1. travel
2. transports
3. air travel
4. airlines

Sample Paper For One Year Course
(+1 Studying Students Moving To +2)
GENERAL APTITUDE (I.Q.)
1.
Find the missing number
36
49
9
26
64
81
2.
24
25
21
25
(A)
25
64
?
16
(B)
25
(C)
144
36
23
(D)
31
A person spends 40% of his salary on food items and 1/3rd of the remaining on transport. After spending
on food items and transport, he spends 50% of the balance on other items and saves Rs. 450/- per month.
His monthly salary is
(A)
3.
Rs.1125/-
(B)
Rs.1575/-
(C)
Rs.2250/-
(D)
Rs.4500/-
60% of the students in a school are boys. If the number of girl students in the school is 300, then the
number of boys is :
(A)
4.
300
(B)
450
(C)
500
(D)
750
If ENGLAND is written as 1234526 and FRANCE is written as 785291, how is GREECE coded ?
(A)
381171
(B)
381191
(C)
832252
(D)
835545
Directions for Q.5 – Q.7
A, B, C, D, E and F are a group of friends. There are two housewives, one professor, one engineer, one
accountant and one lawyer in the group. The lawyer is married to D, who is a housewife. No woman in the
group is either an engineer or an accountant C, the accountant, is married to F, who is a professor. A is married
to a housewife. E is not a housewife.
5.
How many members of the group are males ?
(A)
6.
2
(B)
3
(C)
4
(D)
Cannot be determined
Lawyer
(C)
Professor
(D)
Accountant
What is E’s profession ?
(A)
Engineer
(B)
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7.
Which of the following is one of the married couples ?
(A)
A&B
(B)
B&E
(C)
D&E
(D)
A&D
Directions (Q.8 & Q.9) : Sometimes we are given figures showing the same die in various positions. After
observing these figures, we have to find the number opposite a given number on the die. The procedure to be
adopted for solving such problems, will be clear from the following examples :
Example: A die is thrown four times and its four different positions are given below. Find the number on the
face opposite the face showing 2.
(A)
3
(B)
4
(C)
5
(D)
6
Solution :
Here, the number 2 appears in three dice, namely (i), (ii) and (iv). In these dice, we observe that the numbers 2,
4, 1 and 6 appear adjacent to 3. So, none of these numbers can be present opposite 2. The only number left is 5.

The answer is (c)
8.
What number is opposite 4 ?
(A)
1
(B)
2
(C)
5
(D)
6
2
(C)
4
(D)
6
9.
Which number is opposite 3 ?
(A)
1
(B)
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Directions (Q.10 & Q.11) : Find the missing character in each of the following questions :
10.
7
(A)
72
(B)
70
(C)
68
(D)
66
(A)
10
13
(B)
11
1
(C)
12
(D)
13
286
16
142
34
?
11.
?
2
4
5
3
8
12.
The expression 2 + 2 
(A)
2
1

2 2
(B)
1
equals :
2 2
2– 2
(C)
2+ 2
(D)
2 2
Directions (Q.13 & Q.14) : Question 13 & 14 are based on the following figure.
13.
How many squares are there in adjoining figure ?
(A)
14.
13
(B)
15
(C)
16
(D)
17
How many minimum colours are required if the figure is to be coloured such that no two adjacent sides
have the same colour ?
(A)
15.
2
(B)
3
(C)
4
(D)
5
If 2 < x < 4 and 1 < y < 3, then find the ratio of the upper limit for x + y and the lower limit of x – y.
(A)
6
(B)
GIITJEE (GURUS FOR IITJEE)
7
(C)
8
(D)
None of these
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16.
The simplest form of 1 –
(A)
17.
a
1
1 a
(B)
1
is
(C)
a if a  – 1
(D)
none of these
(C)
1
50
(D)
1
5
If 102y = 25, then 10–y equals :
(A)
18.
a if a  0
1
–
1
5
(B)
1
625
In our number system the base is ten. If the base were changed to four you would count as follows :
1, 2, 3, 10, 11, 12, 13, 20, 21, 22, 23, 30, …. The twentieth number would be :
(A)
19.
20
(B)
38
(C)
44
(D)
none of these
Raj starts from his office facing west and walks 100 metres straight then takes a right turn and walks 100
metres. Further he takes a left turn and walks 50 metres. In which direction is Raj now form the starting
point ?
(A)
20.
North–East
(B)
South–West
(C)
North
(D)
North–West
The sum of the numerator and denominator of a fraction is 11. If 1 is added to the numerator and 2 is
subtracted form the denominator, it becomes 2/3, the fraction is
(A)
5/6
(B)
6/5
(C)
3/8
(D)
8/3
PHYSICS
21.
A siren placed at a railway platform is emitting sound of frequency 5 kHz. A passenger sitting in a
moving train A records a frequency 5.5 kHz while the train approaches the siren. During his return
journey in a different train B he records a frequency of 6.0 kHz while approaching the same siren. The
ratio of the velocity of train B to that of train A is
(A)
22.
242
256
(B)
2
(C)
5
6
(D)
11
6
Two blocks of masses 10 kg and 4 kg are connected by a spring of negligible mass and placed on a
frictionless horizontal surface. An impulse gives a velocity of 14 m/s to the heavier block in the
direction of the lighter block. The velocity of the centre of mass is
(A)
23.
30 m/s
(B)
20 m/s
(C)
10 m/s
(D)
5 m/s
A geo–stationary satellite orbits around the earth in a circular orbit of radius 36000 km. Then, the time
period of a spy satellite orbiting a few hundred kilometers above the earth’s surface (R earth = 6400 km)
will approximately be
(A)
1/2 hr
(B)
GIITJEE (GURUS FOR IITJEE)
1 hr
(C)
2 hr
(D)
4 hr
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24.
25.
26.
An ideal spring with spring constant k is hung form the ceiling and a block of mass M is attached to its
lower end. The mass is released with the spring initially unstretched. Then the maximum extension in
the spring is
2 Mg
4 Mg
Mg
Mg
(A)
(B)
(C)
(D)
k
k
k
2k
An ideal gas is taken through the cycle A  B  C  A, as shown in the figure. If the net heat is
supplied to the gas in the cycle is 5 J, the work done by the gas in the
process C  A is
(A)
–5J
(B)
– 10 J
(C)
– 15 J
(D)
– 20 J
Which of the following graphs correctly represents the variation of  = –
(dV / dP)
with P for an ideal gas at constant temperature ?
V
(A)
27.
28.
(B)
(C)
(D)
A wooden block, with a coin placed on its top, floats in water as shown in figure. The distances l and h
are shown there. After some time the coin falls into the water. Then
(A)
l decreases and h increases
(B)
l increases and h decreases
(C)
both l and h increase
(D)
both l and h decrease
A simple pendulum is oscillating without damping. When the displacement of the bob is less than

maximum, its acceleration vector a is correctly shown in
(A)
(B)
(C)
(D)
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29.
A cylinder rolls up an inclined plane, reaches some height, and then rolls down (without slipping
throughout these motions). The directions of the frictional force acting on the cylinder are :
30.
(A)
up the incline while ascending and down the incline while descending
(B)
up the incline while ascending as well as descending
(C)
down the incline while ascending and up the incline while descending
(D)
down the incline while ascending as well as descending
When a block of iron floats in mercury at 0°C, a fraction k1 of its volume submerged, while at the temp
60°C, a fraction k2 is seen to be submerged, the coeff. of volume expansion of iron is V Fe & that of
mercury is VHg then the ratio k1 / k2 can be expressed as :
(A)
31.
33.
1  60 Fe
1  60 Hg
(B)
(C)
1  60 Fe
1  60 Hg
1  60  Hg
(D)
1  60  Fe
Three rods made of same material and having same cross–section have been joined as shown in fig.
Each rod is of same length. The temp. of the function will be
(A)
32.
1  60 Fe
1  60 Hg
45°C
(B)
60°C
(C)
30°C
(D)
20°C
A small block is shot into each of the four tracks as shown below. Each of the track rises to the same
height. The speed with which the block enters the track is the same in all cases. At the highest point of
the track, the normal reaction is maximum in :
(A)
(B)
(C)
(D)
A simple pendulum has a time period T1 when on earth’s surface and T2 when taken to a height R above
the earth’s surface, where R is the radius of earth. The value of T 2/T1 is
(A)
1
2
(B)
(C)
4
(D)
2

34.

Two particles of masses m1 and m2 in projectile motion have velocities v 1 and v 2 respectively at time


t = 0. They collide at time t0. Their velocities become v 1 and v 2  at time 2t0 while still moving in air.




The value of | (m1 v1  + m2 v 2  ) – (m1 v 1 + m2 v 2 ) | is :
(A)
Zero
(B)
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(m1 + m2) gt0 (C)
2(m1 + m2)gt0 (D)
1
(m1 + m2)gt0
2
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35.
One quarter sector is cut from a uniform circular disc of radius R. This sector has mass M. It is made to
rotate about a line perpendicular to its plane and passing through the center of the original disc. Its
moment of inertia about the axis of rotation is :
(A)
36.
1/2 MR2
(B)
1/4 MR2
(C)
1/8 MR2
(D)
2 MR2
The ends of a stretched wire of length L are fixed at x = 0 and x = L. In one experiment, the
displacement of the wire is y1 =A sin (x/L) sin t and energy is
E1 and in another experiment its
displacement is y2 = sin (2x/L) sin 2t and energy is E2. Then :
(A)
37.
E2 = E1
(B)
E2 = 2E1
(C)
E2 = 4E1
(D)
E2 = 16E1
Two pulses in a stretched string, whose centres are initially 8 cm apart, are moving towards each other as
shown in the figure. The speed of each pulse is 2 cm/s. After 2 seconds the total energy of the pulses will be :
38.
(A)
zero
(B)
purely kinetic
(C)
purely potential
(D)
partly kinetic and partly potential
An insect crawls up a hemispherical surface very slowly (see fig.). The coefficient of friction between
the insect and surface is 1/3. If the line joining the center of the hemispherical surface to the insect
makes an angle  with the vertical, the maximum possible value of  is given by :
(A)
39.
cot  = 3
(B)
tan  = 3
(C)
sec  = 3
(D)
cosec  = 3
A string of negligible mass going over a clamped pulley of mass m supports a block of mass M as
shown in figure. The force on the pulley by the clamp is given by
(A)
2 Mg
(B)
GIITJEE (GURUS FOR IITJEE)
2 mg (C)
(M  m) 2  m 2 g
(D)
(M  m) 2  M 2 g
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40.
An aluminium rod (length l1 and coefficient of linear expansion A) and a steel rod (length l2 and
coefficient of linear expansion B) are joined together. If the length of each rod increases by the same
amount when their temperatures are raised by t°C, then
(A)
41.
A
s
s
A
(B)
(C)
l1
is
l1  l2
s
A  A
(D)
A
s  A
A particle is performing an uniform circular motion on a horizontal place. Its angular momentum is
constant about
42.
(A)
origin at centre of circle
(B)
point on circumference of circle
(C)
point outside the circle
(D)
point inside the circle
A rod of negligible mass of length l connected with two identical masses at both ends, placed on
horizontal surface (frictionless). A sudden impulse of Mv is given (as shown in figure) calculate the
angular velocity of rod.
(A)
43.
4v/l
(B)
v/l
(C)
2v/l
(D)
3v/l
The adjacent graph shows the extension (l) of a wire of length I m suspended form the top of a roof at one
end and with a load W connected to the other end. Area of cross section of wire is 10–6 m2. find Y is SI units
(A)
44.
2  106 N/m2
(B)
5  106 N/m2
(C)
2  1011 N/m2 (D)
5  1011
For a particle executing simple harmonic motion the displacement x is given by x = A sin t. Identify
the graph which represents the variation of potential energy (PE) as a function of time t and
displacement x.
(A)
I, III
(B)
GIITJEE (GURUS FOR IITJEE)
II, III
(C)
I, IV
(D)
II, IV
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45.
The graph, shown in the diagram, represents the variation of temperature (T) of the bodies, x and y
having same surface area, with time (t) due to the emission of radiation. Find the correct relation
between the emissivity and absorptivity power of the two bodies. :
(A)
Ex > Ey and ax < ay
(B)
Ex < Ey and ax > ay
(C)
Ex > Ey and ax > ay
(D)
Ex < Ey and ax < ay
CHEMISTRY
46.
If the nitrogen atom had electronic configuration 1s7, it would have energy lower than that of the normal
ground state configuration 1s2, 2s2 2p3 because the electrons would be closer to the nucleus. Yet 1s7 is
not observed. It violates :
47.
48.
49.
50.
(A)
Heisenberg uncertainty principle
(B)
Hund’s rule
(C)
Pauli’s exclusion principle
(D)
Bohr postulate of stationary orbits
In which of the following arrangements the order is not according to property indicated against it ?
(A)
I < Br < F < Cl (increasing electron gain enthalpy with negative sign)
(B)
Li < Na < K < Rb (increasing metallic radius)
(C)
Al+ 3 < Mg+ 2 < Na+ < F– (increasing ionic size)
(D)
B < C < N < O (increasing first I.E.)
The molecular shapes of SF4, CF4 and XeF4 are :
(A)
different with 0, 1 and 2 lone pairs of electrons on central atom respectively
(B)
different with 1, 0 and 2 lone pair of electrons on central atom
(C)
same with 2, 0 and 1 lone pairs
(D)
same with 1 lone pair in each case
Specify the Co–ordination geometry around and hybridization of N and B atoms in a 1 : 1 complex of
BF3 and NH3 :
(A)
N : Tetrahedral, sp3 ; B : Tetrahedral, sp3
(B)
N : Pyramidal, sp3 ; B : Pyramidal, sp3
(C)
N : Pyramidal, sp3 ; B : Planar, sp2
(D)
N : Pyramidal, sp3 ; B : Tetrahedral, sp3
Van der Waal’s equation for ‘n’ moles of a gas is :
(A)

na 
 P 

v2 

(C)
2 

P  n a 

v 2 

(v – nb) = RT
(v – b) = nRT
GIITJEE (GURUS FOR IITJEE)
(B)
2 

P  n a 

v 2 

(D)

a
 P 
v2




(v – nb) = nRT
(v – b) = nRT
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51.
NH3 and HCl gas are introduced simultaneously from the two ends of a long tube. A white ring of
NH4Cl appears first :
52.
(A)
Through out the tube
(B)
Nearer the NH3 end
(C)
Nearer the HCl end
(D)
At the centre of the tube
Two moles of an ideal gas expand isothermally and reversibly from 1 litre to 10 litre at 300 K.
The enthalpy change (in kJ) for the process is :
(A)
53.
11.4 kJ
(B)
– 11.4 kJ
(C)
0 kJ
(D)
4.8 kJ
Consider the equilibrium state of the following reaction carried out in a closed container :
N2O4 (g)
2 NO2 (g)
At constant temperature, the volume of the reaction vessel is halved. For this change, which of the
following statements is correct about equilibrium constant (Kp) and degree of dissociation () :
54.
(A)
Neither Kp nor  changes
(B)
Kp and  both one changed
(C)
Kp changes but  does not change
(D)
Kp does not change but  changes
A schematic plot of ln Keq versus inverse of temperature for a reactions is shown below :
The reaction must be :
55.
(A)
one with negligible enthalpy change
(B)
highly spontaneous at ordinary temperature
(C)
exothermic
(D)
endothermic
The solubility of A2X3 is y mol dm– 3. It solubility product is :
(A)
56.
6y4
(B)
64y4
(C)
36y5
(D)
108y5
The correct sequence in order of increasing pH of 0.1 M solution of NaCl (I), NH 4Cl (II), NaCN (III)
and HCl (IV) will be :
57.
(A)
I < II < III < IV
(B)
III < II < I < IV
(C)
IV < II < I < III
(D)
IV < I < II < III
(C)
3.0
The volume strength of 1.5 N H2O2 :
(A)
58.
4.8
(B)
8.4
(D)
8.0
In a compound, C, H and N atoms are present in 9 : 1 : 3.5 by weight. If the molecular weight of the
compound is 108, then the molecular formula of the compound is :
(A)
C9H12N3
(B)
GIITJEE (GURUS FOR IITJEE)
C3H4N
(C)
C2H6N2
(D)
C6H8N2
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59.
Na in
Lindlar 's
[A] 

 CH3 – C  CH3   [B]. [A] and [B] are respectively :
liq. NH 3
Catalyst
60.
(A)
cis, trans–2–Butene
(B)
both trans–2–Butene
(C)
trans, cis–2–Butene
(D)
both cis–2–butene
An alkene having molecular formula C9H18 on ozonolysis gives 2,2–dimethylpropanal and 2–butanone.
The alkene is :
61.
(A)
2,2,4–Trimethyl–3–hexane
(B)
2,2,6–Trimethyl–3–hexane
(C)
2,3,4–Trimethyl–2–hexane
(D)
2,3,4–Trimethyl–2–hexene
2

Hg / H
Ph – C  C – CH3 
  A, A is :
OH
O
Ph
(A)
(B)
O
Ph
(C)
(D)
H3C
H 3C
62.
Ph
Ph
OH
H3C
H 3C
Which of the following compounds is not aromatic ?
+

(A)
+
(B)
(C)
(D)
N
63.
The number of isomers for the compound with molecular formula C 2BrClFI is :
(A)
64.
3
(B)
4
(C)
1
(A)
1 > 2 > 3 > 4 (B)
Cl
2
NO 2
3
4 > 3 > 2 > 1 (C)
conc. H2SO4
(B)
Br2 in CCl4
(C)
4
2>1>3>4
(D)
2>3>1>4
dil. H2SO4
(D)
AgNO3 in ammonia
The intermediate during the addition of HCl to propene in the presence of peroxide is :

(A)
CH3CH – C H2 Cl
(C)
CH3CH2 C H 2

(B)
CH3 C HCH3
(D)
CH3CH2 C H 2

67.
6
Propyne and propene can be distinguished by :
(A)
66.
(D)
Identify the correct order of reactivity in electrophilic substitution reactions of the following compounds
CH 3
65.
5

Lithium is strongest reducing agent among alkali metals due to which of the following factor ?
(A)
Ionization energy
(B)
Electron affinity
(C)
Hydration energy
(D)
Lattice energy
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68.
Which has lowest thermal stability ?
(A)
69.
Li2CO3
(B)
Na2CO3
(C)
K2CO3
(D)
Rb2CO3
To neutralize completely 20 mL of 0.1 M aqueous solution of phosphorous acid (H 3PO3), the volume of
0.1 M aqueous KOH solution required is :
(A)
70.
60 mL
(B)
20 mL
(C)
40 mL
(D)
10 mL
If a molecule MX3 has zero dipole moment the sigma bonding orbitals used by M (at. no. < 21) is :
(A)
Pure p
(B)
sp–hybrid
(C)
sp2–hybrid
sp3–hybrid
(D)
MATHEMATICS
71.
72.
73.
74.
75.
Which of the following is correct ?
(A)
2 + 3i > 1 + 4i
If z =
3 i
, then z69 is equal to
2
(A)
–i
(  1  i 3 )15
(1  i) 20
(  1  i 3 )15
(1  i) 20
(B)
1
1
= 1, then x2000 + 2000 is equal to
x
x
(A)
1
(B)
(C) 2 + 8i > 5 + 7i (D)
none of these
(C)
1
(D)
–1
(C)
– 64
(D)
None of these
(C)
0
(D)
none of these
is equal to
If x +
64
–1
If x2 + x + 1 = 0 then the numerical value of ;
2

1
+  x 2  2
x

54



2

1
+  x 3 
x3

(B)




2
+
1 
 4
x  4 
x 

36
(C)
2

1
+ ….+  x 27  27
x

27



2
=
(D)
18
(D)
4
The number of real solution of the equation x2 – 3|x| + 2 = 0 is
(A)
1
(B)
2
(C)
3
If the equation (a – 5) x2 + 2 (a – 10) x + a + 10 = 0 has roots of the opposite sign, then
(A)
78.
+
i
32
(A)
77.
(B)
(A)
1

x  
x

76.
(B) 6 + 2i > 3 + 3i
a > 10
(B)
– 15 < a < 5
The number of positive integral solutions of
(A)
4
(B)
GIITJEE (GURUS FOR IITJEE)
3
(C)
– 10 < a < 5
x 2 ( 3 x  4 ) 3 ( x  2) 4
( x  5) 5 (2x  7) 6
(C)
2
(D)
none of these
 0 is :
(D)
1
SCO 382, Sector 37–D, Chandigarh, Ph. 0172–2628810, 2628811, 4652111
P – 12
79.
For the equation 3x2 + px + 3 = 0, p > 0, if one of the roots is square of the other, then p is equal to
(A)
80.
1/3
(B)
1
(C)
3
(D)
2/3
A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of the terms
occupying odd places, the common ratio will be
(A)
81.
86.
75
(B)
750
(C)
AP
(B)
GP
(C)
21
(B)
19
(C)
0
(B)
1
(C)
Given A = sin2  + cos4 , then for all real ,
3
(A)
1A2
(B)
A1
(C)
4
5
(B)
6
(C)
100 100
The coefficient of x53 in the expansion 
m0
(A)
88.
100
C47
(B)
100
C53
5
900
(D)
909
HP
(D)
none of these
20
(D)
91
–1
(D)
2
13
A1
16
(D)
3
13
A
4
16
7
(D)
8
C m (x – 3)100 – m . 2m is
(C)
– 100C53
(D)
– 100C100
The number of permutations that can be formed by arranging all the letters of word ‘NINETEEN’ in
which no two E’s occur together is
5!
8
(A)
(B)
3! 3!
3!  6 c 2
89.
(D)
The expression [x  (x3  1)1/2]5 + [x  (x3  1)1/2]5 is a polynomial of degree
(A)
87.
4
If sin x + sin2 x = 1, then the value of cos 12x + 3 cos 10x + 3 cos 8x + cos 6x – 1 is equal to
(A)
85.
(C)
The number of common terms to the two sequences 17, 21, 25, …., 417 and 16, 21, 26, … 466 is
(A)
84.
3
If ax3 + bx2 + cx + d is divisible by ax2 + c, then a, b, c, d are in
(A)
83.
(B)
If a1, a2, a3,…is an A.P. such that a1 + a5 + a10 + a15 + a20 + a24 = 225 then a1 + a2 + a3 + …… + a24 =
(A)
82.
2
(C)
5! 6
 c3
3!
(D)
8! 6
 c3
5!
Everybody in a room shakes hand with everybody else. The total number of hand shakes is equal to 153.
The total number of persons in the room is equal to
(A)
90.
18
(B)
19
The incentre of the triangle with vertices (1,
(A)


1, 3 

2 

(B)
GIITJEE (GURUS FOR IITJEE)
2 1 
 ,

3 3 
(C)
17
(D)
16
3 ), (0, 0) and (2, 0) is
(C)
2 3 
 ,

3 2 


(D)

1 
1,

3

SCO 382, Sector 37–D, Chandigarh, Ph. 0172–2628810, 2628811, 4652111
P – 13
91.
Let 0 <  < /2 be a fixed angle.
If P = (cos , sin ) and Q = (cos ( – ), sin ( – )), then Q is obtained from P by
92.
(A)
clockwise rotation around origin thro’ an angle 
(B)
anticlockwise rotation around origin thro’ an angle 
(C)
reflection in the line through origin with slope tan 
(D)
reflection in the line through origin with slope /2
If the abcissae and ordinates of two points P and Q are the roots of the equations x 2 + 2ax – b2 = 0 and
x2 + 2px – q2 = 0, respectively then the equation of the circle with PQ as diameter is
93.
(A)
x2 + y2 + 2ax + 2py – b2 – q2 = 0
(B)
x2 + y2 – 2ax – 2py + b2 + q2 = 0
(C)
x2 + y2 – 2ax – 2py – b2 – q2 = 0
(D)
x2 + y2 + 2ax + 2py + b2 + q2 = 0
The angle between the two tangents from the origin to the circle (x – 7)2 + (y + 1)2 = 25 equals
(A)
94.
/4
/3
(B)
(C)
/2
(D)
none
The lines 2x – 3y = 5 and 3x – 4y = 7 passes through the center of the circle whose area is 154 sq. units,
then equation is of circle is
95.
96.
(A)
x2 + y2 – 2x + 2y = 47
(B)
x2 + y2 + 2x – 2y = 31
(C)
x2 + y2 – 2x – 2y = 47
(D)
x2 + y2 – 2x – 2y = 31
The least distance from origin to the circle (x – 6)2 + (y – 8)2 = 92 is
3
(A)
(B)
(C)
2
(D)
2
The two ends of latus rectum of a parabola are the points (3, 6) and (– 5, 6). The focus is
(A)
97.
98.
99.
100.
1
(1, 6)
(B)
(– 1, 6)
(C)
(1, – 6)
(D)
(– 1, – 6)
The length of the latus rectum of the parabola 169 {(x – 1)2 + (y – 3)2} = (5x – 12y + 17)2 is
(A)
12/13
(B)
14/13
(C)
28/13
(D)
none
If the latus rectum of an ellipse is equal to half the minor axes then its eccentricity is equal to
1
1
3
3
(A)
(B)
(C)
(D)
2
4
4
2
An ellipse has OB as a semi–minor axis, F, F as its foci and the angle FBF is a right angle. Then, the
eccentricity of the ellipse is
1
1
3
(A)
(B)
(C)
(D)
none of these
2
2
2
For the hyperbola
(A)
(C)
x2
cos 2 
–
abscissae of vertices
eccentricity
GIITJEE (GURUS FOR IITJEE)
y2
sin 2 
= 1 which of the following remains constant with change in ‘’
(B)
(D)
abscissae of foci
directrix
SCO 382, Sector 37–D, Chandigarh, Ph. 0172–2628810, 2628811, 4652111
P – 14
Answer key
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
(D)
(C)
(B)
(B)
(B)
(A)
(D)
(A)
(C)
(B)
(C)
(A)
(D)
(B)
(B)
(D)
(A)
(D)
(B)
(C)
(D)
(C)
(C)
(A)
(A)
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
GIITJEE (GURUS FOR IITJEE)
(A)
(C)
(B)
(B)
(A)
(B)
(A)
(D)
(C)
(A)
(C)
(B)
(A)
(D)
(D)
(A)
(B)
(C)
(A)
(D)
(C)
(D)
(B)
(A)
(B)
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74.
75.
(C)
(C)
(D)
(C)
(D)
(C)
(B)
(D)
(A)
(A)
(A)
(C)
(D)
(C)
(D)
(B)
(C)
(A)
(C)
(C)
(D)
(A)
(C)
(B)
(A)
76.
77.
78.
79.
80.
81.
82.
83.
84.
85.
86.
87.
88.
89.
90.
91.
92.
93.
94.
95.
96.
97.
98.
99.
100.
SCO 382, Sector 37–D, Chandigarh, Ph. 0172–2628810, 2628811, 4652111
(D)
(C)
(B)
(C)
(C)
(C)
(B)
(C)
(A)
(B)
(C)
(C)
(C)
(A)
(D)
(D)
(A)
(C)
(A)
(D)
(B)
(C)
(B)
(A)
(B)
P – 15