As per the given figure, two blocks each of mass \(250\,g\) are connected to a spring of spring constant \(2\,Nm ^{-1}\). If both are given velocity \(V\) in opposite directions, then maximum elongation of the spring is:

A uniform rod of mass 250 g having length 100 cm is balanced on a sharp edge at 40 cm mark. A mass of 400 g is suspended at 10 cm mark. To maintain the balance of the rod, the mass to be suspended at 90 cm mark, is

Consider a circular loop that is uniformly charged and has a radius \(\mathrm{a} \sqrt{2}\). Find the position along the positive z -axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in xy-plane at the origin :

A current of \(2\, mA\) was passed through an unknown resistor which dissipated a power of \(4.4\, W\). Dissipated power when an ideal power supply of \(11\, V\) is connected across it is

A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle \(60^o\) with ground level. But he finds the aeroplane right vertically above his position. If \(\upsilon \) is the speed of sound, speed of the plane is

A particle starts with an initial velocity of \(10.0\,ms ^{-1}\) along \(x\)-direction and accelerates uniformly at the rate of \(2.0\,ms ^{-2}\). The time taken by the particle to reach the velocity of \(60.0\,ms ^{-1}\) is \(.......\,s\)

A Laser light of wavelength \(660\,nm\) is used to weld Retina detachment. If a Laser pulse of width \(60\, ms\) and power \(0.5\, kW\) is used the approximate number of photons in the pulse are : [Take Planck's constant \(h\, = 6.62\times10^{- 34}\, Js\)]

A deuteron and a proton moving with equal kinetic energy enter into to a uniform magnetic field at right angle to the field. If \(r_{d}\) and \(r_{p}\) are the radii of their circular paths respectively, then the ratio \(\frac{r_{d}}{r_{p}}\) will be \(\sqrt{ x }: 1\) where \(x\) is ..........

Consider an electrical circuit containing a two way switch \(^{\prime}{S}^{\prime}\). Initially \({S}\) is open and then \({T}_{1}\) is connected to \({T}_{2} .\) As the current in \({R}=6 \,\Omega\) attains a maximum value of steady state level, \({T}_{1}\) is disconnected from \({T}_{2}\) and immediately connected to \({T}_{3} .\) Potential drop across \({r}=3\, \Omega\) resistor immediately after \(T_{1}\) is connected to \(T_{3}\) is \(....\,V.\) (Round off to the Nearest Integer)

Match List-I with List-II.

List-I	List-II
A. Meter (L)	I. \(\sqrt{\dfrac{hc}{G}}\)
B. Second (S)	II. \(\sqrt{\dfrac{Gh}{c^5}}\)
C. Kilogram (M)	III. \(\sqrt{\dfrac{K^2L^2c^3}{Gh}}\)
D. Kelvin (K)	IV. \(\sqrt{\dfrac{Gh}{c^3}}\)

where \(h\) (Planck's constant), \(G\) (gravitational constant) and \(c\) (speed of light in vacuum) as fundamental units.
Choose the correct answer from the options given below :

In the figure shown below, a resistance of \(150.4 \Omega\) is connected in series to an ammeter A of resistance \(240 \Omega\). A shunt resistance of \(10 \Omega\) is connected in parallel with the ammeter. The reading of the ammeter is _____ mA.

Two beams of light having intensities \(I\) and \(4\,I\) interfere to produce a fringe pattern on a screen. The phase difference between the two beams are \(\pi / 2\) and \(\pi / 3\) at points \(A\) and \(B\) respectively. The difference between the resultant intensities at the two points is \(x I\). The value of \(x\) will be.

The ratio of speeds of electromagnetic waves in vacuum and a medium, having dielectric constant k=3 and permeability \(\mu=2\mu_{0}\), is
( \(\mu_0=\) permeability of vacuum)