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In a single slit diffraction experiment, light of wavelength $\lambda$ passes through a slit of width $a$ and produces a diffraction pattern with $I_0$ as the intensity of the central maximum.

Find the ratio of intensity at a point midway between second and third minima to the intensity at the central maxima.

1. 1.15

Three identical cars A, B and C are moving at the same speed on three bridges. The car A goes on a plane bridge, B on a bridge convex upward and C goes on a bridge concave upward. Let $F_A,F_{B}and{F}_C$ be the normal forces exerted by the cars on the bridges when they are at the middle of bridges.

The current density across a cylindrical conductor of radius $R$ varies according to the equation $J=J_0(1-\frac{r}{R}),$ where $r$ is the distance from the axis. Thus, the current density is a maximum $J_0$ at the axis $r=0$ and decreases linearly to zero at the surface $r=R$. Calculate the current, $I$ in terms of $J_0$ if the conductor's cross sectional area is $A=\pi R^2$.

The path of a projectile is given by $y=ax-b{x}^2$. What is the value of the angle ${\theta }_0$ and speed $v_0$ , about a point at which the projectile is launched?

What is the minimum speed I need to cross the river which is flowing in the west direction at 3 Km/hr? Be aware of the crocodiles.

A rocket of mass $40\text{kg}$ has $160\text{kg}$ fuel. The exhaust velocity of the fuel is $2\text{km/s}$. The rate of consumption of fuel is $4\text{kg/s}$. Calculate the ultimate vertical speed gained by the rocket. Assume that value of $g$ does not vary.

$(g=10{\text{m/s}}^2\text{and}\ln 5=1.609)$

A particle is projected with a velocity v so that its horizontal range twice the greatest height attained. The horizontal range is:

A solid cylinder wire of radius $R$ carries a current $I$. The magnetic field is $5\mu \text{T}$ at a point, which is $2R$ distance away from the axis of wire. Magnetic field at a point which is $\frac{R}{3}$ distance inside from the surface of the wire is

The driver of a car travelling at velocity $v$ suddenly see a broad wall in front of him at a distance $d$. He should

A solid circular rod AB of diameter D and length L is fixed at both ends.A torque T is applied at a section x such that AX=$\frac{L}{4}andBX=\frac{3L}{4}$What is the maximum shear stress developed in $\frac{L}{4}andBX=\frac{3L}{4}$ the rod?

There are two bodies of different masses of 2 kg and 4 kg moving with velocities 10m/s and 2 m/s towards each other due to mutual gravitational attraction. What is the velocity of their centre of mass?

The acceleration due to gravity at a height $1\text{km}$ above the earth's surface is the same as at a depth $d$ below the surface of earth. Then

If the system shown in the figure is at rest, find the value of $m$

A
man can swim with a speed of 4.0 km/h in still water. How long does
he take to cross a river 1.0 km wide if the river flows steadily at
3.0 km/h and he makes his strokes normal to the river current? How
far down the river does he go when he reaches the other bank?

The angle between the dipole moment and electric field at any point on the equatorial plane is

Figure shows a charge $+Q$ clamped at a point in free space. From a large distance another charge particle of charge $-q$ and mass of $m$ is thrown towards $+Q$ with an impact parameter $d$ as shown with speed $v$. How many positions for minimum separation would be attained for the particle.

A proton and an electron are accelerated by the same potential difference. Let${\lambda }_e$ and ${\lambda }_p$ denote the de Broglie wavelengths of the electron and the proton respectively.

A load of 4 kg is suspended from a ceiling through a steel wire of length 20 m and radius 2 mm. It is found that the length of the wire increases by 0.031 mm, as equilibrium is achieved. If g = 3.1 $\times \pi m{s}^{-2}$ the value of

Young’s modulus is

Vector $A$ and $B$ are as shown in the figure having magnitude of $2$ units each. Find $\overrightarrow{A}+\overrightarrow{B}$.

Which one of the following is smallest in size ?

The intensity of passive earth pressure at a depth of 5 m in a cohesion less soil with an angle of internal friction of ${30}^{\circ }$ when water rises to ground level is $kN/m^2$. Take saturated unit weight of sand as $21kN/m^3$and ${\gamma }_w=9.81kN/m^3$.

1. 216.9

The range of a particle when launched at an angle of ${15}^{\circ }$ with the horizontal is $1.5\text{km}$. What is the range of the projectile when launched at an angle of ${45}^{\circ }$ to the horizontal ?

Two blocks $A$ and $B$ of masses $6\text{kg}$ and $3\text{kg}$ rest on a smooth horizontal surface as shown in the figure. If coefficient of friction between $A$ and $B$ is $0.4$, find the maximum horizontal force which can make them move without separation. (Take $g=10m/s^2$)

There is some change in length when a $33,000\text{N}$ tensile force is applied on a steel rod of area of cross-section ${10}^{-3}{\text{m}}^2$. The change of temperature required to produce the same elongation, if the steel rod is heated, is -

[Take modulus of elasticity $Y=3\times {10}^{11}{\text{N/m}}^2$ and the coefficient of linear expansion of steel is $\alpha =1.1\times {10}^{-5}{/}^{\circ }\text{C}$]

The momentum p of a particle changes with time t according to the relation $\frac{dp}{dt}$ = (10 N) + $\left(2\frac{N}{s}\right)$t. If the momentum is zero at t= 0, what will the momentum be at t = 10 s?

An electron having charge $1.6\times {10}^{-19}\text{C}$ and mass $9\times {10}^{-31}\text{kg}$ is moving in a circular orbit with a speed of $4\times {10}^6{\text{ms}}^{-1}$ in a magnetic field of $2\times {10}^{-1}\text{T}.$ The force acting on electron and the radius of the circular orbit will be:-