Five charges $$+q,+5q,-2q,+3q$$ and $$-4q$$ are situated as shown in the figure. The electric flux due to this configuration through the surface $$S$$ is :

An infinitely long positively charged straight thread has a linear charge density $$\lambda {\mathrm{Cm}}^{-1}$$. An electron revolves along a circular path having axis along the length of the wire. The graph that correctly represents the variation of the kinetic energy of electron as a function of radius of circular path from the wire is :

A charge $$q$$ is placed at the center of one of the surface of a cube. The flux linked with the cube is:

Two charged conducting spheres of radii $$a$$ and $$b$$ are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:

In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of :

The vehicles carrying inflammable fluids usually have metallic chains touching the ground:

Two identical conducting spheres P and S with charge Q on each, repel each other with a force $$16\mathrm{N}$$. A third identical uncharged conducting sphere $$\mathrm{R}$$ is successively brought in contact with the two spheres. The new force of repulsion between $$\mathrm{P}$$ and $$\mathrm{S}$$ is :

$$\sigma$$ is the uniform surface charge density of a thin spherical shell of radius R. The electric field at any point on the surface of the spherical shell is :

Position of an ant ($$\mathrm{S}$$ in metres) moving in $$\mathrm{Y}$$-$$\mathrm{Z}$$ plane is given by $$S=2t^2\hat{j}+5\hat{k}$$ (where $$t$$ is in second). The magnitude and direction of velocity of the ant at $$\mathrm{t}=1\mathrm{s}$$ will be :

The co-ordinates of a particle moving in $$x$$-$$y$$ plane are given by : $$x=2+4\mathrm{t},y=3\mathrm{t}+8{\mathrm{t}}^2$$. The motion of the particle is :

The angle of projection for a projectile to have same horizontal range and maximum height is :

Train A is moving along two parallel rail tracks towards north with speed $$72\mathrm{km}/\mathrm{h}$$ and train B is moving towards south with speed $$108\mathrm{km}/\mathrm{h}$$. Velocity of train B with respect to A and velocity of ground with respect to B are (in $${\mathrm{ms}}^{-1}$$):

The relation between time '$$t$$' and distance '$$x$$' is $$t=\alpha x^2+\beta x$$, where $$\alpha$$ and $$\beta$$ are constants. The relation between acceleration $$(a)$$ and velocity $$(v)$$ is :

A body starts moving from rest with constant acceleration covers displacement $$S_1$$ in first $$(p-1)$$ seconds and $${\mathrm{S}}_2$$ in first $$p$$ seconds. The displacement $${\mathrm{S}}_1+{\mathrm{S}}_2$$ will be made in time :

A particle is moving in a straight line. The variation of position '$$x$$' as a function of time '$$t$$' is given as $$x=\left(t^3-6t^2+20t+15\right)m$$. The velocity of the body when its acceleration becomes zero is :

Two cars are travelling towards each other at speed of $$20\mathrm{m}{\mathrm{s}}^{-1}$$ each. When the cars are $$300\mathrm{m}$$ apart, both the drivers apply brakes and the cars retard at the rate of $$2\mathrm{m}{\mathrm{s}}^{-2}$$. The distance between them when they come to rest is :

A particle moving in a straight line covers half the distance with speed $$6\mathrm{m}/\mathrm{s}$$. The other half is covered in two equal time intervals with speeds $$9\mathrm{m}/\mathrm{s}$$ and $$15\mathrm{m}/\mathrm{s}$$ respectively. The average speed of the particle during the motion is :

A body travels $$102.5\mathrm{m}$$ in $${\mathrm{n}}^{\text{th }}$$ second and $$115.0\mathrm{m}$$ in $$(\mathrm{n}+2{)}^{\text{th }}$$ second. The acceleration is :

A body projected vertically upwards with a certain speed from the top of a tower reaches the ground in $$t_1$$. If it is projected vertically downwards from the same point with the same speed, it reaches the ground in $$t_2$$. Time required to reach the ground, if it is dropped from the top of the tower, is :

A train starting from rest first accelerates uniformly up to a speed of $$80\mathrm{km}/\mathrm{h}$$ for time $$t$$, then it moves with a constant speed for time $$3t$$. The average speed of the train for this duration of journey will be (in $$\mathrm{km}/\mathrm{h}$$) :