Blogger Widgets APEX INSTITUTE : wave optics assignment for IIT-JEE aspirants

Tuesday, September 20, 2011

wave optics assignment for IIT-JEE aspirants




















Short Questions
Q.1 A person wets his eyeglass to clean them. As the water evaporates he notices that for a short time the glass become markedly more non reflecting. Explain.
Q.2 A lens is coated to reduce reflection. What happens to the energy that had previously been reflected? Is it absorbed by the coating?
Q.3 If interference between light waves of different frequencies is possible, one should observe light beats, just as one obtains sound beats from two sources of sound with slightly different frequencies. Discuss how one might experimentally look for this possibility.
Q.4 What is the shape of interference fringes as seen on a screen perpendicular to the line joining the sources in Young's interference experiment if the source are (a) pinholes, (b) slits?
Q.5 In Young's double slit experiment why must the slits be close and of same width?
Q.6 In Young's double slit experiment why do we use monochromatic light ? If white light is used, how would the pattern change?
Q.7 Will interference be observed in Young's double-slit experiment if the light from a source falls directly on the two slits?
Q.8 In what direction will the fringe system shift if a glass plate is interposed in the path of one of the interfering beams?
Q.9 Suppose that a radio station broadcasts simultaneously from two transmitting antennas at two different locations. Is it clear that your radio will have better reception with two transmitting antennas rather than one? Justify your answer.
Only one option is correct.
Take approx. 2 minutes for answering each question.
Q.1 Figure, shows wave fronts in still water, moving in the direction
of the arrow towards the interface PQ between a shallow region
and a deep(denser) region. Which of the lines shown may represent
one of the wave fronts in the deep region?
(A) I (B) II (C) III (D) IV
Q.2 Two coherent monochromatic light beams of intensities I and 4I are superposed. The maximum and minimum possible intensities in the resulting beam are :
(A) 5I and I (B) 5I and 3I (C) 9I and I (D) 9I and 3I
Q.3 Two point monochromatic and coherent sources of light of wavelength l are placed on the dotted line in front of an large screen. The source emit waves in phase with each other. The distance between S1 and S2 is 'd' while their distance from the screen is much larger. Then,
(1) ® If d = 7l/2, O will be a minima
(2) ® If d = 4.3l, there will be a total of 8 minima on y axis.
(3) ® If d = 7l, O will be a maxima.
(4) ® If d = l, there will be only one maxima on the screen.
Which is the set of correct statement :
(A) 1, 2 & 3 (B) 2, 3 & 4 (C) 1, 2, 3 & 4 (D) 1, 3 & 4
Q.4 Figure shown plane waves refracted for air to water using Huygen's
principle a, b, c, d, e are lengths on the diagram. The refractive index
of water wrt air is the ratio.
(A) a/e (B) b/e (C) b/d (D) d/b
Q.5 When light is refracted into a denser medium,
(A) its wavelength and frequeny both increases
(B) its wavelength increase but freqnency remains unchanged
(C) its wavelength decrease but freqnency remains unchanged
(D) its wavelength and freqnency both decrease.
Q.6 Two point source separated by d = 5 mm emit light of wavelength l = 2 mm in phase. A circular wire of radius 20 mm is placed around the source as shown in figure.
(A) Point A and B are dark and points C and D are bright.
(B) Points A and B are bright and point C and D are dark.
(C) Points A and C are dark and points B and D are bright.
(D) Points A and C are bright and points B and D are dark.
Q.7 Plane microwaves from a transmitter are directed normally towards a plane reflector. A detector moves along the normal to the reflector. Between positions of 14 successive maxima, the detector travels a distance 0.13 m. If the velocity of light is 3 × 108 m/s, find the frequency of the transmitter.
(A) 1.5 × 1010 Hz (B) 1010 Hz (C) 3 × 1010 Hz (D) 6 × 1010 Hz
Q.8 Two monochromatic (wavelength = a/5) and coherent sources of electromagnetic waves are placed on the x-axis at the points (2a, 0) and (–a, 0). A detector moves in a circle of radius R(>>2a) whose centre is at the origin. The number of maximas detected during one circular revolution by the detector are
(A) 60 (B) 15 (C) 64 (D) None
Q.9 Two coherent narrow slits emitting light of wavelength l in the
same phase are placed parallel to each other at a small separation
of 3l. The light is collected on a screen S which is placed at a distance D
(>> l) from the slits. The smallest distance x such that the P is a maxima
(A) (B)
(C) (D)
Q.10 Two coherent sources of light are placed at points (– , 0) and (+ , 0). Wavelength of the light is
l = . How many maximas will be obtained on a CD planar circle of large radius with centre at origin.
(A) 12 (B) 15 (C) 16 (D) 14
Q.11 In YDSE how many maxima can be obtained on the screen if wavelength of light used is 200nm and d = 700 nm:
(A) 12 (B) 7 (C) 18 (D) none of these
Q.12 In a YDSE, the central bright fringe can be identified :
(A) as it has greater intensity than the other bright fringes.
(B) as it is wider than the other bright fringes.
(C) as it is narrower than the other bright fringes.
(D) by using white light instead of single wavelength light.
Q.13 In Young's double slit experiment, the wavelength of red light is 7800 Å and that of blue light is 5200 Å. The value of n for which nth bright band due to red light coincides with (n + 1)th bright band due to blue light, is :
(A) 1 (B) 2 (C) 3 (D) 4
Q.14 If the Young's double slit experiment is performed with white light, then which of the following is not true.
(A) the central maximum will be white (B) there will not be a completely dark fringe
(C) the fringe next to the central will be red (D) the fringe next to the central will be violet
Q.15 Imagine a Young's double slit interference experiment performed with waves associated with fast moving electrons produced from an electron gun. The distance between successive maxima will decrease maximum if
(A) the accelerating voltage in the electron gun is decreased
(B) the accelerating voltage is increased and the distance of the screen from the slits is decreased
(C) the distance of the screen from the slits is increased.
(D) the distance between the slits is decreased.
Q.16 Two identical narrow slits S1 and S2 are illuminated by light of wavelength
l from a point source P. If, as shown in the diagram above the light is then
allowed to fall on a screen, and if n is a positive integer, the condition for
destructive interference at Q is that
(A) (l1l2) = (2n + 1)l/2 (B) (l3l4) = (2n + 1)l/2
(C) (l1 + l2) – (l2 + l4) = nl (D) (l1 + l3) – (l2 + l4) = (2n + 1)l/2
Q.17 In Young's double slit experiment, the two slits act as coherent sources of equal amplitude A and wavelength l. In another experiment with the same setup the two slits are sources of equal amplitude A and wavelength l but are incoherent. The ratio of the intensity of light at the midpoint of the screen in the first case to that in the second case is
(A) 1 : 1 (B) 2 : 1 (C) 4 : 1 (D) none of these
Q.18 In a Young's double slit experiment, a small detector measures an intensity of illumination of I units at the centre of the fringe pattern. If one of the two (identical) slits is now covered, the measured intensity will be
(A) 2I (B) I (C) I/4 (D) I/2
Q.19 A student is asked to measure the wavelength of monochromatic light.
He sets up the apparatus sketched below. S1, S2, S3 are narrow parallel
slits, L is a sodium lamp and M is a microscope eyepiece. The student fails
to observe interference fringes. Your first advice to him will be
(A) increase the width of S1
(B) decrease the distance between S2 and S3
(C) replace L with a white light source
(D) replace M with a telescope
(E) make S2 and S3 wider.
Q.20 Light of wavelength 520 nm passing through a double slit,
produces interference pattern of relative intensity versus
deflection angle q as shown in the figure. The separation
d between the slits is
(A) 2 × 10–2 mm (B) 5 × 10–2 mm
(C) 4.5 × 10–2 mm (D) 1.1 × 10–2 mm
Q.21 In Young's double slit experiment the slits are 0.5 mm apart and the interference is observed on a screen at a distance of 100 cm from the slit. It is found that the 9th bright fringe is at a distance of 7.5 mm from the second dark fringe from the centre of the fringe pattern. The wavelength of the light used is
(A) (B) 2500 Å (C) 5000 Å (D)
Q.22 In a YDSE apparatus, two identical slits are separated by 1 mm and distance between slits and screen is 1 m. The wavelength of light used is 6000 Å. The minimum distance between two points on the screen having 75% intensity of the maximum intensity is :
(A) 0.45 mm (B) 0.40 mm (C) 0.30 mm (D) 0.20 mm
Q.23 In a young double slit experiment D equals the distance of screen and d is the separation between the slit. The distance of the nearest point to the central maximum where the intensity is same as that due to a single slit, is equal to
(A) (B) (C) (D)
Q.24 A beam of light consisting of two wavelength 6300 Å and l Å is used to obtain interference fringes in a Young's double slit experiment. If 4th bright fringe of 6300 Å coincides with 5th dark fringe of l Å, the value of l (in Å) is
(A) 5200 (B) 4800 (C) 6200 (D) 5600
Q.25 A beam of light consisting of two wavelengths 6500Å and 5200Å is used to obtain interference fringes in Young’s double slit experiment. The distance between slits is 2 mm and the distance of screen from slits is 120 cm. What is the least distance from central maximum where the bright due to both wavelength coincide?
(A) 0.156 cm (B) 0.312 cm (C) 0.078 cm (D) 0.468 cm
Q.26 In a two slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the slits. If the screen is moved by 5 × 10–2 m towards the slits, the change in fringe width is 3 × 10–5 m. If separation between the slits is 10–3m, the wavelength of light used is:
(A) 6000 Å (B) 5000 Å (C) 3000 Å (D) 4500 Å
Q.27 The ratio of the intensity at the centre of a bright fringe to the intensity at a point one–quarter of the fringwidth from the centre is
(A) 2 (B) 1/2 (C) 4 (D) 16
Q.28 In YDSE, let S1 and S2 be the two slits, and C be the centre of the screen. If q is the angle S1CS2 and l is the wavelength, the fringe width will be :
(A) (B) lq (C) (D)
Q.29 In a Young's Double slit experiment, first maxima is observed at a fixed
point P on the screen. Now the screen is continuously moved away from
the plane of slits. The ratio of intensity at point P to the intensity at point
O (centre of the screen)
(A) remains constant
(B) keeps on decreasing
(C) first decreases and then increases
(D) First decreases and then becomes constant
Q.30 In a double slit experiment, the separation between the slits is d = 0.25 cm and the distance of the screen D = 100 cm from the slits. If the wavelength of light used is l = 6000Å and I0 is the intensity of the central bright fringe, the intensity at a distance x = 4 × 10–5 m from the central maximum is
(A) I0 (B) (C) (D)
Q.31 A monochromatic light source of wavelength l is placed at S. Three slits
S1, S2 and S3 are equidistant from the source S and the point P on the
screen. S1P – S2P = l/6 and S1P – S3P = 2l/3. If I be the intensity at P
when only one slit is open, the intensity at P when all the three slits are open is
(A) 3 I (B) 5 I
(C) 8 I (D) zero
Q.32 In young’s double slit experiment, the value of l = 500 nm. The value of d = 1 mm, D = 1 m. Then the minimum distance from central maximum for which the intensity is half the maximum intensity will be
(A) 2.5 × 10–4 m (B) 2 × 10–4 m (C) 1.25 × 10–4 m (D) 10–4 m
Q.33 Two slits are separated by 0.3 mm. A beam of 500 nm light strikes
the slits producing an interference pattern. The number of maxima
observed in the angular range – 30° < q < 30°.
(A) 300 (B) 150
(C) 599 (D) 149
Q.34 In the figure shown if a parallel beam of white light is incident
on the plane of the slits then the distance of the white spot on
the screen from O is [Assume d << D, l << d]
(A) 0 (B) d/2
(C) d/3 (D) d/6
Q.35 In the above question if the light incident is monochromatic and point O is a maxima, then the wavelength of the light incident cannot be
(A) (B)
(C) (D)
Q.36 In Young's double slit arrangement, water is filled in the space between screen and slits. Then :
(A) fringe pattern shifts upwards but fringe width remains unchanged.
(B) fringe width decreases and central bright fringe shifts upwards.
(C) fringe width increases and central bright fringe does not shift.
(D) fringe width decreases and central bright fringe does not shift.
Q.37 A parallel beam of light 500nm is incident at an angle 30° with the
normal to the slit plane in a young's double slit experiment. The
intensity due to each slit is Io. Point O is equidistant from S1 and S2.
The distance between slits is 1mm.
(A) the intensity at O is 4Io
(B) the intensity at O is zero.
(C) the intensity at a point on the screen 4mm from O is 4Io
(D) the intensity at a point on the screen 4mm from O is zero.
Q.38 Light of wavelength l in air enters a medium of refractive index m. Two points in this medium, lying along the path of this light, are at a distance x apart. The phase difference between these points is :
(A) (B) (C) (D)
Q.39 In YDSE, the source placed symmetrically with respect to the slit is now moved parallel to the plane of the slits so that it is closer to the upper slit, as shown. Then,
(A) the fringe width will increase and fringe pattern will shift down.
(B) the fringe width will remain same but fringe pattern will shift up.
(C) the fringe width will decrease and fringe pattern will shift down.
(D) the fringe width will remain same but fringe pattern will shift down.
Q.40 In the figure shown in YDSE, a parallel beam of light is incident on the
slit from a medium of refractive index n1. The wavelength of light in this
medium is l1. A transparent slab of thickness ‘t’ and refractive index n3
is put infront of one slit. The medium between the screen and the plane
of the slits is n2. The phase difference between the light waves reaching
point ‘O’ (symmetrical, relative to the slits) is :
(A) (n3 – n2) t (B) (n3 – n2) t
(C) t (D) (n3 – n1) t
Q.41 In a YDSE experiment if a slab whose refractive index can be varied is placed in front of one of the slits then the variation of resultant intensity at mid-point of screen with ‘m’ will be best represented by
(m ³ 1).[Assume slits of equal width and there is no absorption by slab]
(A) (B) (C) (D)
Q.42 Young’s double slit experiment is carried with two thin sheets of
thickness 10.4 mm each and refractive index m1= 1.52 and m2 = 1.40
covering the slits S1 and S2, respectively. If white light of range 400 nm
to 780 nm is used then which wavelength will form maxima exactly at point
O, the centre of the screen ?
(A) 416 nm only (B) 624 nm only (C) 416 nm and 624 nm only (D) none of these
Q.43 A light of wavelength 6300Å shine on a two narrow slits separated by a distance 1.0 mm and illuminates a screen at a distance 1.5 m away. When one slit is covered by a thin glass of refractive index 1.8 and other slit by a thin glass plate of refractive index m, the central maxima shifts by 6°. Both plates have same thickness of 0.5 mm. The value of refractive index m of the plate is
(A) 1.6 (B) 1.7 (C) 1.5 (D) 1.4
Q.44 Minimum thickness of a mica sheet having m =which shoule be placed in front of one of the slits in YDSE is required to reduce the intensity at the centre of screen to half of maximum intensity is
(A) l/4 (B) l/8 (C) l/2 (D) l/3
Q.45 In the YDSE shown the two slits are covered with thin sheets
having thickness t & 2t and refractive index 2m and m. Find the
position (y) of central maxima
(A) zero (B)
(C) (D) None
Q.46 In a YDSE with two identical slits, when the upper slits is covered with a thin, perfectly transparent sheet of mica, the intensity at the centre of screen reduces to 75% of the initial value. Second minima is observed to be above this point and third maxima below it. Which of the following cannot be a possible value of phase difference caused by the mica sheet
(A) (B) (C) (D)
Q.47 The figure shows a transparent slab of length 1m placed
in air whose refractive index in x direction varies as
m = 1 + x2(0 < x < 1). The optical path length of ray R will be
(A) 1 m (B) m
(C) m (D) m
Q.48 Two monochromatic and coherent point sources of light are placed at a certain distance from each other in the horizontal plane. The locus of all those points in the horizontal plane which have construct interference will be
(A) a hyperbola (B) family of hyperbolas
(C) family of straight lines (D) family of parabolas
Q.49 A thin slice is cut out of a glass cylinder along a plane parallel to its axis. The slice is placed on a flat glass plate with the curved surface downwards. Monochromatic light is incident normally from the top. The observed interference fringes from this combination do not follow one of the following statements.
(A) the fringes are straight and parallel to the length of the piece.
(B) the line of contact of the cylindrical glass piece and the glass plate appears dark.
(C) the fringe spacing increases as we go outwards.
(D) the fringes are formed due to the interference of light rays reflected from the curved surface of the cylindrical piece and the top surface of the glass plate.
Q.50 A circular planar wire loop is dipped in a soap solution and after taking it out, held with its plane vertical in air. Assuming thickness of film at the top very small, as sunlight falls on the soap film, & observer receive reflected light
(A) the top portion appears dark while the first colour to be observed as one moves down is red.
(B) the top portion appears violet while the first colour to be observed as one moves down is indigo.
(C) the top portion appears dark while the first colour to be observed as one move down is violet.
(D) the top portion appears dark while the first colour to be observed as one move down depends on the refractive index of the soap solution.
Q.51 A thin film of thickness t and index of refraction 1.33 coats a glass with index of refraction 1.50. What is the least thickness t that will strongly reflect light with wavelength 600 nm incident normally?
(A) 225 nm (B) 300 nm (C) 400 nm (D) 450 nm
Q.52 It is necessary to coat a glass lens with a non-reflecting layer. If the wavelength of the light in the coating is l, the best choice is a layer of material having an index of refraction between those of glass and air and a thickness of
(A) (B) (C) (D) l
Q.53 Radio waves coming at Ð a to vertical are recieved by a radar after
reflection from a nearby water surface & directly. What should be
height of antenna from water surface so that it records a maximum
intensity. (wavelength = l).
(A) (B)
(C) (D)
Q.54 In a biprism experiment the distance of source from biprism is 1 m and the distance of screen from biprism is 4 metres. The angle of refraction of biprism is 2 × 10–3 radians. m of biprism is 1.5 and the wavelength of light used is 6000Å. How many fringes will be seen on the screen?
(A) 4 (B) 5 (C) 3 (D) 6
Q.55 In a biprism experiment using sodium light l = 6000 Å an interference pattern is obtained in which 20 fringes occupy 2 cm. On replacing sodium light by another source of wavelength l2 without making any other change 30 fringes occupy 2.7 cm on the screen. What is the value of l2?
(A) 4500 Å (B) 5400 Å (C) 5600 Å (D) 4200 Å
Q.56 A parallel coherent beam of light falls on fresnel biprism of refractive index m and angle a. The fringe width on a screen at a distance D from biprism will be (wavelength = l)
(A) (B) (C) (D) none
One or more than one option may be correct
Take approx. 3 minutes for answering each question.
Q.1 To observe a stationary interference pattern formed by two light waves, it is not necessary that they must have :
(A) the same frequency (B) same amplitude
(C) a constant phase difference (D) the same intensity
Q.2 A light of wavelength 600nm in air enters a medium of refractive index 1.5. Inside the medium :
(A) its frequency is 5 × 1014 Hz (B) its frequency is 7.5 × 1014 Hz
(C) its wavelength is 400nm (D) its wavelength is 900nm
Q.3 Four monochromatic and coherent sources of light, emitting waves in phase of wavelength l, are placed at the points ® x = 0, d, 2d and 3d on the x-axis. Then
(A) points having | x | >> d appear dark if d = l/4
(B) points having | x | >> d appear dark if d = l/8
(C) points having | x | >> d appear maximum bright if d = l/4
(D) points having | x | >> d appear maximum bright if d = l/8
Q.4 In the above question, the intensity of the waves reaching a point P far away on the +x axis from each of the four sources is almost the same, and equal to I0. Then,
(A) If d = l/4, the intensity at P is 4I0. (B) If d = l/6, the intensity at P is 3I0.
(C) If d = l/2, the intensity at P is 3I0. (D) none of these is true.
Q.5 The figure shows two points source which emit light of wavelength
l in phase with each other and are at a distance d = 5.5 l apart along
a line which is perpendicular to a large screen at a distance L from the
centre of the source. Assume that d is much less than L. Which of the
following statement is (are) correct?
(A) Only five bright fringes appear on the screen
(B) Only six bright fringes appear on the screen
(C) Point y = 0 corresponds to bright fringe
(D) Point y = 0 corresponds to dark fringe.
Q.6 White light is used to illuminate two slits in a YDSE. The separation between the slits is d and the screen is at a distance D (D >> d) from the slits. At a point on the screen directly in front of one of the slits, which of the following wavelengths are missing.
(A) (B) (C) (D)
Q.7 In a YDSE apparatus, we use white light then :
(A) the fringe next to the central will be red (B) the central fringe will be white.
(C) the fringe next to the central will be violet (D) there will not be a completely dark fringe.
Q.8 If the source of light used in a Young's Double Slit Experiment is changed from red to blue, then
(A) the fringes will become brighter
(B) consecutive fringes will come closer
(C) the number of maxima formed on the screen increases
(D) the central bright fringe will become a dark fringe.
Q.9 In a Young's double slit experiment, green light is incident on
the two slits. The interference pattern is observed on a screen.
Which of the following changes would cause the observed fringes
to be more closely spaced?
(A) Reducing the separation between the slits
(B) Using blue light instead of green light
(C) Used red light instead of green light
(D) Moving the light source further away from the slits.
Q.10 In a Young's double-slit experiment, let A and B be the two slits. A thin film of thickness t and refractive index m is placed in front of A. Let b = fringe width. The central maximum will shift :
(A) towards A (B) towards B (C) by t (m – 1) (D) by m t
Q.11 In the previous question, films of thicknesses tA and tB and refractive indices mA and mB, are placed in front of A and B respectively. If mAtA = mBtB, the central maximum will :
(A) not shift (B) shift towards A
(C) shift towards B (D) option (B), if tB > tA; option (C) if tB < tA
Q.12 In a double slit experiment, instead of taking slits of equal widths, one slit is made twice as wide as the other. Then in the interference pattern :
(A) the intensities of both the maxima and minima increase.
(B) the intensity of the maxima increases and the minima has zero intensity.
(C) the intensity of the maxima decreases and that of minima increases.
(D) the intensity of the maxima decreases and the minima has zero intensity.
Q.13 In a YDSE, if the slits are of unequal width :
(A) fringes will not be formed
(B) the positions of minimum intensity will not be completely dark
(C) bright fringe will not be formed at the centre of the screen.
(D) distance between two consecutive bright fringes will not be equal to the distance between two consecutive dark fringes.
Q.14 If one of the slits of a standard YDSE apparatus is covered by a thin parallel sided glass slab so that it transmit only one half of the light intensity of the other, then :
(A) the fringe pattern will get shifted towards the covered slit.
(B) the fringe pattern will get shifted away from the covered slit.
(C) the bright fringes will be less bright and the dark ones will be more bright.
(D) the fringe width will remain unchanged.
Q.15 To make the central fringe at the centre O, a mica sheet of refractive index 1.5 is introduced. Choose the correct statements (s).
(A) The thickness of sheet is infront of S1.
(B) The thickness of sheet is infront of S2.
(C) The thickness of sheet is infront of S1.
(D) The thickness of sheet is infront of S1.
Question No. 16 to 19 (4 questions)
The figure shows a schematic diagram showing the arrangement of Young's
Double Slit Experiment
Q.16 Choose the correct statement(s) related to the wavelength of light used
(A) Larger the wavelength of light larger the fringe width
(B) The position of central maxima depends on the wavelength of light used
(C) If white light is used in YDSE, then the violet colour forms its first maxima closest to the central maxima
(D) The central maxima of all the wavelengths coincide
Q.17 If the distance D is varied, then choose the correct statement(s)
(A) The angular fringe width does not change
(B) The fringe width changes in direct proportion
(C) The change in fringe width is same for all wavelengths
(D) The position of central maxima remains unchanged
Q.18 If the distance d is varied, then identify the correct statement
(A) The angular width does not change
(B) The fringe width changes in inverse proportion
(C) The positions of all maxima change
(D) The positions of all minima change
Q.19 Identify the correct statement(s) if the source slit S moved closer to S1S2, i.e. the distance l decreases
(A) nothing happens to fringe pattern (B) fringe pattern may gets less sharp
(C) fringe width remains unchanged (D) fringe pattern may disappear




Answer Key

Only one option is correct.
Q.1 A Q.2 C Q.3 C Q.4 C Q.5 C Q.6 D Q.7 A
Q.8 A Q.9 D Q.10 D Q.11 B Q.12 D Q.13 B Q.14 C
Q.15 B Q.16 D Q.17 B Q.18 C Q.19 B Q.20 A Q.21 C
Q.22 D Q.23 C Q.24 D Q.25 A Q.26 A Q.27 A Q.28 A
Q.29 C Q.30 C Q.31 A Q.32 C Q.33 C Q.34 D Q.35 A
Q.36 D Q.37 A Q.38 A Q.39 D Q.40 A Q.41 C Q.42 C
Q.43 A Q.44 C Q.45 B Q.46 A Q.47 C Q.48 B Q.49 C
Q.50 C Q.51 A Q.52 A Q.53 D Q.54 B Q.55 B Q.56 A
One or more than one option may be correct
Q.1 B,D Q.2 A,C Q.3 A Q.4 B
Q.5 A,D Q.6 A,C Q.7 B,C,D Q.8 B,C
Q.9 B Q.10 A,C Q.11 D Q.12 A
Q.13 B Q.14 A,C,D Q.15 A Q.16 A,C,D
Q.17 A,B,D Q.18 B,D Q.19 B,C,D

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