s}}^2$]

A swimmer wishes to cross a $800\text{m}$ wide river flowing at $6\text{km/hr}$. His speed with respect to water is $4\text{km/hr}$. He crosses the river in shortest possible time. He is drifted downstream on reaching the other bank by a distance of

Figure shows a cross section of a large metal sheet carrying an electric current along its surface as shown in the figure. The current in a strip of width $dl$ is $kdl$, where $k$ is a constant. The magnetic field at a point $\text{P}$ distance $y$ from the metal sheet will be

A force is acting on a body of mass $3\text{kg}$ kept on a rough horizontal surface. If a friction force of $40\text{N}$ is required to keep the body at rest under the action of this external force. Then find the contact force acting on the body. $(g=10{\text{m/s}}^2)$

Five identical plates, each of area A are arranged such that adjacent plates are at a distance d apart and are numbered as 1, 2, 3, 4 and 5 from left to right. The plates are connected to a battery of voltage V as shown in figure If $Q_1$ is the charge on the plate 1 and $Q_4$ on plate 4, then,

1. 11.4285

A particle of mass $m$ is projected vertically upwards from point $\Delta$ on the ground. The ratio of potential energy at point $A$ and potential energy at $B$ is