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44551.

Rutherford investigated nuclear structure by bombarding foil with:

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X-RAYS
`GAMMA`-rays
`BETA`-rays
`ALPHA`-rays

Answer :D
44552.

Compare Biot-Sevart's law with coulomb's law for electrostatic field

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SOLUTION :REFER TEXT
44553.

The dimensional formula of magnetic moment of a curent- carrying coil is :

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`[L^(2)A^(-1)]`
`[L^(2)A]`
`[L^(2)A^(-3)]`
`[LA^(2)]`

Solution :Magnetic DIPOLE moment of a CURRENT LOOP is the product of current and area of the loop.
`:.[L^(2)A]` is the CHOICE `i.e.` `(b)` is the choice.
44554.

What is meant by average life of a radioactive element ? Derive an expression for it. What is the relation between average life and half life ?

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Solution :AVERAGE life. The average life of a radioactive substance is the ratio of sum of lives of all the atoms to the total number of atoms.
`"Average life"=("Sum of lives of ALLTHE atoms")/("Total number of atoms")`
Since `N=N_(0)e^(-LAMBDA t)`
`:. dN= - lambda N_(0)e^(-lambda t) dt`.
It means that dN atoms disintegrate between time t and t + dt i.e. they have survived for time t.
`:.` Total life of dNatoms `=t` dN
Hence total life time of all the atoms
`tau_("total")=int_(0)^(N_(0)) t dN = - lambda N_(0) int_(oo)^(0) t e^(-lambda t) dt`
`=lambda N_(0) int_(0)^(oo) t e^(-lambda t) dt`
`tau_("total")=lambdaN_(0)[t{(e^(-lambda t))/(-lambda)}_(0)^(oo) - int_(0)^(oo) e^(-lambda t) dt]`
`=N_(0)[t{(e^(-lambda t))/(-lambda)}_(0)^(oo)-{(e^(-lambda t))/(-lambda)}_(0)^(oo)]`
`=N_(0)[0-(e^(-oo))/(lambda)+(e^(0))/(lambda)]`
or `tau_("total")=N_(0)[0+1/lambda ]=(N_(0))/(lambda)`
`:.` average life or MEAN life,
`tau_(a)=(tau_("total"))/(N_(0))=(N_(0)//lambda)/(N_(0))=1/lambda`
Hence average life `tau_(a)` of the atom is the reciprocal of the radioactive disintegration constant `lambda`.
Relation between average life and half life
Since average life of a radioactive element is given by
`tau_(a)=1/lambda`...(i)
and half life of a radioactive element is given by
`T=(0.693)/(lambda)`
Using Eq. (i), we get
`T=0.693 tau_(a)`
44555.

The distance travelled by a body during last second of its total flight is d when the body is projected vertically up with certain velocity.If the velocity of projection is doubled ,the distance travelled by the body during last second of its total flight is

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2D
d
`2d+(G)/(2)`
`2d-(g)/(2)`

Answer :C
44556.

A dipole, of dipole moment vec P is present in an uniform electric field vec E. What is the angle between vec E and vec P to have minimum torque.

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SOLUTION :When ANGLE between `vec P` and `vec E` is O, `TAU= PE sin0^@=0.`
44557.

In the circuit of Fig 27-57 epsi=1.2kV, c=6.5muF, R_(1)=R_(2)=R_(3)=0.73 M Omega. With C completely uncharged switch S is suddenly closed (at t=0). At t=0, what are (a) current i_(1) in resistor 1, (b) current i_(2) in resistor 2, and (c) current i_(3) in resistor 3? At t=oo (thta is after many time constants). what are (d) i_(1), (e) i_(2) and (f) i_(3)? What is the potential difference V_(2) across resistor 2 at (g) t=0 and (h) t=oo? Sketch V_(2) versus t between these two extreme times.

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Answer :(a) `1.1 xx 10^(-3) A; (B) 5.5 xx 10^(-4) A; (C) 5 xx 10^(-4) A (d) 8.2 xx 10^(-4) A; (E) 8.2 xx 10^(-4) A; (f) 0; (g) 4.2 xx 10^(2) V; (h) 6.0 xx 10^(2) V` (i) `(##MST_AG_JEE_MA_PHY_V02_C27_E02_034_A01##)`
44558.

The figure shows the location of a source and detector at time t = 0. The source and detector are moving with velocities v_s = 5hati m s^(-1)and v_D = 10 hatj ms^(-1)respectively . The frequency of signals received by the detector at the moment when the source cros the origin is (the frequency of the source is 100 Hz . Velocity bof sound 330 m s^(-1) .)

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97 Hz
47 Hz
90 Hz
60 Hz

Answer :A
44559.

Answer the following questions: (b) What is so special about the combination e/m? Why do we not simply talk of e and m separately?

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Solution :Both the BASIC relations `E V = (1//2) m v^(2) or e E = m a and e B v =m v^(2)//R`, for electric and MAGNETIC fields, respectively, show that the dynamics of electrons is determined not by e, and m SEPARATELY but by the combination e/m.
44560.

The dimensions [ML^(-1)T^(-2)] can correspond to :

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MOMENT of force
SURFACE tension
MODULUS of elasticity
Coefficient of viscosity

Solution :Modulus of elasticity `=("STRESS")/("strain")`
`=(ML^(-1)T^(-2))/(1)=[ML^(-1)T^(-2)]`
Hence correct answer is `(c )`.
44561.

Equal charges of +4 mu Care placed at the three corners of an equilateral triangle of side 2m. Calculate the magnitude and direction of the force on one of the charges.

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ANSWER :0.0024 N,AWAYS from trangleand NORMALTO oppositeside
44562.

The half-life period of a radioactive element A is same as the mean life time of another radioactive element B. Initially both have the same number of atoms. Then

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A and B have the same decay rate initially
A and B decay at the same rate ALWAYS
B will decay at faster rate than A
A will decay at faster rate than B

Answer :C
44563.

A ball of mass 600 gm strikes a wall with a velocity of 5ms at an angle 30^(@) with the wall and rebounds with the same speed at the same angle with the wall. The change in momentum of the ball is, (in kg ms^(-1))

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15
10
5
3

Answer :D
44564.

A particle moves in a circular path of radius 5 cm in a plane perpendicular to the principal axis of a concave mirror with radius of curvature 20 cm. The center of circle lies on the principal axis at distance of 15 cm in front of the mirror. The radius of the circular path of the image is

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15cm
20cm
10cm
40cm

Answer :C
44565.

If height of a transmitting tower increases by 21% then the area to be covered increases by

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`10%`
`21%`
`42%`
`84%`

ANSWER :B
44566.

A uniform rod of length l and mass m is given a charge Q and is suspended vertically by means of a hinge at the top end. A horizontal electric field E is switched on, in the direction in which the rod can sway freely. Find the angle made by the rod with the vertical in equilibrium.

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ANSWER :`TAN^(-1)((QE)/(MG))`
44567.

A ring of radius 1 cm is placed at 1.0 m infront of a spherical glass ball of radius 25 cm with mu=1.5. Determine the position of the final image of the ring and its magnification.

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at 29 cm to the RIGH of 2nd face, m=-0.44
at 10 cm to the RIGHT of 2nd face, m=-0.3
at 10 cm to the LEFT of 2nd face, m=-0.3
at 29 cm to the left of 2nd face, m=-0.44

Answer :A
44568.

A screen is placed 50 cm from a single slit, which is illuminated with 6000 dotA light. If distance between the first and third minima in the diffraction pattern is 3.00mm, what is the width of the slit?

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Solution :In case of diffraction at SINGLE slit, the position of minima is given by `d SIN theta = n lambda`. Where d is the aperture size and for small `theta : sin theta = theta =(y"/"D)`
`therefore d(y/D)= n lambda, i.e., y= (D)/(d)(n lambda)`
So that, `y_(3)-y_(1)= (D)/(d)(3lambda- lambda)= (D)/(d)(2lambda)` and hence,
`d= (0.50xx(2xx6xx10^(-7)))/(3xx 10^(-3))= 2xx 10^(-4)m = 0.2 mm`.
44569.

Define dielectric constant of a medium. Briefly explain why the capacitance of a parallel plate capacitor increases, on introducing a dielectric medium between the plates.

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Solution :Dielectric constant (K) of a medium is defined as the ratio of absolute permittivity (`epsi`) of the medium to the permittivity of FREE SPACE (`epsi_0`). Alternately dielectric constant of a medium is defined as the ratio of the capacitance of a parallel plate capacitor when filled with that medium to its capacitance with free space as the dielectric.
When a dielectric medium is introduced between the plates of a parallel plate capacitor, the dielectric is polarised by the electric field between the plates. As a RESULT, the electric field and hence potential DIFFERENCE between the plates of capacitor DECREASES. Consequently, the capacitance of the capacitor increases.
44570.

Neeldes N_(1),N_(2) and N_(3)are made of a ferromagnetic a paramagnetic and a diamagnetic substance respectivelya magnet when broughtclose to them will

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ATTRACT `n_(1)` and `n_(2)` strongly but repel `n_(3)`
attract `n_(1)` strongly `n_(2)` weakly and repel `n_(3)` weakly
attract `n_(1)`strongly but repel `n_(2)` and `n_(3)` weakly
attract all THREE of them

SOLUTION :Ferromagnetic & PARAMAGNETIC substances are attracted by magnets whereas diamgnetic substances are repelled by magnets
44571.

Undercertaincondinatesthe polarrizationof an infinite unchargeddielectric plate , takesthe formP = P_(0)is a vectorperpendicularto theplate, x is the distance from theof the electricfield insidethe plate and the potentaildifference between its surface.

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SOLUTION :Since there are no free extraneous chagres anywhere
`di vvec(D) = (del D)/(del X) = 0` or, `D_(x)` = constant
But`D_(x) = 0` at `oo`, so`D_(x) = 0`, EVERY where.
Thus, `vec(E) = - (vec(P_(0)))/(epsilon_(0)) (1 - (x^(2))/(d^(2)))` or`E_(x) = (P_(0))/(epsilon_(0)) (1 - (x^(2))/(d^(2)))`
So, `varphi = (P_(0)x)/(epsilon_(0)) - (P_(0) x^(3))/(3 epsilon_(0) d^(2)) +` constant
HENCE,`varphi(+d) - varphi(-d) = (2P_(0))/(epsilon_(0)) - (2 P_(0) d^(3))/(3 d^(2) epsilon_(0)) = (4 P_(0) d)/(3 epsilon_(0))`
44572.

In meter bridge experiment AB is wire of 1m of uniform cross section area. If resistivity of AB wire isrho, null point is obtained at a point 'l_(1)'distance from A. If resistivity is 2rho,null point will be 'l_(2)' from A and if left half of the wire has resistivity rhoand right half has resistivity 2rho,then null point is at'l_(3)'. Choose the correct statement:

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`l_(1)=l_(2)=l_(3)`
`l_(1)=l_(2) GT l_(3)`
`l_(1) gt l_(2) gt l_(3)`
`l_(1)=l_(2)LT l_(3)`

Solution :if resistivity is uniform then position of null point does not DEPEND on its value so `l_(1)=l_(2)`.
If LEFT half has resistivity `rho`and right half has resistivity `2rho`then to get some ratio null point has to be shifted towards right `l_(3) gt l_(2)`.
44573.

If M_(O) is the mass of an oxygen isotope ""_(8)O^(17), M_(p) and M_(N) are the masses of a proton and a neutron respectively, the nuclear binding energy of the isotope is:

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`(M_(O)-8M_(P)-9M_(N))C^(2)`
`M_(O)C^(2)`
`(M_(O)-17M_(N))C^(2)`
`(M_(O)-8M_(P))^(2)`

ANSWER :A
44574.

The electric field lines never intersect . Justify.

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Solution :As a consequence, if some charge is PLACED in the intersection point, then it has to move in two different DIRECTIONS at the same time, which is physically IMPOSSIBLE. HENCE, electric FIELD lines do not intersect.
44575.

10C and 20C are separated by a distance d. If the electric field at the location of a charge 10C is vec(E ), the field at the location of 20C is

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`VEC(E )//2`
`-vec( E)//2`
`-vec(E )`
`vec(E )`

ANSWER :B
44576.

Two parallel long wire carry currents i_(1) and i_(2) with i_(1) gt i_(2) . When the currents are in the same direction , the magnetic field midway between the wires is 10 muT . When the direction of i_(2) is reversed, it becomes 40 muT . The ratio i_(1)//i_(2) is

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`3:4`
`11:7`
`7:11`
`5:3`

ANSWER :D
44577.

Two clocks are being tested against a standard clock located in a national laboratory. At 12:00:00 noon by the standard clock, the readings of the clocks are : {:(1,"Clock 1", "Clock 2"),("Monday ", 12:00:06, 10:15:08),("Tuesday",12:01:25,10:14:59),("Wednesday " ,11:59:06,10:15:07),("Thursday" ,12:01:50,10:15:07),("Friday" ,11:59:25,10:14:42),("Saturday",12:01:40,10:15:14),("Sunday" ,12:01:40,10:15:21):} If you are doing an experiment that requires 'precisiom timme interval" measurements, which of the wo clocks will you preler ?

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Solution :The range of viriation over the Neven days of OBSERVATIONS is 164s for CLOCK-1. and 32 s for clock 2. The average reading of clock I is much closer to thestandard time than the average reading of clock 2.
The important point is that a clock is ZERO error is not as significant tor precision work as its variation. because a zero -error can always be easily corrected . Hence clock 2 is to be PREFERRED to clock 1.
44578.

A transparent glass plate of thickness 0.5 mm and refractive index 1.5 is placed infront of one of the slits in a double slit experiment. If the wavelength of light used is 6000 A^(@), the ratio of maximum to minimum intensity in the interference pattern is 25/4. Then the ratio of light intensity transmitted to incident on thin transparent glass plate is

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`9:7`
`9:49`
`3:7`
`7:3`

SOLUTION :9:49
44579.

A body is projected vertically upwards. Its momentum is gradually decreasing. In this

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It is a VIOLATION of law of conservation of LINEAR momentum
momentum of the body alone GETS conserved
momentum of the body, EARTH and air molecules TOGETHER remains constant
violates law of conservation of energy

Answer :C
44580.

A copper disc of radius 0.1 m is rotated about its natural axis with 10 rps in a uniform magnetic field of 0.1 T with its plane perpendicular to the field. The emf induced across the radius of the disc is

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`PI XX 10V`
`2pi xx 10V`
`pi xx 10^(-2) V`
`2pi xx 10^(-2) V`

Answer :C
44581.

Water can not be made conducting by adding small amount of any of the following except

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SODIUM CHLORIDE
COPPER sulphate
Ammonium chloride
Sugar

ANSWER :D
44582.

In an npn transistor circuit, the emitter current 10mA. If 90%of the emitted electrons reach the collector then the base current is

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9mA
1mA
2mA
8mA

Answer :B
44583.

A metal bar clamped at its centre resonates in its fundamental mode to produce longitudinal waves of frequency 4 kHz . Now the clamp is moved to one end. If f_1 and f_2 are the frequencies of first overtone and second overtone , respectively ,then

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`3f_2=5f_1`
`3f_1=5f_2`
`f_2=2f_1`
`2f_2=f_1`

ANSWER :A
44584.

Why does a paramagnetic sample display greater magnetisation (for the same magnetising field) when cooled?

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SOLUTION :(a) When any paramagnetic sample is cooled down, average kinetic energy of thermal VIBRATIONS of atomic dipoles decreases. As a result, angle between `overset(to) (m)and overset(to)(B)` decreases. In other words, atomic dipoles TEND to be aligned more and more in the direction ofexternal magnetising field `overset(to) (B)`. That is why such a sample SHOWS more MAGNETISATION with the same magnetising field.
44585.

If 13.6 eV energy is required to ionize the hydrogen atom, then the energy required to remove an electron from

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10.2 eV
0 eV
3.4 eV
6.8 eV

Solution :`E_(N)=(13.6)/(n^(2))impliesE_(2)=(13.6)/((2)^(2))=3.4eV`
44586.

Find the power of a thin glass lens (mu = 1.5) in a liquid with refractive index mu_(0) = 1.7, if its power in air is : -5D.

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<P>`+ 4D`
` + 2D`
` -4D`
` -2D`

SOLUTION :`(b) P_(0)=(mu-1)[(1)/(R_(1))-(1)/(R_(2))]` in air
`P=(mu-mu_(0))[(1)/(R_(1))-(1)/(R_(1))]"in liquid"`
`therefore P=P_(0)(mu-mu_(0))/(mu-1)=-5xx(1.5-1.7)/(1.5-1)=+2D`
44587.

In Young.s double slit experiment the 10^(th) maximum of wavelength lambda_(1) is at a distance of y_(1) from the central maximum . When the wavelength of the sources is changed to lambda_(2) , 5^(th) maximum is at a disatnce of y_(2) from its central maximum .The ratio (y_(1)/(y_(2))) is

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`(2lambda_(1))/(lambda_(2))`
`(2lambda_(2))/(lambda_(1))`
`(lambda_(1))/(2lambda_(2))`
`(lambda_(2))/(2lambda_(1))`

ANSWER :A
44588.

Photoelectric effect can be explained by

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corpusular THEORY of light
wave NATURE of light
Bohr's theory
quantum theory of light

Answer :D
44589.

Light transmitted by Nicol prism is,

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partiallypolarised
unpolarised
plane polarised
ellitpically polarised

Answer :A::D
44590.

The energy of electron in first excited state of H-atom is - 3.4 eV. Its kinetic energy is.

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-3.4 EV
`+3.4 eV`
`-6.8 eV`
`+6.8 eV`

SOLUTION :`K= - E = - (-3.4e V) = + 3.4 eV`
44591.

A cyclotron is operating at a frequency of 12xx10^(6)Hz. Mass of deuteron is 3.3xx10^(-27) kg and its charge is 1.6xx10^(-19) C. To accelerate the deuterons, the magnetic induction of the field required is :

Answer»

16 T
1.6 T
0.16 T
0.016T

Solution :Here `B q v=(MV^(2))/(r)`
`:. (v)/(r)=(Bq)/(m)`
`:. omega= (Bq)/(m)`
or `2pi n=(Bq)/(m)`
`B=(2pi nm)/(q)`
Here `n=12xx10^(6)Hz`
`m=3*3xx10^(-27)kg`
`q=1*6xx10^(-10)C`
`:.B=(2XX3*14xx12xx10^(6)xx3*3xx10^(-27))/(1*6xx10^(-19))T`
`=1*6T`
44592.

What is the value of constant of proportionately K= 1/4pi epsilon_0 ?

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Solution :`1/4pi epsilon_0 = 1/4pi xx 8.85 xx 10^(-12)C^2N^(-1)m^(-2) = 9 xx 10^@ Nm^2C^(-2)`
44593.

The process of nuclear fusion in the sum requires

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very high temperature and very high pressure
low temperatureand high pressure
high temperature and low pressure
very high temperature and no pressure

Solution :NUCLEAR fusion is a nuclear reaction in which two or more atomic nuclei COLLIDE at very high speed and join to form a NEW type of atomic nucleus (e. g. The energy that the Sum emits into space is produced by nuclear reactions that happen in its core DUE to the collision of hydrogen nuclei and the formation of helium nuclei). During this process, matter is not CONSERVED because some of the mass of the fusing nuclei is converted to photons which are released through a cycle that even our sun uses.
44594.

What is the probability of extracting from a pack of cards (a) a court-card, (b) a red court-card?

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Solution :(a) There are THREE court-cards of each suit: the jack, the queen, the king. Therefore the total number of court-cards is `3 xx 4 = 12`.
(b) The number of red court-cards is `3 xx 2 = 6`. One can also reason as follows. The probability of extracting a red court-card is the probability of the compound event: extracting a court-card `(w_1 = = 12//36 = 1//3)` and extracting a red card `(w_2 = 1//2)`. The probability of a simultaneous realization of TWO independent events is the product of their individual probabilities:
`w = w_1w_2 = 1/3 CDOT 1/2 = 1/6`.
44595.

(a) The mass of a particle moving with velocity 5xx 10^(6) ms^(-1) has de-Broglie wave length associated with it to be 0.135 nm. Calculate its mass. (b) In which region of the electromagnetic spectrum does this wave length lie?

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Solution :(a) Here ,
`v=5xx10^(6)m//s`
`LAMBDA=0.135nm=0.135xx10^(-9)m`
So we know that
`lambda=(h)/(mv)`
or, `m=(h)/(lambda v)`
`=(6.63xx10^(-34))/(0.135xx10^(-19)mxx5xx10xx^(6))`
`=9.1xx10^(-31)Kg`
(B) It lies in ultravoilet region.
44596.

What are the advantages of using a reflecting telescope?

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Solution :(i) The main ADAVANTAGE is reflector telecope can escape from chromatic aberration because WAVELENGHT does not effect reflection.
(ii) The PRIMARY mirror is very stable because it is located at the back of the telesope and can be support in the back.
(iii) More cost EFFECTIVE than refractor of similar size.
(iv) EASIER to make a high quality mirror than lens because mirror need to only concern with one side of the curvature.
44597.

A person throws balls into air vertically upward in regular intervals of time of one second . The next ball is thrown when the velocity of the ball thrown earlier becomes zero . The height to which the balls rise is … (Assume , g = 10 ms^(-2))

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5 m
10 m
7.5m
20m

Solution :Sice the ball are THROWN after a gap of 1S. So 1s is TIME of ascent of first ball.
`:.` time of descent is also 1s
`:. H=(1)/(2)G t^(2)`
`=(1)/(2)xx10xx1^(2)=5m`
44598.

The velocity of light in the core of a step index fibre 2xx10^(8) m//s and the critical angle at the core-cladding interface is 80^(@).Find the numerical aperture and the acceptance angle for the fibre in air.The velocity of light in vacuum is 3xx10^(8)m//s

Answer»


ANSWER :0.264,`15.3^(@)`
44599.

A slit of width a is illuminated by white light. For what value of a does the first minimum for red light of wavelength 650 nm fall at angle of diffraction theta=15^(@)?

Answer»


ANSWER :A slitofwidth aisilluminatedbywhi
44600.

You are given several identical resistors each of value 5Omega and each capable of carrying a maximum current of 2A. It is required to make a suitable combination of these resistances to produce a resistance of 2.5Omega which can carry current of 4A. The minimum number of resistances required for this job is

Answer»

2
4
6
8

Answer :A