Test 4 - Physics

Section A

1.

Given below are two statements:

Assertion (A):	The resolving power of a telescope is more if the diameter of the objective lens is more.
Reason (R):	An objective lens of large diameter collects more light.

1.	Both (A) and (R) are true and (R) is the correct explanation of (A).
2.	Both (A) and (R) are true but (R) is not the correct explanation of (A).
3.	(A) is true but (R) is false.
4.	Both (A) and (R) are false.

2.

A person with a normal near point \((25~\text{cm})\) using a compound microscope with an objective of focal length \(8.0~\text{mm}\) and an eyepiece of focal length \(2.5~\text{cm}\) can bring an object placed at \(9.0~\text{mm}\) from the objective in sharp focus. What is the separation between the two lenses?
1. \(7.20~\text{cm}\)
2. \(9.47~\text{cm}\)
3. \(2.50~\text{cm}\)
4. \(2.27~\text{cm}\)

3.

A small pin fixed on a table top is viewed from above from a distance of \(50~\text{cm}\). By what distance would the pin appear to be raised if it is viewed from the same point through a \(15~\text{cm}\) thick glass slab held parallel to the table? (The refractive index of glass is \(1.5\))

1.	\(5~\text{cm}\)	2.	\(3~\text{cm}\)
3.	\(3.5~\text{cm}\)	4.	\(4.5~\text{cm}\)

4. White light is used to illuminate the double slit in Young's double-slit experiment. Which of the following is/are true?

I.	The central fringe will be white.
II.	Closest bright fringe to the central fringe will be a violet fringe.
III.	There will not be any dark fringe.

1. I only
2. I, II
3. I, III
4. I, II, III

5.

The figure shows three transparent media of refractive indices \(\mu_1,~\mu_2\) and \(\mu_3\). A point object \(O\) is placed in the medium \(\mu_2\). If the entire medium on the right of the spherical surface has refractive index \(\mu_1\), the image forms at \(O'.\) If this entire medium has refractive index \(\mu_3\), the image forms at \(O''.\) In the situation shown,

1.	the image forms between \(O'\) and \(O''.\)
2.	the image forms to the left of \(O'.\)
3.	the image forms to the right of \(O''.\)
4.	two images form, one at \(O'\) and the other at \(O''.\)

6. A biconvex lens \((\mu=1.5)\) has a radius of curvature of magnitude \(20~\text{cm}\). Which one of the following options, best describes, the image formed by an object of height \(2\) cm placed \(30~\text{cm}\) from the lens?

1.	virtual, upright, height \(=0.5\) cm
2.	real, inverted, height \(=4\) cm
3.	real, inverted, height \(=1\) cm
4.	virtual, upright, height \(=1\) cm

7.

A person can see objects clearly only when they lie between \(50\) cm and \(400\) cm from his eyes. In order to increase the maximum distance of distinct vision to infinity, the type and power of the correcting lens, the person has to use, will be:

1.	convex, \(+2.25\) D	2.	concave, \(-0.25\) D
3.	concave, \(-0.2\) D	4.	convex, \(+0.5\) D

8. A ray is incident normally onto the surface \(AB\) of the prism \((\angle A=30^\circ,\angle B=90^\circ).\) The refractive index of the material of the prism is \(\sqrt2.\) The deviation of this ray is:

1. \(30^\circ\) downward
2. \(15^\circ\) downward
3. \(30^\circ\) upward
4. \(15^\circ\) upward

9.

Consider a light beam incident from air to a glass slab at Brewster's angle as shown in the figure. A polaroid is placed in the path of the emergent ray at point \(P\) and rotated about an axis passing through the centre and perpendicular to the plane of the polaroid. Then:

1.	for a particular orientation, there shall be darkness as observed through the polaroid.
2.	the intensity of light as seen through the polaroid shall be independent of the rotation.
3.	the intensity of light as seen through the polaroid shall go through a minimum but not zero for two orientations of the polaroid.
4.	the intensity of light as seen through the polaroid shall go through a minimum for four orientations of the polaroid.

10.

An astronomical refracting telescope will have large angular magnification and high angular resolution when it has an objective lens of:

1.	small focal length and large diameter.
2.	large focal length and small diameter.
3.	large focal length and large diameter.
4.	small focal length and small diameter.

11. An equilateral triangular prism of glass \((\mu=1.5)\) is placed in air. A ray of light is incident normally onto the surface \(AB.\) The ray will finally emerge:

1.	normally from the surface \(BC.\)
2.	normally from the surface \(AC.\)
3.	either from the surface \(BC\) or \(AC,\) normally.
4.	either from the surface \(BC\) or \(AC,\) at an angle of emergence greater than \(60^{\circ}\) but less than \(90^{\circ}.\)

12.

A man with a normal near point (\(25~\text{cm}\)) reads a book with small print, using a magnifying glass: a thin convex lens of focal length \(5~\text{cm}\). What is the closest distance at which he should keep the lens from the page so that he can read the book when viewing through the magnifying glass?
1. \(3.5~\text{cm}\)
2. \(4.2~\text{cm}\)
3. \(4.9~\text{cm}\)
4. \(5.0~\text{cm}\)

13.

Double-convex lenses are to be manufactured from a glass of refractive index \(1.55\) with both faces of the same radius of curvature. What is the radius of curvature required if the focal length is to be \(20~\text{cm}?\)
1. \(20~\text{cm}\)
2. \(22~\text{cm}\)
3. \(24~\text{cm}\)
4. \(15~\text{cm}\)

14. An interference pattern is obtained with two coherent light sources of intensity ratio \(n.\) In the interference pattern, the ratio of their intensities \(\left(\frac{I_{max}-I_{min}}{I_{max}+I_{min}}\right)\) will be:

1.	\(\dfrac{\sqrt{n}}{n+1}\)	2.	\(\dfrac{2\sqrt{n}}{n+1}\)
3.	\(\dfrac{\sqrt{n}}{(n+1)^2}\)	4.	\(\dfrac{2\sqrt{n}}{(n+1)^2}\)

15. Given below are two statements:

Assertion (A):	The angle of deviation depends on the angle of the prism.
Reason (R):	For the thin prism, \(\delta=(\mu-1)A.\)

1.	Both (A) and (R) are True and (R) is the correct explanation of (A).
2.	Both (A) and (R) are True but (R) is not the correct explanation of (A).
3.	(A) is True but (R) is False.
4.	Both (A) and (R) are False.

16. Two coherent monochromatic light beams of intensities \(9I\) and \(4I\) are superposed. The maximum possible intensity in the resulting beam is:
1. \(I\)
2. \(3I\)
3. \(16I\)
4. \(25I\)

17. When a parallel beam of light of wavelength \(\lambda\) falls onto a convex lens of diameter \(D,\) focal length \(f\) parallel to its principal axis, the image has a bright spot at the focal plane. As one moves away from the central point, the intensity becomes zero at a distance \(r_1.\) Then \(r_1=\)
1. \(\frac{f\lambda}{D}\)
2. \(\frac{f\lambda}{2D}\)
3. \(\frac{0.61f\lambda}{D}\)
4. \(\frac{1.22f\lambda}{D}\)

18.

According to Einstein's photoelectric equation, the graph between the kinetic energy of photoelectrons ejected and the frequency of incident radiation is:

1.		2.
3.		4.

19.

The inverse square law of intensity (i.e., the intensity \(\propto \frac{1}{r^2})\) is valid for:
1. a point source
2. a line source
3. a plane source
4. a cylindrical source

20.

Two photons have:

1.	equal wavelengths have equal linear momenta.
2.	equal energies have equal linear momenta.
3.	equal frequencies have equal linear momenta.
4.	equal linear momenta have equal wavelengths.

21. If \(E_1\), \(E_2\) and \(E_3\) represent respectively the kinetic energies of an electron, an alpha particle and a proton each having same de-Broglie wavelength then:
1. \({E}_{1}>{E}_{3}>{E}_{2}\)
2. \({E}_{2}>{E}_{3}>{E}_{1}\)
3. \({E}_{1}>{E}_{2}>{E}_{3}\)
4. \({E}_{1}{=}{E}_{2}{=}{E}_{3}\)

22.

Which of the following is not the property of cathode rays?

1.	It produces a heating effect.
2.	It does not deflect in the electric field.
3.	It casts a shadow.
4.	It produces fluorescence.

23.

The graph that shows the variation of the de-Broglie wavelength \((\lambda)\) of a particle and its associated momentum \((p)\) is:

1.		2.
3.		4.

24.

A photosensitive metallic surface has work function, \(h\nu_{0}.\)If the photons of energy, \(2h\nu_{0}\) falls on the surface, the electrons come out with a maximum velocity of \(4\times10^{6}\) m/s. When the photon energy is increased to \(5h\nu_{0},\) then the maximum velocity of photo-electrons will be:
1. \(2\times10^{7}\) m/s
2. \(2\times10^{6}\) m/s
3. \(8\times10^{5}\) m/s
4. \(8\times10^{6}\) m/s

25. The first experimental evidence for the existence of matter waves was observed by Davisson and Germer in their experiment on electron beam. In their experiment they observed:

1.	diffraction of electron beam from a single slit.
2.	diffraction of electron beam from crystals.
3.	interference of electron beam in a double-slit experiment.
4.	formation of standing waves between the lattice of crystals.

26.

In which of the following systems will the wavelength corresponding to \(n=2\) to \(n=1\) be minimum?

1.	hydrogen atom
2.	deuterium atom
3.	singly ionized helium
4.	doubly ionized lithium

27. The ionization energy of the electron in the hydrogen atom in its ground state is \(13.6~\text{eV}\). The atoms are excited to higher energy levels to emit radiations of \(6\) wavelengths. The maximum wavelength of emitted radiation corresponds to the transition between:

1.	\(n= 3~\text{to}~n=2~\text{states}\)
2.	\(n= 3~\text{to}~n=1~\text{states}\)
3.	\(n= 2~\text{to}~n=1~\text{states}\)
4.	\(n= 4~\text{to}~n=3~\text{states}\)

28.

The \((I\text-V)\) characteristics of a \(\mathrm{p\text-n}\) junction diode is as shown. If \(R_1\) and \(R_2\) be the dynamic resistance of the \(\mathrm{p\text-n}\) junction when (i) a forward bias of \(1\) volt is applied and (ii) a forward bias of \(2\) volts is applied respectively, then \(\frac{R_1}{R_2}=?\)

1. \(160\)
2. \(16\)
3. \(1.6\)
4. \(0.16\)

29.

Zener diode is used as:
1. Half-wave rectifier
2. Full-wave rectifier
3. AC voltage stabilizer
4. DC voltage stabilizer

30. The radius of a nucleus \((r)\) is directly proportional to the cube-root of the number of nucleons \((N).\) Assume that the mass of a nucleon is fixed \((m_n).\) The density \((\rho)\) of a nucleus varies as:
1. \(N^3\)
2. \(N^1\)
3. \(N^0\)
4. \(N^{-1}\)

31.

The decay constants of two radioactive materials X₁ and X₂ are \(5\lambda\) and \(\lambda\) respectively. Initially, they have the same number of nuclei. The ratio of the number of nuclei of X₁ to that of X₂ will be \(1/e\) after a time:
1. \(\lambda\)
2. \(\frac{1}{2\lambda }\)
3. \(\frac{1}{4\lambda }\)
4. \(\frac{e}{\lambda }\)

32. The peak voltage in the output of a half-wave rectifier is \(30 ~\text{V}.\) The RMS voltage of the output wave is: (assuming no distortion in wave)

1.	\(\dfrac{30}{\sqrt2}~\text{V}\)	2.	\(15 ~\text{V}\)
3.	\(\dfrac{15}{\sqrt2}~\text{V}\)	4.	\(10 ~\text{V}\)

33.

When an \(\alpha\text-\)particle of mass \(m\) moving with velocity \(v\) bombards on a heavy nucleus of charge \(Ze\), its distance of closest approach from the nucleus depends on \(m\) as:
1. \(\frac{1}{\sqrt{m}}\)
2. \(\frac{1}{m^{2}}\)
3. \(m\)
4. \( \frac{1}{m}\)

34.

If \(M(A,~Z)\), \(M_p\), and \(M_n\) denote the masses of the nucleus \(^{A}_{Z}X,\) proton, and neutron respectively in units of \(u\) \((1~u=931.5~\text{MeV/c}^2)\) and represent its binding energy \((BE)\) in \(\text{MeV}\). Then:

1.	\(M(A, Z) = ZM_p + (A-Z)M_n- \dfrac{BE}{c^2}\)
2.	\(M(A, Z) = ZM_p + (A-Z)M_n+ BE\)
3.	\(M(A, Z) = ZM_p + (A-Z)M_n- BE\)
4.	\(M(A, Z) = ZM_p + (A-Z)M_n+ \dfrac{BE}{c^2}\)

35. The half-life of radioactive iodine, \(I^{131}\) is 8 days. A sample of iodine has an activity of 40 \(\mu Ci\). What will be its activity after 4 days?
1. 20 \(\mu Ci\)
2. 20\(\sqrt 2\) \(\mu Ci\)
3. 32 \(\mu Ci\)
4. 10 \(\mu Ci\)

Section B

36. The given truth table is for which logic gate:

A	B	Y
\(1\)	\(1\)	\(0\)
\(0\)	\(1\)	\(1\)
\(1\)	\(0\)	\(1\)
\(0\)	\(0\)	\(1\)

1. NAND
2. XOR
3. NOR
4. OR

37.

The energy of a hydrogen atom in the ground state is \(-13.6\) eV. The energy of a \(\mathrm{He}^{+}\)ion in the first excited state will be:
1. \(-13.6\) eV
2. \(-27.2\) eV
3. \(-54.4\) eV
4. \(-6.8\) eV

38.

The ratio of momenta of an electron and an \(\alpha \text-\)particle which are accelerated from rest by a potential difference of \(100~\text{V}\) is:
1. \(1\)
2. \(\sqrt{\frac{2m_e}{m_{\alpha}}}\)
3. \(\sqrt{\frac{m_e}{m_{\alpha}}}\)
4. \(\sqrt{\frac{m_e}{2m_{\alpha}}}\)

39.

Two amplifiers of voltage gain 20 each, are cascaded in series. If 0.01 volt a.c. input signal is applied across the first amplifier, the output a.c. signal of the second amplifier in volts is:
1. 2.0
2. 4.0
3. 0.01
4. 0.20

40.

In a semiconductor;

(A)	there are no free electrons at \(0^\circ\text{K}.\)
(B)	there are no free electrons at any temperature.
(C)	the number of free electrons increases with temperature.
(D)	the number of free electrons is less than that in a conductor.

Choose the correct option from the given ones:

1.	(A) and (B) only
2.	(B) and (C) only
3.	(A), (C), and (D) only
4.	(A), (B), and (D) only

41.

In a transistor,

1.	the emitter has the least concentration of impurity.
2.	the collector has the least concentration of impurity.
3.	the base has the least concentration of impurity.
4.	all three regions have an equal concentration of impurity.

42.

Let \(n_{p}\) and \(n_{e}\) be the number of holes and conduction electrons in an intrinsic semiconductor. Then:
1. \(n_{p}> n_{e}\)
2. \(n_{p}= n_{e}\)
3. \(n_{p}< n_{e}\)
4. \(n_{p}\neq n_{e}\)

43. The impurity atoms with which pure silicon may be doped to make it a \(\mathrm{p\text{-}}\)type semiconductor are those of:

(a)	phosphorus	(b)	boron
(c)	antimony	(d)	aluminium

Then choose the correct option:

1.	(a), (b)	2.	(b), (d)
3.	(a), (c)	4.	(a), (d)

44. A \(\mathrm{p\text-n}\) junction diode is connected in a series circuit with a battery (internal resistance \(0.5~\Omega)\) and a \(5~\Omega\) resistance. A current is found to pass through the circuit. If the polarity of the battery is reversed, the current drops to almost zero. This is because the resistance in the circuit is:
1. \(5~\Omega\)
2. \(5.5~\Omega\)
3. \(10~\Omega\)
4. infinite

45. The collector current in a common base amplifier using n-p-n transistor is \(24\) mA. If \(80\text{%}\) of the electrons released by the emitter are accepted by the collector, then the base current is numerically:
1. \(6\) mA and leaving the base.
2. \(3\) mA and leaving the base.
3. \(6\) mA and entering the base.
4. \(3\) mA and entering the base.

46.

The peak voltage in the output of a half-wave diode rectifier fed with a sinusoidal signal without a filter is \(10~\text V.\) The DC component of the output voltage is:
1. \(\dfrac{10}{\pi }~\text V\)
2. \(10~\text V\)
3. \(\dfrac{20}{\pi }~\text V\)
4. \(\dfrac{10}{\sqrt{2}}~\text V\)

47.

In a transistor, the base is very lightly doped as compared to the emitter because by doing so:

1.	the flow across the base region is mainly because of electrons.
2.	the flow across the base region is mainly because of holes.
3.	recombination is decreased in the base region.
4.	base current is high.

48. The two inputs \((A)\) and \((B)\) of a logic circuit are shown along with the output \((Y)\) as functions of time. The 'highs' represent logic \(1\) and the 'lows' represents logic \(0.\) The correct truth table for this circuit is:

1.

\(A\)	\(B\)	\(Y\)
\(0\)	\(0\)	\(0\)
\(0\)	\(1\)	\(0\)
\(1\)	\(0\)	\(1\)
\(1\)	\(1\)	\(0\)

2.

\(A\)	\(B\)	\(Y\)
\(0\)	\(0\)	\(0\)
\(0\)	\(1\)	\(1\)
\(1\)	\(0\)	\(0\)
\(1\)	\(1\)	\(0\)

3.

\(A\)	\(B\)	\(Y\)
\(0\)	\(0\)	\(1\)
\(0\)	\(1\)	\(0\)
\(1\)	\(0\)	\(0\)
\(1\)	\(1\)	\(1\)

4.

\(A\)	\(B\)	\(Y\)
\(0\)	\(0\)	\(0\)
\(0\)	\(1\)	\(1\)
\(1\)	\(0\)	\(1\)
\(1\)	\(1\)	\(0\)

49. When semiconductor is heated, its resistance:

1.	decreases
2.	increases
3.	remains the same
4.	may increase or decrease depending on the semiconductor

50.

The depletion layer has (for an unbiased \(\mathrm{p\text-n}\) junction):
1. electrons
2. holes
3. static ions
4. neutral atoms

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