Two equal resistances when connected in series to a battery, consume electric power of 60 W. If these resistances are now connected in parallel combination to the same battery, the electric power consumed will be:
(1) 60 W
(2) 240 W
(3) 120 W
(4) 30 W

An ideal battery of emf $4 V$ and resistance $R$ are connected in series in the primary circuit of a potentiometer of length $1 m$ and resistance $5 \Omega$. The value of $R$, to give a potential difference of $5 m \mathrm {~V}$ across $10 c m$ of potentiometer wire, is:
(1) $480 \Omega$
(2) $495 \Omega$
(3) $395 \Omega$
(4) $490 \Omega$

A moving coil galvanometer allows a full scale current of $10 ^ { - 4 } \mathrm {~A}$. A series resistance of $2 \times 10 ^ { 4 } \Omega$ is required to convert the galvanometer into a voltmeter of range $0 - 5 \mathrm {~V}$. Therefore, the value of shunt resistance required to convert the above galvanometer into an ammeter of range $0 - 10 \mathrm {~mA}$ is:
(1) $100 \Omega$
(2) $200 \Omega$
(3) $300 \Omega$
(4) $10 \Omega$

In a Wheatstone bridge (see fig.), Resistances $P$ and $Q$ are approximately equal. When $R = 400 \Omega$, the bridge is balanced. On interchanging P and Q, the value of R, for balance, is $405 \Omega$. The value of $Y$ is close to
(1) 401.5 ohm
(2) 404.5 ohm
(3) 403.5 ohm
(4) 402.5 ohm

Two electric bulbs, rated at $( 25 \mathrm {~W} , 220 \mathrm {~V} )$ and $( 100 \mathrm {~W} , 220 \mathrm {~V} )$, are connected in series across a 220 V voltage source. If the 25 W and 100 W bulbs draw powers $P _ { 1 }$ and $P _ { 2 }$ respectively, then:
(1) $P _ { 1 } = 4 \mathrm {~W} , P _ { 2 } = 16 \mathrm {~W}$
(2) $P _ { 1 } = 9 \mathrm {~W} , P _ { 2 } = 16 \mathrm {~W}$
(3) $P _ { 1 } = 16 \mathrm {~W} , P _ { 2 } = 9 \mathrm {~W}$
(4) $P _ { 1 } = 16 \mathrm {~W} , P _ { 2 } = 4 \mathrm {~W}$

In an experiment, electrons are accelerated, from rest, by applying a voltage of 500 V. Calculate the radius of the path if a magnetic field 100 mT is then applied. [Charge of the electron $= 1.6 \times 10 ^ { - 19 } \mathrm { C }$, Mass of the electron $= 9.1 \times 10 ^ { - 31 } \mathrm {~kg}$]
(1) $7.5 \times 10 ^ { - 3 } \mathrm {~m}$
(2) $7.5 \times 10 ^ { - 2 } \mathrm {~m}$
(3) 7.5 m
(4) $7.5 \times 10 ^ { - 4 } \mathrm {~m}$

A proton and an $\alpha$-particle (with their masses in the ratio of $1 : 4$ and charges in the ratio of $1 : 2$) are accelerated from rest through a potential difference $V$. If a uniform magnetic field $(B)$ is set up perpendicular to their velocities, the ratio of the radii $r _ { p } : r _ { \alpha }$ of the circular paths described by them will be:
(1) $1 : 3$
(2) $1 : \sqrt { 2 }$
(3) $1 : 2$
(4) $1 : \sqrt { 3 }$

The resistive network shown below is connected to a D.C. source of 16 V. The power consumed by the network is 4 Watt. The value of R is:
(1) $16\,\Omega$
(2) $8\,\Omega$
(3) $6\,\Omega$
(4) $1\,\Omega$

Two wires $A$ \& $B$ are carrying currents $I _ { 1 }$ and $I _ { 2 }$ as shown in the figure. The separation between them is $d$. A third wire C carrying a current I is to be kept parallel to them at a distance $x$ from A such that the net force acting on it is zero. The possible values of $x$ are:
(1) $x = \pm \frac { \mathrm { I } _ { 1 } \mathrm {~d} } { \left( \mathrm { I } _ { 1 } - \mathrm { I } _ { 2 } \right) }$
(2) $x = \left( \frac { \mathrm { I } _ { 1 } } { \mathrm { I } _ { 1 } + \mathrm { I } _ { 2 } } \right) \mathrm { d }$ and $x = \frac { \mathrm { I } _ { 2 } } { \left( \mathrm { I } _ { 1 } - \mathrm { I } _ { 2 } \right) } \mathrm { d }$
(3) $x = \left( \frac { \mathrm { I } _ { 2 } } { \mathrm { I } _ { 1 } + \mathrm { I } _ { 2 } } \right) \mathrm { d }$ and $x = \left( \frac { \mathrm { I } _ { 2 } } { \mathrm { I } _ { 1 } - \mathrm { I } _ { 2 } } \right) \mathrm { d }$
(4) $x = \left( \frac { \mathrm { I } _ { 1 } } { \mathrm { I } _ { 1 } - \mathrm { I } _ { 2 } } \right) \mathrm { d }$ and $x = \frac { \mathrm { I } _ { 2 } } { \left( \mathrm { I } _ { 1 } + \mathrm { I } _ { 2 } \right) } \mathrm { d }$

In free space, a particle $A$ of charge $1 \mu \mathrm { C }$ is held fixed at point $P$. Another particle $B$ of the same charge and mass $4 \mu \mathrm {~g}$ is kept at a distance of 1 mm from $P$. If $B$ is released, then its velocity at a distance of 9 mm from $P$ is: [Take $\frac { 1 } { 4 \pi \epsilon _ { 0 } } = 9 \times 10 ^ { 9 } \mathrm {~N} \mathrm {~m} ^ { 2 } \mathrm { C } ^ { - 2 }$ ]
(1) $1.0 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(2) $1.5 \times 10 ^ { 2 } \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(3) $2.0 \times 10 ^ { 3 } \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(4) $3.0 \times 10 ^ { 4 } \mathrm {~m} \mathrm {~s} ^ { - 1 }$

There are two long co-axial solenoids of same length $l$. The inner and outer coils have radii $r _ { 1 }$ and $r _ { 2 }$ and number of turns per unit length $\mathrm { n } _ { 1 }$ and $\mathrm { n } _ { 2 }$, respectively. The ratio of mutual inductance to the self-inductance of the inner-coil is:
(1) $\frac { n _ { 1 } } { n _ { 2 } }$
(2) $\frac { n _ { 2 } } { n _ { 1 } } \cdot \frac { r _ { 1 } } { r _ { 2 } }$
(3) $\frac { n _ { 2 } } { n _ { 1 } } \cdot \frac { r _ { 2 } ^ { 2 } } { r _ { 1 } ^ { 2 } }$
(4) $\frac { n _ { 2 } } { n _ { 1 } }$

A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbits in a plane due to magnetic field perpendicular to the plane. Let $\mathrm { r } _ { \mathrm { p } } , \mathrm { r } _ { \mathrm { e } }$ and $\mathrm { r } _ { \mathrm { He } }$ be their respective radii, then,
(1) $r _ { e } > r _ { p } = r _ { H e }$
(2) $r _ { e } < r _ { p } = r _ { H e }$
(3) $\mathrm { r } _ { \mathrm { e } } < \mathrm { r } _ { \mathrm { p } } < \mathrm { r } _ { \mathrm { He } }$
(4) $r _ { e } > r _ { p } > r _ { H e }$

Space between two concentric conducting spheres of radii a and $\mathrm { b } ( \mathrm { b } > \mathrm { a } )$ is filled with a medium of resistivity $\rho$. The resistance between the two spheres will be:
(1) $\frac { \rho } { 4 \pi } \left( \frac { 1 } { a } + \frac { 1 } { b } \right)$
(2) $\frac { \rho } { 2 \pi } \left( \frac { 1 } { a } + \frac { 1 } { b } \right)$
(3) $\frac { \rho } { 4 \pi } \left( \frac { 1 } { a } - \frac { 1 } { b } \right)$
(4) $\frac { \rho } { 2 \pi } \left( \frac { 1 } { a } - \frac { 1 } { b } \right)$

A particle of mass $m$ and charge $q$ is in an electric and magnetic field given by $$\overrightarrow { \mathrm { E } } = 2 \hat { i } + 3 \hat { j } ; \overrightarrow { \mathrm { B } } = 4 \hat { j } + 6 \hat { k }$$ The charged particle is shifted from the origin to the point $\mathrm { P } ( x = 1 ; y = 1 )$ along a straight path. The magnitude of the total work done is:
(1) (0.35)q
(2) $5 q$
(3) $( 2.5 ) q$
(4) $( 0.15 ) q$

A transformer consisting of 300 turns in the primary and 150 turns in the secondary gives output power of 2.2 kW. If the current in the secondary coil is 10 A, then the input voltage and current in the primary coil are:
(1) 440 V and 20 A
(2) 220 V and 20 A
(3) 440 V and 5 A
(4) 220 V and 10 A

A square loop is carrying a steady current I and the magnitude of its magnetic dipole moment is m . If this square loop is changed to a circular loop and it carries the same current, the magnitude of the magnetic dipole moment of circular loop will be:
(1) $\frac { 4 m } { \pi }$
(2) $\frac { 3 m } { \pi }$
(3) $\frac { 2 m } { \pi }$
(4) $\frac { m } { \pi }$

The magnitude of the magnetic field at the centre of an equilateral triangular loop of side 1 m which is carrying a current of 10 A is: [Take $\mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm { NA } ^ { - 2 }$ ]
(1) $3 \mu \mathrm {~T}$
(2) $1 \mu \mathrm {~T}$
(3) $18 \mu \mathrm {~T}$
(4) $9 \mu \mathrm {~T}$

An object is at a distance of 20 m from a convex lens of focal length 0.3 m. The lens forms an image of the object. If the object moves away from the lens at a speed of $5 \mathrm {~m} / \mathrm { s }$ the speed and direction of the image will be
(1) $2.26 \times 10 ^ { - 3 } \mathrm {~m} / \mathrm { s }$ away from the lens
(2) $0.92 \times 10 ^ { - 3 } \mathrm {~m} / \mathrm { s }$ away from the lens
(3) $3.22 \times 10 ^ { - 3 } \mathrm {~m} / \mathrm { s }$ towards the lens
(4) $1.16 \times 10 ^ { - 3 } \mathrm {~m} / \mathrm { s }$ towards the lens

A coil of self inductance 10 mH and resistance of $0.1 \Omega$ is connected through a switch to a battery of internal resistance $0.9 \Omega$. After the switch is closed, the time taken for the current to attain $80\%$ of the saturation value is: $[\ln 5 = 1.6]$
(1) 0.103 s
(2) 0.002 s
(3) 0.324 s
(4) 0.016 s

The graph shows how the magnification $m$ produced by a thin lens varies with image distance $v$. The focal length of the lens used is
(1) $\frac { b } { c }$
(2) $\frac { a } { c }$
(3) $\frac { b ^ { 2 } c } { a }$
(4) $\frac { b ^ { 2 } } { a c }$

In a Young's double slit experiment, the path difference, at a certain point on the screen, between two interfering waves is $\frac { 1 } { 8 }$th of wavelength. The ratio of the intensity at this point to that at the centre of a bright fringe is close to:
(1) 0.74
(2) 0.85
(3) 0.94
(4) 0.8

A particle A of mass $m$ and charge $q$ is accelerated by a potential difference of 50 V. Another particle B of mass $4 m$ and charge $q$ is accelerated by a potential difference of 2500 V. The ratio of de-Broglie wavelengths $\frac { \lambda _ { A } } { \lambda _ { B } }$ is close to:
(1) 0.07
(2) 10.00
(3) 4.47
(4) 14.14

In a double-slit experiment, green light $( 5303 \mathrm {~\AA} )$ falls on a double slit having a separation of $19.44 \mu \mathrm {~m}$ and a width of $4.05 \mu \mathrm {~m}$. The number of bright fringes between the first and the second diffraction minima is
(1) 10
(2) 5
(3) 4
(4) 9

In a Young's double-slit experiment, the ratio of the slit's width is $4 : 1$. The ratio of the intensity of maxima to minima, close to the central fringe on the screen, will be
(1) $25 : 9$
(2) $9 : 1$
(3) $\left(\sqrt { 3 } + 1\right) ^ { 4 } : 16$
(4) $4 : 1$

If the deBroglie wavelength of an electron is equal to $10^{-3}$ times the wavelength of a photon of frequency $6 \times 10 ^ { 14 } \mathrm {~Hz}$, then the speed of electron is equal to: (Speed of light $= 3 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s }$, Planck's constant $= 6.63 \times 10 ^ { - 34 } \mathrm { J.s }$, Mass of electron $= 9.1 \times 10 ^ { - 31 } \mathrm {~kg}$)
(1) $1.1 \times 10 ^ { 6 } \mathrm {~m} / \mathrm { s }$
(2) $1.7 \times 10 ^ { 6 } \mathrm {~m} / \mathrm { s }$
(3) $1.8 \times 10 ^ { 6 } \mathrm {~m} / \mathrm { s }$
(4) $1.45 \times 10 ^ { 6 } \mathrm {~m} / \mathrm { s }$