RANK ENHANCEMENT SHEET GEOMETRICAL OPTICS JEE Advance

Straight Objective Type

1. A glass sphere (µ = 1.5) with an inbuilt point source of light P eye

is placed on a table. The source P is just inside the surface of

glass and lies on the lower end of the vertical diameter. The Glowing
apparatus is placed in a dark room. The surface area of the portion
glowing portion of the glass sphere as observed by the eye is
1 2 2 2
Glass
(A) (4πR ) (B) (4πR ) R
2 3 O sphere
4 2 5 2
(C) (4πR ) (D) (4πR )
9 9 P
Small point source
of light

2. If the optic axis of convex and concave f = 20 cm

lenses are separated by a distance 5 mm f = −10

as shown in the figure. Find, the co- Principle axis of concave lens
ordinate of the final image formed by the (0,0) 5 mm
Principle axis of convex lens
combination if parallel beam of light is
incident on lens origin is at the optical
centre of convex lens. 30 cm

(A) (25 cm, 0.5 cm) (B) (25 cm, 0.25 cm)
(C) (25 cm, 0.5 cm) (D) (25 cm, −0.25 cm)

3. A ray of light is incident on a plane mirror along a line represented by ˆi + ˆj + kˆ . The possible
vector orientation parallel to the plane of the mirror to get the light retraced is
(A) 2iˆ − 4ˆj + 2kˆ (B) ˆi − ˆj − kˆ
(C) 2iˆ + ˆj − 2kˆ (D) −ˆi − ˆj − kˆ

4. A slab of thickness 10 cm is kept on x-y plane (z=0) and its refractive index varies as
 Z 
µ = 1.63  1 +  where Z is in cm. If it is viewed from top its apparent thickness will be (in cm)
 20 
(A) 5 (B) 6
(C) 4 (D) 3

5. A light ray (AB) incident parallel to principal axis (xy) at a distance of

A
R/2 from principal axis as shown. If BCD is reflected ray which B
intersect principal axis at C. The value of x if O be centre of R/2
curvature P be the pole of concave mirror. O C P
X x Y
(A) R/2 (B) 3R/8 R

(C)
R ( 3 −1) (D) none of these
D

6. A light ray AB is incident normally on a glass plate of thickness t = A C E

i=0
1µm and refractive index µ = 1.5 as shown. Find the phase
B D µ=1
difference between the light ray BC & DE if wavelength of light
incident is λ = 500 nm. 1 µm
(A) 12 π (B) 13π
µ = 1.5
(C) 14π (D) none of these
µ = 1.6

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RANK ENHANCEMENT SHEET GEOMETRICAL OPTICS JEE Advance

7. A point object is moving with a velocity of 4 cm/s in front of a

4 cm/s
concave mirror of focal length 100 cm. The object is at a distance of
30o
50 cm from the mirror. The speed of the image at the given instant is
(A) 208 m/s (B) 196 m/s
(C) 108 m/s (D) 98 m/s

8. In the displacement method, magnifications for two positions of the lens are 3 and 2 and distance
between the two positions of lens is 30 cm. The focal length of the lens is
(A) 30 cm (B) 20 cm
(C) 10 cm (D) 15 cm

9. The critical angle for a prism and its surrounding interface is 36°. The maximum angle of prism
for which any emergent ray is possible is
(A) 18° (B) 36°
(C) 72° (D) 144°

10. The adjacent figure shows cross section of a hollow glass tube of C B
internal radius r, external radius R and index of refraction n. For two r1 A
rays DE and ABC (in which DE lies on ODE and DE and BC are or
parallel), the separation r1 will be E D air
(A) r1 = (n − 1)R
2
(B) r1 = n R glass
2
(C) r1 = nr (D) r1 = n r

11. An object is projected from A and reaches B on the same horizontal

surface. A plane mirror inclined at an angle θ to the horizontal is placed on
the ground as shown in the figure. Which of the following best describes θ
O A B
the path of the image?
(B) B′

A′
θ
θ O A B
(A) B′ A′ O A B

B′ (D) B′

A′
θ A′ θ
(C) O A B O A B

12. ABCD represents a square glass block of refractive index 3/2. An object O is O
A B
placed near the face AB as shown. When observed from face AD, the object will
(A) appear midway between A and D (B) appear nearer to A
(C) appear nearer to D (D) not be seen at all
D C

13. STATEMENT-1: The focal length of a lens depends on the material of the lens but the focal
length of a mirror is independent of the material from which the mirror is made.
because
STATEMENT-2: Law of reflection is independent of material and surrounding medium where as
law of refraction depends on the mediums.
(A) Statement-1 is True, Statement-2 is True; Statement -2 is a correct explanation for
Statement-1.
(B) Statement-1 is True, Statement-2 is True; Statement -2 is NOT a correct explanation for
Statement-1.

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RANK ENHANCEMENT SHEET GEOMETRICAL OPTICS JEE Advance

(C) Statement -1 is True, Statement-2 is False.

(D) Statement -1 is False, Statement-2 is True.

14. An object is moving with speed v parallel to mirror M2. Relative velocity M1
of the image in M1 w.r.t. the image in mirror M2 will be
(A) 2v sin2α (B) 2v sinα
α
2v
(C) (D) 2v tanα
sin2α

v
M2

O Observer
15. Two identical rectangular glass-
slabs of different materials whose
P″″ B′′ air
height is 1m has a thin cylindrical
wire. Observer is situated at O in M Interface

air as shown in the figure. If the A′′ P′′ Glass I Glass II

90 cm
end points of image of the wire AP µ = 1.5 µ = 1.8
is A′P′ and PB is P″B′. If we join A A P B 10 cm
to P″ and P′ to B′, it will form a
AP = PB = 2 mm
parallelogram. The area of
OM = 2 m
parallelogram will be
2 2
(A) 2 cm (B) 1 cm
2 2
(C) 2 mm (D) 1 mm

16. A light ray incident along vector 2iˆ + 4ˆj + 5kˆ strikes on the x-z plane from medium I of
refractive index 3 and enters into medium II of refractive index is µ2. The value of µ2 for which
the value of angle of refraction becomes 90°, is
4 3 3 3
(A) (B)
5 5
2 3 3
(C) (D)
5 5

17. A glass prism of refractive index µ is kept in air as shown in the A

figure. An incident ray strikes at face AB at point M at an angle of 90°° A

incidence i. A is the angle of prism. Choose the correct statement. i
M
(A) For all value of angle of incidence i, the ray will emerge out Air Air
µ
from face AC if µ sin A > 1
(B) For all value of angle of incidence i, the ray will not emerge out B C

from face AC if µ sin (A/2) > 1.

(C) If A = 45° and µ = 2 , the maximum deviation will occurs at i =
0°
(D) If A = 60° and µ = 2 , the minimum deviation will occurs at i = 60°

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RANK ENHANCEMENT SHEET GEOMETRICAL OPTICS JEE Advance

R
18. The image of a point source, kept at origin O,
10 cm
forms at point A due to transparent sphere of 40 cm
radius 10 cm as shown in the figure. Here OX is
O P C Q A x
the optical axis of the sphere. Now, the sphere is
cut into two equal parts, along a plane
S
perpendicular to the horizontal axis OX and the
plane surface of the left half (PRCS) is silvered.
The right half (PQSC) is removed. Now the co-
ordinate of image of point source O formed by
remaining silvered hemisphere will be
(A) (10 cm, 0) (B) (20 cm, 0)
(C) (30 cm, 0) (D) (40 cm, 0)
Ist Refracting IInd Refracting
surface surface
19. Upper part of a prism is cut. Ray diagram of a ray incident
36°° 32°°
at first refracting surface is as shown in the diagram.
Minimum deviation that can be given by two refracting 67°° 53°°
surfaces for any ray may be
(A) 10°
(B) 12°
(C) 8°
(D) less than 8°

20. A ray of light is incident at the origin at an angle Y

o
60 with Y-axis as shown in figure. The refractive
index is a function of y according to the
2
relation µ = . What is the value of H, shown H
1+ y2
in figure?
2
(A) −1
3
2 X
(B) 60o
3 The path of the light
(C) ( 3 − 1) followed after successive
refraction is as shown
(D) none

21. A black spot is present just inside one of the face of an equilateral prism. A
man places his eye directly at the opposite corner. He sees two images of
o
the spot at an angular separation of 60 . Then the minimum value of
refractive index of the prism is:
3
(A) µ = (B) µ = 2
2
3 2
(C) µ = (D) µ =
2 3
Black spot

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RANK ENHANCEMENT SHEET GEOMETRICAL OPTICS JEE Advance

22. The refractive index of space changes with y, whose function is given as
 y B
1 if y≤0 2y0

µ(y) =  ky 2 if 0 ≤ y ≤ 2y 0 y0


 2 if 2y 0 ≤ y ≤ 4y 0 A x
 y α

where k and
are positive constant. When a light ray is incident at point A as shown in figure.
When the ray reaches to point B, it becomes parallel to xz-plane. Choose the correct statement.
(A) α is independent of k (B) α is independent of

(C) α is independent of both k and
(D) none of these

23. The plane side of a thin plano convex lens is silvered so that the lens acts as concave mirror of
focal length 40 cm. The material of lens has refractive index 1.5. The radius of curvature of the
curved surface of the lens is
(A) 30 cm (B) 40 cm
(C) 50 cm (D) 60 cm

24. The approximate maximum angle of incidence of a ray that will

60o
not be transmitted through the prism as shown is figure is
(A) 30° (B) 60°
θ
(C) 15° (D)45°
µ = 7/3

Multiple Correct Answer Type

1. A long tube contains a single optical device. Parallel beam of

light entering from one end is found coming out diverging.
Optical device may be
(A) converging lens (B) diverging lens
(C) Plane mirror (D) prism

2. A lens forms a blurred image of a point object on a screen as

shown in figure. Which of the following can lead to a sharp
image on the screen? O
(A) By moving the screen towards lens
(B) By moving the object towards lens
(C) By using a lens of larger focal length
(D) By using a lens of smaller focal length

3. An object is placed at a distance 40 cm from a convex

lens of focal length = 20 cm. A concave mirror of focal
length 30 cm is also place on other side of lens at a
distance 100 cm. Final image of object is formed
through lens after reflection from mirror ; then
(A) The final image is real, erect and of same size of
object
(B) The final image is real, inverted and of same size of object
(C) Distance between final image and mirror is 60 cm
(D) Distance between final image and lens is 40 cm
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RANK ENHANCEMENT SHEET GEOMETRICAL OPTICS JEE Advance

4. A point source S of light is fixed on a vertical wall and plane wall

mirror starts moving with a velocity v towards the wall. The S

adjoining figure shows the top view of the situation. Now

v
choose the correct option(s) y

v
(A) Velocity of light spot formed on the wall is î d x
2
(B) Light spot is at rest
(C) size of the light spot would increase
(D) size of the light spot would remains same.

5. A hollow cardboard tube contains a single or combination of

two optical devices. If a parallel beam of light is incident
from left, along the axis of the tube and a parallel beam
emerges from the right along the axis, which of the
following optical system can be used inside the tube
(A) converging lens + diverging lens (B) converging lens + converging lens
(C) diverging lens + diverging lens (D) prism

COMPREHENSION TYPE

Paragraph for Question Nos. 1 to 3

A small fish touching the surface of a spherical air bubble is observed from µ=4/3
opposite surface from point P. The diameter of bubble is 12 cm. (Refractive
index of water is 4/3). Answer following questions on basis of above said P
B
situation. A 12cm

1. Find the location of image of fish, assuming B as origin.

(A) +9.6 cm (B) −9.6 cm
(C) −48 cm (D) −96 cm
2. The fish will appear
(A) touch to the surface of bubble
(B) Inside the bubble
(C) At some distance behind the surface of bubble
(D) none of the above
3. The shape of bubble will appear to be
(A) spherical (B) conical
(C) ovalaoid (D) none of the above
Paragraph for Question Nos. 4 to 6

N
A ray goes from medium I to medium II of refractive indices as µ1
and µ2 respectively [As shown in the figure]. The Medium II
µ2 Interface
refractive index of medium I and medium II can be
Medium I O
changed and hypothetically their ranges are given by 1 ≤ µ1
µ1 < ∞ and 1 ≤ µ2 < ∞. i = 60°°

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RANK ENHANCEMENT SHEET GEOMETRICAL OPTICS JEE Advance

An experiment is performed, keeping i = 60° as constant. First µ2 δ

is increased from 1 to infinity keeping µ1 = 1 and θ0
Region
deviation δ is calculated. Then the refractive index of II
Region III
medium I is increased from 1 to infinity keeping µ2 = 1 θ1
Region
and deviation δ is noted. Now an approximate graph I
between δ and k = µ1/µ2 is plotted which is shown in the k0 k
figure.
Read the above passage carefully and answer the following question
4. The value of θ0/θ1 is equal to
(A) 1.0 (B) 2.0
(C) 1.5 (D) 2.5

5. The value of k0 is equal to

(A) 1.0 (B) 2.0
(C) 1.5 (D) 2.5

6. The phenomenon of total internal reflection will take place in the which region
(A) I (B) II
(C) III (D) none of the above

Paragraph for Question Nos. 7 to 9

An experiment is performed on thin lens in order to determine the radii R1 and R2 of the curvature of its two
surfaces and the refractive index ‘µ’ of its glass.
Experiment I: A real object is placed 36 cm to the left of lens and a real image is formed 72 cm to the right
of lens.
Experiment II: The lens is floated on the surface of mercury with surface having radius of curvature R2
faces air. A real object is placed at 60 cm above it, and a real image is formed at 30 cm above it (assume
mercury to be perfectly reflecting).
Experiment III: The lens is floated on the surface of mercury with surface having radius of curvature R1
20
faces air. A real object is placed at 7.5 cm above it and real image is formed at cm above it. On the
3
bases of Experiments I, II and III, answer the following questions.

7. The refractive index of material of lens is

(A) 1.6 (B) 1.75
(C) 2 (D) none

8. The magnitude of R1 is
(A) 60 cm (B) 30 cm
(C) 120 cm (D) 45 cm

9. The lens can be best represented by

(A) (B)

R1 R2
R1 R2

Biconvex Biconcave
(C) (D)

R2 R1
R2 R1
Convexo-concave Concavo-convex
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RANK ENHANCEMENT SHEET GEOMETRICAL OPTICS JEE Advance

Paragraph for Question Nos. 10 to 12

A point object is placed at a distance 5R/3 from the pole of a ĵ

concave mirror. R is the radius of curvature of mirror. Point
î
object oscillates with amplitude of 1 mm perpendicular to the
principle axis. O Principle axis

10. The amplitude of image is

(A) 3/7 mm (B) 2/7 mm
(C) 4/3 mm (D) 11/7 mm
11. Phase difference between motion of object and image when object crosses the principle axis is
(A) π (B) 0
(C) π/2 (D) none of these
12. Position of image when object is at O
(A) 5/7 R (B) −5/7 R
(C) 4/7 R (D) −4/7R

Paragraph for Question Nos. 13 to 15

A thin converging lens (L1) of focal length f = 12 f1 = 12 cm

cm is placed along y-axis such that its optical S
centre coincides with the origin. A small light (-20, 2)
C1 C2
source S is placed at (-20 cm, 2 cm). Another
(0, 0)
lens (L2) is placed along x-axis such that it (29.5, 0) f2 = 6 cm
centre is located at (29.5 cm, 0) and focal
length 6 cm as shown in diagram.

13. Coordinate of image of source S is

(A) 30 cm, 3 cm (B) 29.96 cm, -2.81 cm
(C) 29.83 cm, −2 cm (D) 31 cm, −3.2 cm

14. If source moves downwards with velocity 4 cm/s, its image will move with speed
8
(A) 6 cm/sec (B) cm/sec
3
72
(C) cm/sec (D) None
3

15. If convex lens L2 is replaced by plane mirror, then final coordinate of image will be
(A) (28 cm, 2 cm) (B) (30 cm, 2 cm)
(C) (30 cm, -2 cm) (D) (30 cm, 3 cm)

Matrix Match Type

1. Two converging lenses L1 of focal length f1 (large) and L2 L1 , f 1

focal length f2 (small) are placed coaxially such that L2 , f 2

distance between them is greater than f1 but less than

f1 + f2. Lens L1 forms a real image of a distant object left to d
f1 < d < f1 + f2
it on its axis which works as an object O for lens L2. L2
forms image I of object O. Match the column

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RANK ENHANCEMENT SHEET GEOMETRICAL OPTICS JEE Advance

Column I Column II
(A) L1 shifts slightly to right (p) Image I shifts slightly to right
(B) L1 shifts slightly up (q) Image I shifts slightly to left
(C) L2 shifts slightly to right (r) No shift of Image I along axis
(D) L2 shifts slightly up (s) Image I becomes bigger
(t) Image I becomes smaller

2. Match the following graphs (in column – II) between position of object (u) and position of image (v).
Take positive sign in the direction of ray.

Column – I Column – II
v
(A) Concave mirror (p)

O
u

v
(B) Convex mirror (q)

O
u

v
(C) Convex lens (r)

O
u

v
(D) Concave lens (s)
O
u

3. A very small circular object is kept infront

of an optical device as shown in figure. A B
The plane of object is parallel to the
optical device. Match the images as seen Object
by the observer (ignoring magnification). Optical Device
Column – I Column – II
Device Probable Image
(A) Plane mirror (The observer is at A) (p)

(B) Concave mirror (The observer is at (q)

A)

(C) Convex mirror (The observer is at A) (r)

(D) Convex lens (The observer is at B) (s)

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RANK ENHANCEMENT SHEET GEOMETRICAL OPTICS JEE Advance

4. A child in a toy car is moving towards a cubical

container with a velocity of 3 cm/s, whereas fish is

Plane mirror
air
moving towards child with a velocity of 4 cm/s as µ = 4/3 4 cm/s
3 cm/s
shown in the figure. The wall behind the fish is silvered
(Refractive index of water is µ = 4/3). Match the
following
Column – I Column – II
(A) Velocity of child as observed by fish by one refraction only (p) zero
(B) Velocity of fish as observed by child by one refraction only (q) 6 cm/s
(C) Velocity of image of fish by reflection from mirror as (r) 8 cm/s
observed by child.
(D) Velocity of image of child by reflection from mirror as (s) 7 m/s
observed by fish

5. A spherical interface whose radius is R divides

Medium I Medium II
the space in two parts such that the x-axis (µ
µ 1) (µ
µ 2)
behaves as principal axis and origin O Positive
behaves as pole as shown in the figure. The X-axis
O C (R, 0) X
−X
refractive index of medium I is µ1 and that of
medium II is µ2. Now match the column I with
Spherical
column II [Assume concept of paraxial rays] interface

Column I Column II
(A) Object is kept at point (−a, 0) and µ1 < µ2 (p) Image may be real
(B) Object is kept at point (−a, 0) and µ1 > µ2 (q) Image may be virtual
(C) Object is kept at point (+a, 0) and µ1 < µ2 (r) The position of image may be in between the
position of object and origin.
(D) Object is kept at point (+a, 0) and µ1 > µ2 (s) The position of image may be in between the
position of object and centre of
curvature of interface.

6. Match the entries of Column I with entries of Column II for real point object O:
Column I Column II
(A) µ µ 2
(p) Number of images formed is 1
1

O µ µ3
1

mirror
(B) µ2 (q) Number of images formed is 2
µ1

Air µ3

O
µ4
Air

(C) µ2 (r) Number of images formed is 3

µ1

Air Air

O
Air Air

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RANK ENHANCEMENT SHEET GEOMETRICAL OPTICS JEE Advance

(D) Air
µ3 (s) Number of images formed is 4
µ1
µ4
O
µ4
Air

(t) Intensity of image is maximum

Integer Answer Type

O C
1. A point source of source of light S is kept on the axis of a cone of B
radius r and height h as shown in the figure. The inner surface of
S
cone is made reflecting. Determine the minimum value semi-
vertical angle α in degrees of the cone for which the rays emitted α h

from source (S) on the axis of the cone will be reflected from
o
conical surface not more than once. Express answer as (α/10) . A

2. Two identical equi-concave lenses made of glass of reflected index 1.5,

placed in contact has power P. When a liquid of refractive index µ is filled
1 2
in the gap between the concave lenses, the power becomes of initial
K
value(P/3). The value of µ is . Find the value of K.
3
3. Find the magnitude velocity of image of a point object O, with 2m/s 2m/s mirror

respect to object, which is moving with velocity 2 m/s in vertical O

45°°
direction as shown in the figure. The plane mirror that is inclined to
horizontal at 45° is also moving horizontally with velocity 2 m/s as
shown in the figure.

4. The xz plane is the boundary between two transparent medium. Medium –I with y ≥ 0 has
refractive index µ and medium –II with y ≤ 0 has a refractive index 1. A ray of light in medium-I,

given by vector n = ˆi − 3ˆj is incident on the plane of separation. If the reflected and refracted
rays make an angle of 90° with each other, then the value of µ is k . Find the value of k.

5. Light rays can enter from flat surface of a transparent L

cylinder if minimum value of refractive index of material of
cylinder is µ such that no ray can emerge from curved L
R=
20
surface of cylinder. Find µ2 .

6. In the arrangement shown in figure, f = 30 cm

image of light source O is to be obtained
at the bottom of beaker containing water 36 cm 1m
 4 o
 µ = 3  upto height 20 cm. Find the O 45
 
H
value of .
17 H

20 cm

7. There are two thin identical equiconvex lens of different refractive indices but of same radius of
curvature R = 60 cm put inside water close together. The focal length of combined lens is 30 cm
in water then find sum of refractive indices of two lens.

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RANK ENHANCEMENT SHEET GEOMETRICAL OPTICS JEE Advance

8. Find the value of x/4 (in cm) for which all the (paraxial) f = 10 cm R = 10 cm

rays coming from O emerges from the plane refracting

surface along a single path.
O
60°°
30 cm
x
µ=2

9. A body of mass 100 gm is attached to one end of a massless string and

released when both the springs are in natural lengths as shown in figure. k1
Consider the string and pulley to be massless. The distance between the
pole of mirror and mean position of body is 20 cm. The focal length of the
convex mirror is 10 cm. The displacement of the image corresponding to
k2
the displacement of block from mean position to lower extreme position is
0.67β cm. Find the value of β . (given k1 = k2 = 100 N/m)
10. Due to a vertical temperature gradient in the atmosphere the index of refraction varies. Suppose
index of refraction varies as n = n0 1 + ay where n0 is the index of refraction at the surface and
6
a = 2.0 × 10− per metre. A person of height h = 2.0 m stands on a level surface. Actual distance
from the person of the farthest point on the road beyond which nothing is visible to him is equal to
1000 λ meter. Then find the value of λ.

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RANK ENHANCEMENT SHEET GEOMETRICAL OPTICS JEE Advance

ANSWERS

Straight Objective Type

1. C 2. B 3. A 4. A 5. C
6. A 7. A 8. A 9. C 10. C
11. C 12. D. 13. A 14. B 15. A
16. B 17. B 18. C 19. B 20. A
21. D 22. A 23. B 24. A

Multiple Correct Answer Type

1. A, B 2. A, B, C 3. B, D 4. B, D 5. A, B, D

COMPREHENSION TYPE
1. B 2. A 3. C 4. B 5. A
6. C 7. D 8. A 9. D 10. A
11. A 12. B 13. C 14. B 15. D

Matrix Match Type

1. (A) → (p,t), (B) → (r), (C) → (q,s), (D) → (r)

2. (A)→ (p), (B)→ (s), (C)→ (q), (D)→ (r)
3. (A)→ (p), (B)→ (p, q), (C)→ (p), (D)→ (q, s)
4. (A)→ (r), (B)→ (q), (C)→ (p), (D)→ (p)
5. (A) → (p, q), (B) → (q, r, s), (C) → (p, q, r), (D) → (q, r, s)
6. (A) – (p, t); (B) – (q); (C) – (p, t); (D) – (q)

Integer Answer Type

1. 6 2. 5 3. 0 4. 3 5. 2 6. 5
7. 4 8. 5 9. 1 10. 2

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