Section – 1
Physics
1.
2.
3.
4.
A plane mirror is moving with velocity 4i + 5j + 8k. A point object in front of the mirror moves
with a velocity 3i + 4j + 5k. here k is along the normal to the plane mirror and facing towards
the object. The velocity of the image is:
(a) – 3i – 4j + 4k
(b) 3i + 4j + 11k
(c) -3i – 4j + 11k
(d) 7i + 9j + 11k
A ray of monochromatic light is incident on one refracting face of a prism of angle 750. It passes
through the prism and is incident on the other face at the critical angle. If the refractive index of
the material of the prism is 2 , the angle of incidence on the first face of the prism is
(a) 300
(b) 450
(c) 600
(d) 00
A convexo – concave diverging lens is made of glass of refractive index 1.5 and focal length
24cm. Radius of curvature for one surface is double that of the other. Then radii of curvature for
the two surfaces are (in cm):
(a) 6, 12
(b) 12, 24
(c) 3, 6
(d) 18, 36
A ray of light travelling in the direction
reflection, it travels along the direction
5.

1
(i  3 j ) is incident on a plane mirror. After
2

1
i  3 j . The angle of incidence is
2
(a) 300
(b) 450
(c) 600
(d) 750
A linear object AB is placed along the axis of a concave mirror. The object is moving towards the
mirror with speed V. The speed of the image of the point  is 4V and the speed of the image of
B is also 4V. If centre of the line AB is at a distance L from the mirror then length of the object
AB will be
B
//
(a)
3L
2
(b)
5L
3
/ ///
A
/ // / //////// // ////
///
/ // //
/
(c) L
(d)
4L
3
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6.
A small rod ABC is put in water making angle 60 with vertical. If it is
viewed (paraxially) from above, it will look like bent shaped ABC’. The


angle of bending ( CBC’) will be in degree……  nw 
(a) 20
(c) 40
4

3
(b) 30
(d) 4.50
7.
A concave lens of glass, refractive index 1.5, has both surfaces of same radius of curvature R. On
immersion in a medium of refractive index 1.75, it will behave as a
(a) convergent lens of focal length 3.5 R
(b) convergent lens of focal length 3.0 R
(c) divergent lens of focal length 3.5 R
(d) divergent lens of focal length 3.0 R
8.
The dispersive power of the material of a lens is 0.04 and the focal length of the lens is 10cm.
Then the difference in the focal length of the lens for violet and red colour is:
(a) 1 mm
(b) 2 mm
(c) 3 mm
(d) 4 mm
9.
The angle of minimum deviation from a prism is 600. If the prism angle is 900, the refractive
index of the material of the prism and the angle of incidence required for minimum deviation is:
(Given that sin 750 = 0.96)
(a)
10.
sin 750
, 450
sin 450
(b)
sin 750
, 750
sin 450
(c)
2
sin 750
, 750
sin 450
(d)
2, 750
Figure shows a concavo- convex lens of refractive index 2. What is the condition on the
refractive indices so that the lens is diverging?
(a) 23 < 1 + 2
(b) 23 > 1 + 2
(c) 3 > 2 (1 - 2)
(d) None of these
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11.
A bird is flying up at angle sin-1 (3/5) with the horizontal. A fish in a pond looks at that bird.
When it is vertically above the fish. The angle at which the bird appears to fly (to the fish) is
[ nwater = 4/3]
(a) sin-1 (3/5)
(b) sin-1 ( 4/5)
(c) 45
(d) sin-1 (9/16)
12.
The given lens is broken into four parts rearranged as shown. If the initial
focal length is f, then after rearrangement the equivalent focal length is
(a) f
(c) f/4
13.
Two identical plano- convex Lenses L1 (1 = 1.4 ) and L2 (2 = 1.5) of
radii of curvature R = 20 cm are placed as shown in fig. Find the
position of the image of the parallel beam of light relative to the
common principal axis .
(a) 100 / 7 cm
(c) 31.2 cm
14.
(b) f/2
(d) 4f
(b) 200 / 9 cm
(d) 21.8 cm
A white light ray is incident on a glass prism, and it
create four refracted rays A, B, C and D. Match the
refracted rays with the colors given ( 1 and D are rays
due to total internal reflection):
Column I (Ray)
(i) A
(ii) B
(iii) C
(iv) D
(a) i –p, ii-r, iii- q, iv-s
(c) i –s, ii-q, iii-r, iv- p
Column II (Colour)
(p) Red
(q) green
(r) yellow
(s) blue
(b) i –q, ii-r, iii-p, iv – s
(d) i,-p, ii-q, iii-r, iv-s
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15.
For a prism of refracting angle A and refractive index 2.
Assume rays are incident at all angles of incidence 0  i
 90 . Ignore partial reflection.
Column I
(p) A = 15
(q) A = 45
(r) A = 70
(s) A = 50
16.
Column II
(a) All rays are reflected back from the second surface
(b) All rays are refracted into air from the second face
(c) Some rays are reflected back from second surface
(d) Some rays are refracted into air from the second surface
(a) p-b, q-c,d , r-a, s- c,d
(b) p-b,c , q-a,d, r- c, s- b
(c) p-b , q-a, r- c, s- a
(d) p-c , q-d, r- c, s- b
Two beams of red and violet colors are made to pass separately through a prism (angle of the
prism is 60). In the position of minimum deviation, the angle of refraction will be.
17.
(a) 30 for both the colors
(b) greater for the violet color
(c) greater for the red color
(d) equal but not 30 for both the colors
Figure shows graph of deviation  versus angle of incidence for a light ray
striking a prism. Angle of prism is.
(a) 30 
(b) 45
(c) 60
(d) 75
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18.
A ray of light is incident on an equilateral triangular prism parallel
to its base as shown in the figure. The ray just fails to emerge from
the face AC. If  be the refractive index of the prism then the correct
relation is:
1 
=
 3
1
 1  
(c) sin-1   +sin-1 
=

 2  3
(a) 2 sin-1 
1
 1  
 +sin-1 
=

 2  6

 
(d) sin-1   +sin-1   =
2
4 3
(b) sin-1 
19.
A thin equiconvex lens (  = 3/2) of focal length 10 cm is cut and
separated and a material of refractive index 3 is filled between them.
What is the focal length of the combination?
(a) – 10 cm
(b) – 10 / 4 cm
(c) – 10/3 cm
(d) None of these
20.
What should be the value of distance d so that final image is
formed on the object itself. (Focal length of the lenses are written
on the lenses)
(a) 10 cm
(b) 20 cm
(c) 5 cm
(d) None of these
21
A cubic container is filed with a liquid whose refractive index increases linearly from top to
bottom. Which of the following represents the path of a ray of light inside the liquid?
(a)
(b)
(c)
(d)
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22.
A square ABCD of side 1 mm is kept at distance 15 cm in front of the
concave
mirror as shown in fig. The focal length of the mirror is
10 cm. The length
of the perimeter of its image will be:
(a) 8 mm
(b) 2 mm
(c) 12 mm
(d) 6 mm
23.
Let r and r’ denote the angles inside an equilateral prism, as usual, in
degrees. Consider that during some time interval from t = 0 to t = t,
r’ varies with time as r’ = 10 + t2.During this time r will vary as
(assume that r and r’ are in degree)
(a) 50 – t2
(b) 50 + t2
(c) 60 – t2
(d) 60 + t2
24.
Find the net deviation produced in the incident ray for the
optical instrument shown in fig. (Take refractive index of the
prism material as 2).
(a) 66 CW
(b) 66ACW
(c) 54ACW
(d) 54CW
25.
The xy – plane separates two media A and B of refractive indices
1 = 1.5 and 2 = 2. A ray of light travels from A to B. Its direction in the two media are given
by unit vectors u1 =ai+bj and u 2  ci  dj . Then:
(a) (a/c) = ( 4/3)
(b) (a/c) = ( 3/ 4)
(c) ( b/d) = ( 4 / 3)
(d) ( b / d) = ( 3 / 4)
26.
Two identical thin plano – convex lenses of refractive index n are silvered, one on the plane side
and the other on the convex side. The ratio of their focal lengths is:
n
n 1
n 1
(a)
(b)
(c)
(d) n
n 1
n
n
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27.
Solar rays are incident at 45 on the surface of water  = 4/3. What is the length of the shadow of
a pole of length 1.2 m erected at the bottom of the pond if the pole is vertical assuming that 0.2
m of the pole is above the water surface?
(a) 1 m
(b) 0.75
(c) 0.825 m
(d) 1.2 m
28.
Seeta and Geeta were asked to draw the trajectory of a light ray near, earth’s surface when
refractive index is decreasing with increase in height. Figure shows the respective ray diagrams:
Vertically up
Earth’s surface
Seeta
(a) Seeta is correct
(c) Both are incorrect
Vertically up
Earth’s surface
Geeta
(b) Geeta is correct
(d) No conclusion can be drawn
29.
For light incident from air on a meta – material, the appropriate ray diagram is
30.
Variation of v with u for a spherical mirror is as shown in fig. this curve is a
hyperbola. A straight line of unit slope intersects the hyperbola at point ‘A’. If
the focal length of mirror is 20 cm, coordinates of point A are:
(a) 20 cm, 10 cm
(b) 40 cm, 40 cm
(c) 40 cm, 20 cm
(d) 20 cm, 20 cm
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Section – 2
Chemistry
31.
What is the decreasing order of stability of the ions?
H3C HC
+
H3C HC
CH3
32.
+
O
H3C HC
CH3
CH3
(I)
(II)
O (III)
(a) I  II  III
(b) II  III  I
(c) III  I  II
(d) II  I  III
Which of the following resonating structures of 1-methoxy-1,3-butadiene is least stable?
()
(-)
(a) C H2  CH  CH  CH  O  CH 3
(-)
(+)
(c) C H2  C H CH  CH  O  CH 3
33.
+
()
(-)
(b) CH2  CH  C H  CH  O  CH3
(-)
(+)
(d) CH 2  CH  C H  C H  O  CH 3
The correct order of basicities of the following compounds is
NH
CH3  C
NH2
1.
(a) 2 > 1 > 3 > 4
34.
35.
O
2. CH3  CH2  NH2
(b) 1 > 3 > 2 > 4
3. (CH3)2NH
(c) 3 > 1 > 2 > 4
CH  C  NH2
3
4.
(d) 1 > 2 > 3 > 4
The dipole moment of NF3 is very much less compared to that of NH3 because
(a) The size of Natom is much less than that of Hatom
(b) Fatom is more electronegative than Natom, whereas Hatom is less electronegative than
Natom
(c) Unshared electron pair is not present in NF3
(d) Number of lone pairs in NF3 is much greater than in NH3

–
The bond angles of NH3, NH4  and NH2 are in the order :
(a) NH2  NH3 > NH+
4
(b) NH4  NH3 > NH2–
(c) NH3  NH2– > NH4+
(d) NH3  NH4+ > NH2–
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36.
Molecular shapes of SF4, CF4 and XeF4 are
(a) the same, with 2, 0 and 1 lone pairs of electrons respectively.
(b) the same, with 1, 1 and 1 lone pairs of electrons respectively.
(c) different, with 0, 1 and 2 lone pairs of electrons respectively.
(d) different, with 1, 0 and 2 lone pairs of electrons respectively.
37.
The correct order of hybridization of the central atom in the following species NH3, [PtCl4]2,
PCl5 and BCl3 is
(a) dsp2, dsp3, sp2 and sp3
(b) sp3, dsp2, dsp3, sp2
(c) dsp2, sp2, sp3, dsp3
(d) dsp2, sp3, sp2, dsp3
38.
Which of the following molecular species has unpaired electron(s)?
(a) N2
39.
40.
41.
(b) F2

(c) O 2
2
(d) O 2
The nodal plane in the bond of ethene is located in
(A) the molecular plane
(B) a plane parallel to the molecular plane
(C) a plane perpendicular to the molecular plane which bisects the carboncarbon bond at
right angle
(D) a plane perpendicular to the molecular plane which contains the carboncarbon bond.
Which of the following hydrocarbons has the lowest dipole moment?
CH3
H 3C
C=C
H
H
(a)
(b) CH3C  CCH3
(c) CH3CH2C  CH
(d) CH2 = CH  C  CH
Match the following column (A) and (B).
(A)
(B)
1.
KO2
(I)
Diamagnetic
2.
Na2O2
(II) Conduction of Electricity
3.
Na/NH3
(III) Paramagnetic
(a) 1–(I), 2–(II), 3–(III)
(b) 1–(III), 2–(I), 3–(II)
(c) 1–(II), 2–(I), 3–(III)
(d) 1–(III), 2–(II), 3–(I)
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42.
How many sp2 and sp-hybridised carbon atoms are present respectively in the
following compound?
(a) 4, 2
(c) 3, 3
43.
(b) 6, 0
(d) 5, 1
The correct order of boiling point is:
(a) I > II > III
(b) III > II > I
(c) II > I > III
(d) III > I > II
44.
Which has maximum dipole moment
45.
Which of the following is the correct order for increasing bond angle?
(a) NH3 < PH3 < AsH3 < SbH3
(b) H2O < OF2 < Cl2O
(c) H3Te+ < H3Se+ < H3S+ < H3O+
(d) BF3 < BCl3 < BBr3 < BI3
46.
Which of the following species contains minimum number of atoms in ‘XY’ plane?

(a) X e F5
47.
(b) SF6
(c) IF7
(d) All
In which of the following pairs, both the species have the same hybridisation?



3
(I) SF4, XeF4
(II) I 3 , XeF2
(III) ICl4 , SiCl4
(IV) ClO3 , PO4
(a) I , II
(b) II, III
(c) II, IV
(d) I, II, III
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Passage 48 to 50
According to VBT the extent of overlapping depends upon types of orbitals involved in
overlapping and nature of overlapping. More will be the overlapping and the bond energy will
also be high.
48.
The incorrect order of bond dissociation energy will be:
(a) H –H > Cl – Cl > Br-Br
(b) Si – Si > P – P > Cl – Cl
(c) C – C > N – N > O – O
(d) H – Cl > H – Br > H – I
49.
Which of the following combinations of oirbitals does not form covalent bond (x-axis is inter
nuclear axis)
(a) s + Py
(b) Py + Py
(c) dyz + dyz
(d) dxy + dxy
50.
Which of the following compound does not form p- p bond?
(a) SO3
51.

(b) NO3
2
(c) SO4
2
(d) CO3
Choose the correct Newman projection for 2-methylpentane
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52.
Number of the positional isomer are:
54.
(a) 4
(b) 5
(c) 6
How many structural isomers of C6H12 having 3-meber ring?
(a) 4
(b) 5
(c) 6
Which of the following compound will not show geometrical isomers?
55.
How many geometrical isomers are possible for?
56.
(a) 2
(b) 3
Which of the following compound is chiral?
53.
(c) 4
(d) 7
(d) 7
(d) 6
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57.
In which of the following compound have plane of symmetry?
58.
How many plane of symmetry is present in above compound?
(a) 0
(b) 1
(c) 2
(d) 3
59.
Write the IUPAC name of the following compound:
(a) ethyl-2-(chlorocarbonyl) benzoate
(b) ethyl-2-(chlorocarbonyl) hexanoate
(c) 2-(thoxycarbonyl) benzoyl chloride
(d) None of these
60.
The IUPAC name of the compound is
CONH2
CHO
(a) 2-methyl-6-oxohex-3-enamide
(c) 2-carbamoylhexanal
(b) 6-keto-2-methyl hexanamide
(d) 2-carbamoylhex-3-enal
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Section – 3
Mathematics
n
61.
62.
1
n(n+1) (n+2), then the value of
12
r 1
2n
n
(a)
(b)
(n  1)
n 1
if
 tr =
64.
is
r 1 r
(c)
4n
n 1
a c

c a
(d)
3n
n 1
p r
 is equal to
r p
b a
(d) 
q p
a c
b q

(c) 
c a
q b
16
The H.M. between two numbers is
, their A.M. us A and G.M. is G. If 2A + G2 = 26, then the
5
(b)
numbers are
(a) 6, 8
(b) 4, 8
(c) 2, 8
(d) 1, 8
If 1, 2, 3 …. Are first terms; 1, 3, 5 … are common differences and S1, S2, S3 … are sums of n
terms of given p AP’s; then S1 + S2 + S3 + … + Sp is equal to
(a)
65.
1
t
If a, b, c are in A.P., p, q, r are in H.P. and ap,bq, cr are in G.P., then
(a)
63.
n
np(np  1)
2
(b)
n(np  1)
2
(c)
np( p  1)
2
(d)
np(np  1)
2
66.
If a, b, c are in GP, a – b, c – a, b – c are in HP, then the value a + 4b + c is
(a) 12
(b) 0
(c) 11
(d) 2
If a2 + b2 + c2 = 1, then ab + bc + ca lies in the interval:
67.
(a)  , 2 
(b) [1, 2]
(c)   ,1
(d)  1, 
 2 
2 
 2
2
,  are roots of the equation (x – X) + X + 5 = 0. If 1 and 2 are the two values of  for which
1

 1 
the roots ,  are connected by the relation
(a) 150
68.
(b) 254
If x1 > x2 > x3 and x1, x2, x3 are roots of
then a, b, c are in.
(a) A.P.
(b) G.P.

1
 
 
  4, then the value of 1  2 is
 
2 1
(c) 180
(d) 1022
(c) H.P.
(d) None
x a x b
b
a



; (a, b > 0) and x1 – x2 – x3 = c,
b
a
x a x b
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69.
If a, b are reals of the same sign such that b2  4ab and ,  are roots of ax2 + bx + b = 0, then

b

+
is

a

(a) 2
70.
b
a
(b) 0
(c) 1
(d) none of these
If  and  be the roots of the equation x2 –a(x+1) – b = 0, b  1, then the value of
 2  2  1  2  2  1
is

 2  2  b  2  2  b
(a) 0
71.
72.
73.
74.
75.
76.
(b) 1
(c) 2
The set of values of x, which satisfy 5x + 2 < 3x + 8 and
x2
< 4 is
x 1
(d) 3
(a) ( 2, 3)
(b) ( -, 1)  ( 2, 3)
(c) (-, 1)
(d) ( 1, 3)
2
If the roots of (b – c)x + (c –a )x + (a – b) = 0 are equal, then a + c =
(a) 2b
(b) b2
(c) 3b
(d) b
2
2
If every pair from among the equations x + px + qr = 0, x + qx + rp = 0 and x2 + rx + pq = 0 has
a common root, then sum of three common roots is
(a) 2( p + q + r)
(b) p + q + r
(c) – (p + q + r)
(d) pqr
2
If the equation x + 2(k + 1)x + 9k -5 = 0 has only negative roots, then
(a) k  0
(b) k  0
(c) k  6
(d) k  6
2
4
4
If  and  are the roots of the equation x + ax + b = 0 and  and  are the roots of
x2 – px + q = 0 the roots of x2 – 4bx + 2b2 – p = 0 are always
(a) both non real
(b) both positive
(c) both negative
(d) positive and negative
If ,  are the roots of the equation ax2 + 3x + 2 = 0 (a < 0), then
(a) 0
(b) 1
2 2

is greater than:
 
(c) 2
(d) none of these
2
77.
If ,  are roots of the equation
(a) 225
x2
1

1

– 15x + 1 =0, then the value of  15  +  15 




(b) 900
(c) 223
3
78.
2
is
(d) none of these
3
 
 
 and   where , ,  are roots of the equation
 
 
The quadratic equation, whose roots are 
x3 – 8 = 0:
(a) x2 + x + 1 = 0
(b) x2 + 2x + 4 = 0
(c) x2-2x + 4 = 0
(d) x2 – 2x + 1 = 0
Space for Rough Work
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79
When a, x, y, z, b are in A.P., x + y + z = 15 and when
then the numbers a and b are
(a) 8, 2
(b) 9, 1
80
pq
2( p  q)
The series 1 +
(a)
82.
(c) 7, 3
(d) none of these
If the (2p)th term of a H.P is q and the (2q)th term is p, then the (2(p+q)th term is
(a)
81
1 1 1 1 1
1 1 1 5
, , , , are in A.P.,    ,
a x y z b
x y z 3
4
3
2 pq
pq
(b)
pq
pq
(c)
1 1
1
 2  .......  n1 +….converges to:
4 4
4
3
1
(b)
(c)
4
4
(d)
pq
pq
(d)
1
3
If S1, S2 and S3 denote the sum of first n1, n2 and n3 terms respectively of an A.P., then
S
S1
S
(n2  n3 )  2 (n3  n1 )  3 (n1  n2 ) 
n1
n2
n3
(a) 0
83.
(b) 1
(d) n1n2n3
The sum to n terms of the series
3
5
7
 2
 2
 .... is
2
2
1 1  2 1  22  32
6n
9n
(a)
(b)
n 1
n 1
84.
(c) S1S2S3
(c)
12n
n 1
(d)
3n
n 1
If a1, a2, a3……, an are in H.P then
a3
an
a1
a2
are in
,
,
,......
a2  a3 ..........  an a1  a3 ..........  an a1  a2  a4 ..........  an
a1  a2 ..........  an 1
(a) A.P
85.
(b) G.P
(c) H.P.
(d) A.G.P
If a, a1, a2,….a2n, b are in A.P and g1, g2…..g2n, b are in G.P and h is the H.M of a and b; then
a1  a2 n a2  a2 n 1
a  an1
is equal to

 .......  n
g1 g 2 n
g 2 g 2 n 1
g n g n 1
2n
(a)
(b) 2nh
h
(c) nh
(d)
n
h
Space for Rough Work
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86.
a1,a2…..n are in A.P. then
(a)
87.
88.
89.
90.
n 1
a1an
1
1
1
=:

 ..... 
a1a2 a2 a3
an1an
n 1
n 1
(b)
(c)
a1an
an
(d)
n 1
a1
If S1,S2…..Sp are the sums of n terms of p A.P’s whose first terms are 1,2,….p and common
differences are 1, 3, 5,…..(2p - 1) respectively. Then S1+S2 + S3 + …..+Sp = :
( p  1)n
np(np  1)
(c)
(d) none of these
2
2
1
1
If a, b, c are in H.P and a > c, then
is :

bc ab
4
4
(a) less than
(b) greater than
ac
ac
4
(c) equal to
(d) none of these
ac
3 33 333
Let P =


 .....to  , then p equals:
17 17 2 173
3
7
3
51
(a)
(b)
(c)
(d)
17
17
7
112
9 36 100
The sum of the series 1 + 
+ ….upto n terms of n = 16 is:

4 9 16
(a) np ( p + 1)
(b)
(a) 446
(b) 746
(c) 646
(d) 546
Space for Rough Work
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