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38451.

How does nuclear radius of an atom depend on its mass number ?

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SOLUTION :`R=R_(0)A^(1//3)` or R is DIRECTLY proportional to A to the power of `(1)/(3)`
38452.

The optical density of turpentine is higher than that of water while its mass density is lower. Figure shows a layer of turpentine floating over water in a container. For which one of the four rays incident on turpentine in as figure, the path shown is correct?

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1
2
3
4

Solution :When a RAY of light enters turpentine from air, it bends towards normal (as it enters from rarer to DENSER medium) and then when it enters air from turpentine, it bends away from normal (as it enters from denser to rarer medium).
In the FIGURE, PATH of light ray no. 2 is correct as it follows the path in above manner.
38453.

Under certain circumstances, a nucleus can decay by emitting a particle more massive than alpha-particle. Consider the following decay processes: " "_(88)^(223)Ra to " "_(82)^(209)Pb + " "_(6)^(14)C " "_(88)^(223)Ra to " "_(86)^(219)Rn + " "_(2)^(4)He. Calculate the Q-values for these decays and determine that both are energetically allowed.

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Solution :For the first PROCESS `Q = [" "_(88)^(223)Ra - " "_(82)^(209)Pb - " "_(6)^(14)C] u= [223.01850 - 208.98107 - 14.00324] u = 0.03419 u = 0.03419 XX 931.5 MEV = 31.85 MeV`
For the second process, `Q = [ " "_(88)^(223)Ra - " "_(86)^(219)Rn- " "_(2)^(4)He ] u= [223.01850 - 219.00948 - 4.00260] u = 0.00642 u = 0.00642 xx 931.5 =5.98 MeV`
Both processes are energetically possible, because both are exothermic.
38454.

Assertion:The mass of beta-particles when they are emitted is higher than the mass of electrons obtained by other means. Reason:beta-particle and electron , both are similar particles.

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If both assertion and reason are true and reason is the correct explanation of assertion .
If both assertion and reason are true but reason is notthe correct explanation of assertion .
If assertion is true but reason is false .
If both assertion and reason are false

Solution :`BETA`-PARTICLES are EMITTED with very high velocity (upto 0.99 c). So, according to Einstein's theory of relatively , the mass of a `beta`-particle is much higher compared to its rest mass `(m_0)`. The velocity of electrons OBTAINED by other means is very small compared to c (velocity of light). So its mass remains NEARLY `m_0`.
38455.

The nucleus which has radius one-third of the radius of Os^(189) is

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A) `Be^9`
B) `Li^7`
C) `F^(19)`
D) `C^(12)`

ANSWER :B
38456.

The output from a LASER is monochromatic. It means that it is :

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directional
polarised
narrow beam
single frequency.

Answer :D
38457.

The energy of the hydrogen atom in its ground state is -13.6 eV. Determine the energy of the energy level whose quantum number is 2.

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Solution :Energy of hydrogen atom in NTH orbit is
`E=-(13.6)/(n^(2))EV`
For IST excited STATE, `n=2`
`E=-(13.6)/(4)=-3.4 eV`
38458.

(A) : If a galvanometer is converted into an ammeter and a milliammeter then the shunt resistance of ammeter is lower than that of milliammeter. (R) : In Ammeter the current through shunt is less than that o galvonameter.

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Both 'A' and 'R' are true and 'R' is the CORRECT explanation of 'A'.
Both 'A' and 'R' are true and 'R' is not the correct explanation of 'A'
'A' is true and 'R' is FALSE
'A' is false and 'R' is false

Answer :C
38459.

The B-H curves (a) and (b) drawn below are associated with :

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a diamagnetic and a ferromagnetic SUBSTANCE respectively
a PARAMAGNETIC and a ferromagnetic substance respectively
SOFT IRON and steel respectively
steel and soft iron respectively

Solution :`a to` for soft iron
`B to` for steel
38460.

The refractive index of a lens material is1.5 and focal length f. Due to some chemical changes in the material, its refractive index has increased by 2%. The percentage change in its focal length is

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`+4.5%`
`-4.5%`
`+5.6%`
`-5.67%`

ANSWER :D
38461.

A particle of charge q and mass m is projected with kinetic energy K. into the region between two plates of uniform magnetic field of induction B as shown. If the particle is to miss collision with opposite plate the maximum value of B is

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`( sqrt(2K ))/(qmd )`
`( sqrt(2KM))/( qd)`
`( sqrt(2Kd))/(qm)`
`( sqrt(2kq))/( MD)`

Answer :B
38462.

Two wires of equal diameters of resistivities p_1 and p_2 and length x_1 and x_2 respectively are joined in series. The equivalent resistivity of the combination is

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`(rho_(1)X_(1)+rho_(2)X_(2))/(X_(1)+X_(2))`
`(rho_(1)X_(2)+rho_(2)X_(1))/(X_(1)-X_(2))`
`(rho_(1)X_(2)+rho_(2)X_(1))/(X_(1)+X_(2))`
`(rho_(1)X_(1)+rho_(2)X_(2))/(X_(1)-X_(2))`

ANSWER :A
38463.

A long straight wire carries a current i. A particle having a positive charge q and mass m, kept at a distance x_0 from the wire is projected towards it with a speed v, as shown in Fig. Find the minimum separation between the wire and the particle.

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SOLUTION :`ln ""(x)/(x_0)= (-v)/(K) or x = x_(0E) (-v)/(k) = x_(0)e^((-2pimv)/(mu_0qi))`
38464.

At night the objects situated outside a brightly illuminated room are not visible through the glass windows. But if the Iights inside the room are off, external objects are visible. Explain the reason.

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SOLUTION :At night from external objects enters a room through glass windows. If the bulb glows INSIDE the room, reflected light from the glass window comes of the EYES of the observer. The intensity of this reflected lightis much greater than that of the light coming from outside. So, the external objects are not visible.
But if the room is MADE dark, the light coming from outside is sufficient to make the external objects visible.
38465.

You are supplied with a 1m long uniform resistance wire of resistance 3Ω and a cell of emf 1.5v.Can you construct a potentiometer using 1m wire? If no, give reason, if yes, what is the least count of the arrangement?

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SOLUTION :YES, LC is 1.5mV
38466.

यदि f(x) =F ax + b, जहाँ a तथा b पूर्णाक है तथा f(-1)=-5 तथा f(3)=3 हो, तो a तथा b का मान है

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a = - 3, B = - 1
a = 2, b = -3
a = 0, b = 2
a=2,b=3

Answer :B
38467.

b.A convex mirror always produces a virtual image independent of the location of the object.

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Solution :b.For a convex mirror,
`(1)/(v) = (1)/(F) - (1)/(u) ` where f `GT` 0 and u `lt`, so .v. is always positive i.e, image LIES on the right side of the mirror and VIRTUAL .
38468.

Identify the parts X and Y in the block diagram of a generalised communication system

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INFORMATION SOURCE, transducer
Information source, communication channel
Communication channel, information source
Transducer, information source

ANSWER :B
38469.

Two metal plates form a parallel plate capacitor.The distance between the plates is d. A metal sheet of thickness d/2 and of the same area is introduced between the plates. What is the ratio of the capacitances in the two cases ?

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`4:1`
`2:1`
`3:1`
`5:1`

ANSWER :B
38470.

When a proton is released from rest in a room, it starts with an initial acceleration a0 towards west. When it is projected towards north with a speed v_(0) it moves with an initial acceleration 3a_(0) towards west. The electric and magnetic fields in the room are respectively.

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`(ma_(0))/(E)"west",(2ma_(0))/(ev_(0))"down"`
`(ma_(0))/(e)"EAST",(3ma_(0))/(ev_(0))"up"`
`(ma_(0))/(e)"east",(3ma_(0))/(ev_(0))"down"`
`(ma_(0))/(e)"west",(2ma_(0))/(ev_(0))"up"`

Answer :A
38471.

During emission of a negative beta - particle

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an electron from the atom is emitted
an electron already present inside the nucleus is emitted
an electron is emitted DUE to DISINTEGRATION of a NEUTRON inside of nucleus.
a PART of nuclear binding energy is converted into an electron .

Answer :C
38472.

A : Torque on the coil is the maximum, when coil is suspended in a radial magnetic field. R : The torque tends to rotate the coil on its own axis.

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ASSERTION is true, reason is true and reason is the correct explanation for assertion.
Assertion is true, reason is true but reason is not the correct explanation for assertion.
Assertion is true, reason is FALSE.
Assertion is false, reason is true.

Solution :The torque ACTING on CURRENT carrying coil which is surpended in a MAGNETIC field is `tau=nIBAsintheta`, now due to radial magnetic field the deflection of coil at any position is `theta=90^(@)`, so torque is maximum and hence assertion is true and reason is true but reason is not the correct explanation for assertion.
38473.

The electric field due to an electric dipole at a distance from its centre position is E. If the dipole is rotated through an angle of 90^(@) about its perpendicular aixs, electric field at the same point will be

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E
E/4
E/2
2E

Answer :C
38474.

A conducting sphere of radius 10 cm has an unknown charge if the electricfield 20 cm from the centre of the sphere is 1.5 xx10^(3)N/Cand pointsradialy inward whatis the net charge on the sphere

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Solution :Electric field at a point OUTSIDE the charged sphere of radius R is,
`E_(0) = (kq)/(r^(2))` (where `r gt R`)
`therefore q = (E_(0) xx r^(2))/(K)`
`=(-1.5 xx 10^(3) xx (0.2)^(2))/(9 xx 10^(9))`
`therefore q = -6.667 xx 10^(-9)` C
(Here `E_(0)`point is radially inward and so it is taken as negative)
38475.

Charge of a circular ring of radius 20 cm is 100muC. Calculate the electric field intensity at distance (i) 5 cm and (ii) 5 m away from the centre of the ring along the axis.

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ANSWER :`3.2xx10^(7)N//C; 3.6xx10^(4)N//C`
38476.

A piece of copper and another of germanium are cooled from room temperature to 80 K. The resistance of

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each of them INCREASES
each of them DECREASES
COPPER increases and GERMANIUM decreases
copper decreases and germanium increases.

Answer :D
38477.

पृथ्वी सम्मेलन किस देश में आयोजित किया गया था?

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अमेरिका
भारत
जापान
ब्राजील

Answer :D
38478.

A Ship 'A' steams down north a speed of 8 kmph. andship B due west at a speed of 6 kmph. The velocity of A w.r.t. B is .

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10 KMPH, `Tan ^(-1)(4/3)N ` of E
10 kmph, `tan^(-1) (4/3) E`of N
10 kmph NE
2 kmph, `Tan^(-1) (4/3) N ` of E

ANSWER :A
38479.

फलक केंद्रित इकाई कोशिका में संकुलन दक्षता होती

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52
68
74
इनमें से कोई नहीं

Answer :B
38480.

A thin circular ring of mass M and radius R is rotating about its central axis with angular velocity omega. Four point objects each of mass m are attached gently to the opposite ends of two perpendicular diameters, the angular velocity of the ring is given by :

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`(M)/(M+m).omega`
`(M)/(M+4m).omega`
`(M+4m)/(M).omega`
`(M-4m)/(M+4m).omega`

Solution :`I_(1)omega_(1)=I_(2)omega_(2)IMPLIES MR^(2)omega=(M+4m)R^(2)omega_(2)`
implies `omega_(2)=(Momega)/(M+4m)`
38481.

In a Huygen's eye piece, the eyelens has a focal length of 'f'. The equivalent focal length of eyepiece is

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3/4 f
4f
3/2f
2f

Answer :C
38482.

If the collector current changes from 2mA to 3mA in a transistor, when collector-emitter voltage is increased from 2 to 10V, then the output resistance of the transistor is

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`2 K OMEGA `
`4 l Omega `
`6 k Omega `
`8 k Omega `

Answer :D
38483.

The magnetic field in a plane electromagnetic wave is given by B_(y)=(2xx10^(-7)) T sin (0.5xx10^(3)x+1.5xx10^(11)t). What is the wavelength and frequency of the wave?

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Solution :COMPARING the given equation with
`B_(y) = B_(o) SIN [2 pi ((x)/(lamda)+(t)/(T))]`
We get, `lamda =(2 pi)/(0.5xx10^(3)) m=1.26 cm, and (1)/(T) =v= (1.5xx10^(11))//2pi =23.9 GHz`
38484.

A battery of emf 10 V and internal resistance 3Omega is connected to a resistor. If the current in the circuit is 0.5 A, what is the resistance of the resistor? What is the terminal voltage of the battery when the circuit is closed?

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SOLUTION :`17 OMEGA , 8.5 Omega`
38485.

A convex mirror of focal length f produces image 1/n th of the size of the object. The distance of the object from the mirror is :

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(N - 1) F
`((n-1)/n) f `
`((n+1)/n)f`
(n+1)f

Answer :A
38486.

An iron core solenoid has self-inductance 2.8 H. When the core is removed, the self-inductance becomes 2 mH. What is the relative permeability of the core used ?

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Solution :Relative PERMEABILITY of iron core `mu_(r) = ("Self-inductance of SOLENOID with iron core")/("Self-inductance of solenoid without iron core")`
`(2.8 H)/(2mH) = (2.8H)/(2 xx 10^(-3)H)=1400`
38487.

A magnetic field in a certain region is given by barB = (40hati - 18hatk)G. How much flux passes through a 5.0 cm^(2) area loop if the loop lies flat on xy - plane ?

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- 900 nwb
- 700 nwb
- 200 nwb
- 800 nwb

Answer :A
38488.

An LCR series circuit with 100 Omegaresistance is connected to an ac source of 200 V and angular frequency 300 rad/s. When only the capacitance is removed, the current lags behind the voltage by 60^@. When only the inductance is removed, the current leads the voltage by 60^@. Impedance of the LCR circuit is

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`200 OMEGA`
`175Omega`
`150 Omega`
`100 Omega`

ANSWER :D
38489.

Two balls roll towards each other. The red ball has a mass kg 0.5 kg and a speed of 4 m/s just before impact. The green ball has a mass of 0.3 kg and a speed of 2m/s. after the head-on collision, the red ball continues forward with a speed of 2m/s. find the speed of the green ball after the collision. was the collision elastic?

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Solution :First remember that MOMENTUM is a vector quantity, so the direction of the velocity is crucial. Since the balls roll TOWARD each other, one ball has a positive velocity while the other has a negative velocity. Let's call the red ball's velocity before the collision positive, then `v_(red)=+4m//s, and v_("green")=-2m//s.` using a PRIME (') to denote after the collision, CONSERVATION of linear momentum GIVES us the following:
total `p_("before")=`total `p_("after")`
`m_(red)v_(red)+m_("green")v_("green")=m_(red)v_(red)'+m_("green")v_("green")'`
`(0.5)(+4)+(0.3)(-2)=(0.5)(+2)+(0.3)v_("green")'`
`v_("green")'=+1.3m//s`
38490.

An LCR series circuit with 100 Omegaresistance is connected to an ac source of 200 V and angular frequency 300 rad/s. When only the capacitance is removed, the current lags behind the voltage by 60^@. When only the inductance is removed, the current leads the voltage by 60^@. when inductor is removed , capacitive reactance of the circuit is

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`sqrt3xx50 OMEGA`
`100sqrt3Omega`
`50 sqrt3Omega`
`20 sqrt2Omega`

ANSWER :B
38491.

An LCR series circuit with 100 Omegaresistance is connected to an ac source of 200 V and angular frequency 300 rad/s. When only the capacitance is removed, the current lags behind the voltage by 60^@. When only the inductance is removed, the current leads the voltage by 60^@. When capacitor is removed, inductive reactance of the circuit is

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`100sqrt3Omega`
`100sqrt2Omega`
`50sqrt2Omega`
`50sqrt2Omega`

ANSWER :A
38492.

Assertion : Black boles highly dense massive object. Reason : Its mass ranges from 20 times mass of the sun to 1 mission times mass of the sun.

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ASSERTION and Reason are correct and Reason is the correct EXPLANATION of Assertion
Assertion and Reason are TRUE but Reason is the false explanation of the Assertion
Assertion is true but Reason is false
Assertion is false but Reason is true

Answer :A
38493.

A wire ab of length l, mass m and resistance R slides on a smooth thick pair of metallic rails joined at the bottom as shown in fig. The plane of the rails makes an angle theta with the horizontal. A vertical magnetic field B exist in the region. If the wire slides on the rails at a constant speed v, then the value of B is -

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`SQRT((MGR)/(VL^(2)cos^(2)theta))`
`sqrt((mgR cos theta)/(vl^(2)sin^(2)theta))`
`sqrt((mgR)/(v^(2)L^(2)sin^(2)theta))`
`sqrt((mgR sin theta)/(vl^(2)cos^(2)theta))`

Answer :D
38494.

In the following diagram the conducting shells are concentric .The amount of charge that flows through the switch (S) after closing it is

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`Q`
`(Q)/(2)`
`(Q)/(3)`
`(Q)/(4)`

Solution :
`q_(2)-q_(1)=-2Q qQ_(1)-q_(2)+q_(3)=4Q`
`RARR (q_(1))/(4piepsilon_(0))-(q_(1))/(4piepsilon_(0)(2R))+(q_(2))/(4piepsilon_(0)2R)`
`-(q_(2))/(4piepsilon_(0)4R)+(q_(3))/(4piepsilon_(0)4R)`
` V_(A)(1)/(4piepsilon_(0))((q_(1)-q_(1)+q_(2)-q_(2)+q_(3)))/(4R)=V_(c)`
`V_(A)=V_(C)=q_(1)-(q_(1))/(2)+q_(2)/(2)-q_(2)/(4)+(q_(3))/(4)=(q_(3))/(4)`
`rArr (q_(1))/(2)+(q_(2))/(4)=0 rArr q_(2)=-2q_(1)rArr -2q_(1)-q_(1)=-2Q`
`rArr q_(1)=(2Q)/(3)`
rArr the charge that FLOWS through the switch is `Q//3`.
38495.

The mass of a disk with a circular hole cut in it (Fig. ) is m. Find its moment of inertia about an axis passing through point A perpendicularly to the disk's plane

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Answer :`(45)/(32)mR^2` [Hint . The cut is CONSIDERED as a negative mass.]
38496.

Number of spectral lines in hydrogen atom is

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3
15
5
infinite

Answer :D
38497.

Both the latitudinal and longitudinal extent of India's mainland is about 30°. But on looking at the map of India which of the following alternatives do you observe about India's size?

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East-west EXTENT APPEARS to be SMALLER than north-south extent
East-west extent appears to be LARGER than north-south extent
East-west and north-south extent appears equal
North-south extent appears to be smaller than east-west extent

Answer :A
38498.

The electric field in a region is given by vec(E )= E_(0) (x)/(L) hat(i). Find the charge contained inside a cubical volume bounded by the surface x=0, x= L, y= 0, y= L, z= 0 and z=L.

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SOLUTION :At x=0, E=0 and at x= l, `vec(E )= E_(0) hat(i)`
The direction of the FIELD is along the x-axis, so it will cross the yz-face of the cube. The FLUX of this field

`phi = phi_("left face") + phi_("right face") = 0 + E_(0)L^(2) = E_(0)L^(2)`
By Gauss.s law `phi= (q)/(in_(0)) THEREFORE q= in_(0) phi = in_(0) E_(0)L^(2)`
38499.

For a spherical capacitor show, at which points the electric field will be zero ? (r is the distance of point from centre O)

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At point` R GT R_2`
Atpoint ` rgt R_1`
ATPOINTS between`R_1and R_2`
NONE of the above

ANSWER :A
38500.

TheresultantoftwovectorsvecAand vecBis perpendiculartovecA. MagnitudeofResultantvecRis equalto half MagnitudeofvecB. FindtheanglebetweenvecAand vecB ?

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Solution :Since `VECR`is perpendicular to `VECA` . figure shows the THREE vectors `vecA, vecB` and `vecR`
and angle between `vecA` and `vecB` is p-q

`SINQ =R/B =B/(2B) =1/2`
`rArr q=30^(@) rArr` angle between A and B is `150^(@)`