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 :

An electron is projected with uniform velocity along the axis inside a current carrying long solenoid. Then :

A metal wire of uniform mass density having length $$L$$ and mass $$M$$ is bent to form a semicircular arc and a particle of mass $$\mathrm{m}$$ is placed at the centre of the arc. The gravitational force on the particle by the wire is :

An effective power of a combination of 5 identical convex lenses which are kept in contact along the principal axis is $$25 \mathrm{D}$$. Focal length of each of the convex lens is:

Given below are two statements :

Statement I : When speed of liquid is zero everywhere, pressure difference at any two points depends on equation $$\mathrm{P}_1-\mathrm{P}_2=\rho g\left(\mathrm{~h}_2-\mathrm{h}_1\right)$$.

Statement II : In ventury tube shown $$2 \mathrm{gh}=v_1^2-v_2^2$$

In the light of the above statements, choose the most appropriate answer from the options given below.

If a rubber ball falls from a height $$h$$ and rebounds upto the height of $$h / 2$$. The percentage loss of total energy of the initial system as well as velocity ball before it strikes the ground, respectively, are :

In an ac circuit, the instantaneous current is zero, when the instantaneous voltage is maximum. In this case, the source may be connected to :

A. pure inductor.

B. pure capacitor.

C. pure resistor.

D. combination of an inductor and capacitor.

Choose the correct answer from the options given below :

Which of the following nuclear fragments corresponding to nuclear fission between neutron $$\left({ }_0^1 \mathrm{n}\right)$$ and uranium isotope $$\left({ }_{92}^{235} \mathrm{U}\right)$$ is correct :

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 :

In an experiment to measure focal length ($$f$$) of convex lens, the least counts of the measuring scales for the position of object (u) and for the position of image (v) are $$\Delta u$$ and $$\Delta v$$, respectively. The error in the measurement of the focal length of the convex lens 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 equation of stationary wave is :

$$y=2 \mathrm{a} \sin \left(\frac{2 \pi \mathrm{nt}}{\lambda}\right) \cos \left(\frac{2 \pi x}{\lambda}\right) \text {. }$$

Which of the following is NOT correct :

Which figure shows the correct variation of applied potential difference (V) with photoelectric current (I) at two different intensities of light $$(\mathrm{I}_1<\mathrm{I}_2)$$ of same wavelengths :

P-T diagram of an ideal gas having three different densities $$\rho_1, \rho_2, \rho_3$$ (in three different cases) is shown in the figure. Which of the following is correct :

The electric field in an electromagnetic wave is given by $$\overrightarrow{\mathrm{E}}=\hat{i} 40 \cos \omega(\mathrm{t}-z / \mathrm{c}) \mathrm{NC}^{-1}$$. The magnetic field induction of this wave is (in SI unit) :

The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are $$8 \Omega$$ and $$10 \Omega$$ respectively. After inserting in a hot bath of temperature $$400^{\circ} \mathrm{C}$$, the resistance of platinum wire is :

The value of net resistance of the network as shown in the given figure is :

A wooden block, initially at rest on the ground, is pushed by a force which increases linearly with time $$t$$. Which of the following curve best describes acceleration of the block with time :

To measure the internal resistance of a battery, potentiometer is used. For $$R=10 \Omega$$, the balance point is observed at $$l=500 \mathrm{~cm}$$ and for $$\mathrm{R}=1 \Omega$$ the balance point is observed at $$l=400 \mathrm{~cm}$$. The internal resistance of the battery is approximately :

On celcius scale the temperature of body increases by $$40^{\circ} \mathrm{C}$$. The increase in temperature on Fahrenheit scale is :

A solid sphere and a hollow cylinder roll up without slipping on same inclined plane with same initial speed $$v$$. The sphere and the cylinder reaches upto maximum heights $$h_1$$ and $$h_2$$ respectively, above the initial level. The ratio $$h_1: h_2$$ is $$\frac{n}{10}$$. The value of $$n$$ is __________.

An infinite plane sheet of charge having uniform surface charge density $$+\sigma_{\mathrm{s}} \mathrm{C} / \mathrm{m}^2$$ is placed on $$x$$-$$y$$ plane. Another infinitely long line charge having uniform linear charge density $$+\lambda_e \mathrm{C} / \mathrm{m}$$ is placed at $$z=4 \mathrm{~m}$$ plane and parallel to $$y$$-axis. If the magnitude values $$\left|\sigma_{\mathrm{s}}\right|=2\left|\lambda_{\mathrm{e}}\right|$$ then at point $$(0,0,2)$$, the ratio of magnitudes of electric field values due to sheet charge to that of line charge is $$\pi \sqrt{n}: 1$$. The value of $$n$$ is _________.

A hydrogen atom changes its state from $$n=3$$ to $$n=2$$. Due to recoil, the percentage change in the wave length of emitted light is approximately $$1 \times 10^{-n}$$. The value of $$n$$ is _______.

[Given Rhc $$=13.6 \mathrm{~eV}, \mathrm{hc}=1242 \mathrm{~eV} \mathrm{~nm}, \mathrm{h}=6.6 \times 10^{-34} \mathrm{~J} \mathrm{~s}$$ mass of the hydrogenatom $$=1.6 \times 10^{-27} \mathrm{~kg}$$]

A soap bubble is blown to a diameter of $$7 \mathrm{~cm}$$. $$36960 \mathrm{~erg}$$ of work is done in blowing it further. If surface tension of soap solution is 40 dyne/$$\mathrm{cm}$$ then the new radius is ________ cm Take $$(\pi=\frac{22}{7})$$.

An elastic spring under tension of $$3 \mathrm{~N}$$ has a length $$a$$. Its length is $$b$$ under tension $$2 \mathrm{~N}$$. For its length $$(3 a-2 b)$$, the value of tension will be _______ N.

The magnetic field existing in a region is given by $$\vec{B}=0.2(1+2 x) \hat{k}$$. A square loop of edge $$50 \mathrm{~cm}$$ carrying 0.5 A current is placed in $$x$$-$$y$$ plane with its edges parallel to the $$x$$-$$y$$ axes, as shown in figure. The magnitude of the net magnetic force experienced by the loop is _________ $$\mathrm{mN}$$.

Two forces $$\overline{\mathrm{F}}_1$$ and $$\overline{\mathrm{F}}_2$$ are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between $$\vec{F}_1$$ and $$\vec{F}_2$$ is $$\cos ^{-1}\left(\frac{1}{n}\right)$$. The value of $$|n|$$ is _______.

A alternating current at any instant is given by $$i=[6+\sqrt{56} \sin (100 \pi t+\pi / 3)]$$ A. The $$r m s$$ value of the current is ______ A.

Twelve wires each having resistance $$2 \Omega$$ are joined to form a cube. A battery of $$6 \mathrm{~V}$$ emf is joined across point $$a$$ and $$c$$. The voltage difference between $$e$$ and $$f$$ is ________ V.

Two wavelengths $$\lambda_1$$ and $$\lambda_2$$ are used in Young's double slit experiment. $$\lambda_1=450 \mathrm{~nm}$$ and $$\lambda_2=650 \mathrm{~nm}$$. The minimum order of fringe produced by $$\lambda_2$$ which overlaps with the fringe produced by $$\lambda_1$$ is $$n$$. The value of $$n$$ is _______.