fiitjee jee (advanced), 2016 jee performance in jee...
TRANSCRIPT
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HALF COURSE TEST – VII
Paper 1
Time Allotted: 3 Hours Maximum Marks: 246 Please r ead the inst ruct ions carefu l l y . You are a l lot ted 5 minutes
speci f i ca l l y for th is purpose. You are not a l lowed to leave the Exam inat ion Hal l before the end of
the test .
INSTRUCTIONS
A. General Instructions
1. Attempt ALL the questions. Answers have to be marked on the OMR sheets. 2. This question paper contains Three Parts. 3. Part-I is Physics, Part-II is Chemistry and Part-III is Mathematics. 4. Each part is further divided into three sections: Section-A, Section-B & Section-C 5. Rough spaces are provided for rough work inside the question paper. No additional sheets will be
provided for rough work. 6. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronic
devices, in any form, are not allowed. B. Filling of OMR Sheet 1. Ensure matching of OMR sheet with the Question paper before you start marking your answers
on OMR sheet. 2. On the OMR sheet, darken the appropriate bubble with black pen for each character of your
Enrolment No. and write your Name, Test Centre and other details at the designated places. 3. OMR sheet contains alphabets, numerals & special characters for marking answers. C. Marking Scheme For All Three Parts.
1. Section – A (01 – 07) contains 7 multiple choice questions which have only one correct answer. Each question carries +3 marks for correct answer and – 1 mark for wrong answer.
Section – A (08 – 11) contains 4 multiple choice questions which have one or more than one correct answer. Each question carries +3 marks for correct answer. There is no negative marking.
Section-A (12 – 16) contains 2 paragraphs. Based upon paragraph, 2 and 3 multiple choice questions have to be answered. Each question has only one correct answer and carries +3 marks for correct answer and – 1 mark for wrong answer.
2. Section – B (01 – 02) contains 2 Matrix Match Type questions containing statements given in 2
columns. Statements in the first column have to be matched with statements in the second column. Each question carries +8 marks for all correct answer. For each correct row +2 marks will be awarded. There may be one or more than one correct matching. No marks will be given for any wrong matching in any question. There is no negative marking.
3. Section-C (01 – 06) contains 6 Numerical based questions with answers as numerical value from 0 to 9 and each question carries +3 marks for correct answer. There is no negative marking.
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Useful Data
PHYSICS
Acceleration due to gravity g = 10 m/s2
Planck constant h = 6.6 1034 J-s
Charge of electron e = 1.6 1019 C
Mass of electron me = 9.1 1031 kg
Permittivity of free space 0 = 8.85 1012 C2/N-m2
Density of water water = 103 kg/m3
Atmospheric pressure Pa = 105 N/m2
Gas constant R = 8.314 J K1 mol1
CHEMISTRY
Gas Constant R = 8.314 J K1 mol1 = 0.0821 Lit atm K1 mol1 = 1.987 2 Cal K1 mol1 Avogadro's Number Na = 6.023 1023 Planck’s constant h = 6.625 1034 Js = 6.625 10–27 ergs 1 Faraday = 96500 coulomb 1 calorie = 4.2 joule 1 amu = 1.66 10–27 kg 1 eV = 1.6 10–19 J Atomic No: H=1, He = 2, Li=3, Be=4, B=5, C=6, N=7, O=8,
N=9, Na=11, Mg=12, Si=14, Al=13, P=15, S=16, Cl=17, Ar=18, K =19, Ca=20, Cr=24, Mn=25, Fe=26, Co=27, Ni=28, Cu = 29, Zn=30, As=33, Br=35, Ag=47, Sn=50, I=53, Xe=54, Ba=56, Pb=82, U=92.
Atomic masses: H=1, He=4, Li=7, Be=9, B=11, C=12, N=14, O=16, F=19, Na=23, Mg=24, Al = 27, Si=28, P=31, S=32, Cl=35.5, K=39, Ca=40, Cr=52, Mn=55, Fe=56, Co=59, Ni=58.7, Cu=63.5, Zn=65.4, As=75, Br=80, Ag=108, Sn=118.7, I=127, Xe=131, Ba=137, Pb=207, U=238.
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PPhhyyssiiccss PART – I
SECTION – A
Straight Objective Type
This section contains 7 multiple choice questions numbered 1 to 7. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct 1. At the middle of the mercury barometer tube there is a little
column of air with the length l0 and there is vacuum at the top as shown. Under the normal atmospheric pressure and the temperature of 300 kelvin, l0 = 10 cm. Neglect expansion of the tube. The length of the air column if the temperature rises to 330 Kelvin will be:
(A) 10011
cm (B) 11 cm
(C) 10 cm (D) 12 cm
air column
vacuum
l0
2. Two cars A and B are moving towards each other with same speed 25 m/s. Wind is blowing with
speed 5 m/s in the direction of motion of car A. The car A blows horn of frequency 300 Hz and the sound is reflected from car B. The wavelength of the reflected sound received by the driver of car A is (velocity of sound in air = 330 m/s)
(A) 25 m36
(B) 31m36
(C) 35 m36
(D) 37 m36
3. A particle is moving along the x axis is acted upon by a single force F = F0e–kx, where F0 and k are
constants. The particle is released from rest at x = 0. It will attain a maximum kinetic energy of :
(A) 0Fk
(B) 0k
Fke
(C) 0k
kFe
(D) kekF0
Space for rough work
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4. First 10 cm piece of a uniform meter strick is cut and kept on the other end as shown in figure. Find the shift in the x-coordinate of center of mass
(A) 5 cm (B) 10 cm (C) 9 cm (D) 45 cm 5. A satellite is in a circular orbit very close to the surface of a planet with speed v0. At some point it is
given an impulse along its direction of motion, causing its velocity to increase times (that is, its speed becomes v0). It now goes into an elliptical orbit. The maximum possible value of for satellite to move in the elliptical orbit is:
(A) 2 (B) 2
(C) 2 + 1 (D) 12 1
6. An elevator is moving upward with an acceleration a. It has velocity v at t = 0. A man inside the
elevator lifts a body of mass m through a height h in interval t = 0 to t = t0. The average power developed by the man is in elevator ref. frame :
(A) 0
m(g a)ht (B) m(g + a) (v + 1
2 at0)
(C) 0
mght
(D) mg (v + 12
at0)
7. A thermally insulated vessel contains some water at 0°C. The vessel is connected to a vacuum pump to pump out water vapour. This results in some water getting frozen. It is given Latent heat of vaporization of water at 0°C = 21 × 105 J/kg and latent heat of freezing of water = 3.36 × 105 J/kg. The maximum percentage amount of water that will be solidified in this manner will be :
(A) 86.2% (B) 33.6% (C) 21% (D) 24.36%
Space for rough work
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Multiple Correct Choice Type
This section contains 4 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONE OR MORE is/are correct 8. As a wave propagates : (A) The wave intensity remains constant for a plane wave (B) The wave intensity decreases as the inverse of the distance from the source for a spherical wave (C) The wave intensity decreases as the inverse square of the distance from the source for a
spherical wave (D) Total power of the spherical wave over the spherical surface centered at the source decreases
with distance. 9. A block of mass 2 kg is hanging over a smooth and light pulley through a light
string. The other end of the string is pulled by a constant force F = 40 N. At t = 0 the system is at rest as shown. Then in the time interval from
t = 0 to t = 210
seconds, pick up the correct statement (s) : (g = 10 m/s2)
(A) tension in the string is 40 N (B) work done by gravity is – 20 J (C) work done by tension on block is 80 J (D) None of these
2kg F=40N
10. A solid cube of mass 5 kg is placed on a rough horizontal surface, in
xy-plane as shown. The friction coefficient between the surface and the cube is 0.4. An external force ˆ ˆ ˆF 3i 4 j 20k
N is applied on
the cube. (use g = 10 m/s2
(A) The block starts slipping over the surface (B) The friction force on the cube by the surface is 5 N. (C) The friction force acts in xy-plane at angle 127° with the positive
x-axis in clockwise direction. (D) The contact force exerted by the surface on the cube is 925 N
y
x
z
11. An ideal monoatomic gas undergoes a processes in which P = 3V3. Choose the correct statements. (A) If volume increases then temperature will also increase (B) If temperature of the gas decreases, then pressure must also decrease. (C) For expansion, heat will have to be supplied to the gas. (D) If temperature increases then work done by gas is positive.
Space for rough work
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Comprehension Type
This section contains 2 paragraphs. Based upon one of paragraphs 2 multiple choice questions and based on the other paragraph 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct
Paragraph for Questions 12 and 13
In an organ pipe (may be closed or open) of 99 cm length standing wave is setup, whose equation is given by longitudinal displacement
= (0.1 mm) cos 20.8 (y + 1 cm) cos 2(400) t
where y is measured from the top of the tube in meters and t in second. Here 1 cm is the end correction.
12. The air column is vibrating in (A) First overtone (B) fifth harmonic (C) Third harmonic (D) Fundamental mode 13. Equation of the standing wave in terms of excess pressure is – (Bulk modulus of air B = 5 × 105 N/m2)
(A) Pex = (125 N/m2) sin 20.8 (y + 1 cm) cos 2(400t)
(B) Pex = (125 N/m2) cos 20.8 (y + 1 cm) sin 2(400t)
(C) Pex = (225 N/m2) sin 20.8
(y + 1 cm) cos 2(200t)
(D) Pex = (225 N/m2) cos 20.8
(y + 1 cm) sin 2(200t)
Space for rough work
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Paragraph for Question Nos. 14 to 16 A rod of mass m and length l is free to rotate in a vertical plane about fixed horizontal axis O passing through one end as shown in the figure. A
sphere of mass m4
hits the rod elastically with horizontal speed v0 at a
distance 23 from O. Before collision, the rod is at rest in vertical position.
2l3 m
4
O
If we consider the sphere and the rod as a system, then gravity and force due to axis O are external forces. For the rod alone, force exerted by O, gravity and impact force are all external forces. Similar conclusion can be drawn for the sphere. Net external force on any system is equal to the product of the mass of the system and the acceleration of the center of the mass of the system. 14. The maximum angular deflection of the rod from the vertical after the collision is
(A) 2
1 0v5cos 116 g
(B)
21 0v3sin 1
16 g
(C) 2
1 0v3cos 116 g
(D)
21 0v5sin 1
16 g
15. The velocity of the sphere just after collision is
(A) 02v7
(B) 0v2
(C) 02v7
(D) 0v2
16. Magnitude of the impulse on the rod exerted by the axis O during the collision is
(A) zero (B) 03mv8
(C) 03mv14
(D) 03 mv7
Space for rough work
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SECTION – B
(Matrix-Match Type) This section contains 2 questions. Each question contains statements given in two columns which have to be matched. Statements (A, B, C, D) in column I have to be matched with statements (p, q, r, s, t) in column II. The answers to these questions have to be appropriately bubbled as illustrated in the following example.
If the correct match are A-p, A-s, B-q, B-r, C-p, C-q and D-s, then the correctly bubbled 4 4 matrix should be as follows:
p q r s
p q r s
p q r s
p q r s
p q r s
D
C
B
A t
t
t
t
t
1. Match the following :
A block P of mass m placed on smooth horizontal surface and connected with a spring. Another block Q of same mass is placed on the block P. The two blocks are pulled by a distance A and released. The blocks oscillates without slipping on each other. Then match the matrix.
P Q
Column – I Column – II (A) Friction force on the block Q, When both block
coming towards equilibrium position form left. (exclude the equilibrium position)
(p) towards right
(B) Friction force at the block Q when both block going right from equilibrium position. (exclude the equilibrium position)
(q) towards left
(C) Friction force will be maximum on Q. (r) at equilibrium position
(D) Friction force on P when both block is coming towards the equilibrium position from right. (exclude the equilibrium position)
(s) at extreme position
(t) none of these
Space for rough work
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2. Match the following columns. Column – I Column – II
(Temperature T in steady state)
(A) 2K0 3K0 6K0
100C 10C
A B C
T
(p) 50C
Three homogenous thermal resistors A, B and C, each of length , cross-sectional area A and thermal conductivity 2K0, 3K0 and 6K0 respectively are joined in series such that there is one dimensional heat flow from left end (temperature 100C) to the right end (temperature 10C). T is the temperature of the interface between resistor B and C in the steady state.
(B)
2R
10C
3R
5R
100C
T
A spherical annular thermal resistor of thermal conductivity K and inner and outer radii 2R and 5R respectively, is in steady state with its inner surface maintained at 100C and its outer surface maintained at 10C(heat flow is radially outwards). The temperature of the concentric spherical interface of radius 3R in steady state is T.
(q) 70C
(C)
R 8R
10C 100C
2R T
A cylindrical and thermal resistor of inner radius R and outer radius 8R is in steady state with its inner surface maintained at 100C and its outer surface maintained at 10C(heat flow is radially outwards). The temperature of the co-axial cylindrical interface of radius 2R in steady state is T.
(r) 55C
(D)
3R b
2L L
100C
6R
A
B
T
10C
(s) 25C
A homogeneous thermal resistor whose outer surface is the frustom of a solid cone, has the two base radii as 6R and 3R respectively and the perpendicular distance between its, two bases is 3L. The two bases are maintained at 100C and 10C. In the steady state(heat flows from left end to the right end) the temperature of the interface at a distance of 2L from the left end is T. Assume that L is very large in comparison to R and the lateral surface of the cylinder is thermally insulated from the surroundings. Find T.
(t) none of these
Space for rough work
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SECTION – C
Integer Answer Type
This section contains 6 questions. The answer to each of the questions is a single-digit integer, ranging from 0 to 9. The appropriate bubbles below the respective question numbers in the ORS have to be darkened. For example, if the correct answers to question numbers X, Y, Z and W (say) are 6, 0, 9 and 2, respectively, then the correct darkening of bubbles will look like the as shown
0 0 0 0
1 1 1 1
2 2 2 2
3 3 3 3
4 4 4 4
5 5 5 5
7 7 7 7
8 8 8 8
9 9 9 9
6 6 6 6
X Y Z W
1. Water at temperature 20º C flows from a tap T into a heated container C. The
container has a heating element (a resistor R) which is generating heat at the rate of P, that may be varied. The rate of water in flow from trap is F = 0.16 cc/minute. The heat generated is sufficient so that the water in the container is boiling and getting converted into steam at a steady rate. What is the minimum power P (in watt) that must be generated as heat in the steady state in resistor R so that the amount of liquid water in the container neither increases nor decreases with time ? (Neglect other losses of heat, such as conduction from the container to the air and heat capacity of container) For water, specific heat c = 4.2 kJ.kg–1 K–1, latent heat of vaporisation Lvap=2.3
MJ.kg–1, density p = 1000 kg.m–3.
2. A cylinder of height h, diameter h/2 and mass M and with a
homogeneous mass distribution is placed on a horizontal table. One end of a string running over a pulley is fastened to the top of the cylinder, a body of mass m is hung from the other end and the system is released. Friction is negligible everywhere. At what minimum ratio m/M will the cylinder tilt?
h M
h/2
m
Space for rough work
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3. Shown in the figure is a system of three particles connected by two springs. The accelerations of A, B and C at any instant are 1 m/sec2, 2 m/sec2 and (1/2) m/sec2, respectively, directed as shown in the figure. External force acting on the system is
(m1 = 1kg, m2 = 2kg and m3 = 4kg)
m1 m2 m3
a1 a2 a3
A B C
4. In a lawn a water sprinkler is sprinkling water in all the possible directions while rotating. What is
maximum area (in m2) on ground that can be sprinkled? The speed of water form nozzle is
1/ 4400 m / s
(g = 10 m/s2)
5. A horizontal board is being moved with a constant velocity v0 on a
smooth horizontal plane. A small block is projected on the block with velocity v1 = 25 m/s at an angle = 37° relative to the ground. The coefficient of friction between the block and the board is = 0.3. If velocity of block (in m/s) relative to ground after time t = 10 sec. is v than v/10 is equal to ……………..
6. The 1/v versus displacement graph of a particle is shown in the
figure, where v is the speed of the particle. The particle is moving in a straight line along positive x-axis. Calculate the time taken (in seconds) by the particle to reach from the point A to B .
x (m) 0
2
4 B
A
1/v (s/m)
2
Space for rough work
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CChheemmiissttrryy PART – II
SECTION – A
Straight Objective Type
This section contains 7 multiple choice questions numbered 1 to 7. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct 1. Find the equivalent weight of H3PO4 in the following reaction: 3 4 2 4 22 2
Ca OH 2H PO Ca H PO 2H O (A) 98 (B) 49 (C) 32.7 (D) 37.2 2. Which one of these does have greatest second ionization energy? (A) B (B) C (C) Sr (D) Ba
3. 3aq 3 aq 2 aq
Ag 2NH Ag NH
What is the relationship between Kc and Ksp(AgCl)?
(A)
2
sp 3
c 3 2
K NH1K Ag NH Cl
(B)
2
sp 3c
3 2
K NHK
Ag NH Cl
(C)
spc 2
3 32
K ClK
Ag NH NH
(D)
sp 3 2
c 2
3
K Ag NHK
NH Cl
4. The shape of XeOF2 is similar to
(A) T (B) (C) (D)
Space for rough work
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5. Find de – Broglie wavelength of the electron in the first Bohr’s orbit: (A) 103 10 m (B) 104 10 m (C) 113 10 m (D) 114 10 m 6.
CH3 CH2 C
CH3
CH CH3 2 2HBr /H O
(A)
CH3 CH2 C
CH3
CH2 CH3
Br
(B)
CH3 CH2 C
CH3
CH3
Br (C) CH3 CH CH CH2 CH3
CH3Br
(D)
CH3 CH2 CH C CH3
CH3
Br 7. For the following reaction:
2 2
1CO g O g CO g at 298K2
The standard entropy change is 0.094 kJ mol1. The values of standard Gibbs free energy of formation of CO2 and CO are 394.4 and 137.2 kJ mol1 respectively. The reaction is
(A) non-spontaneous, endothermic (B) non – spontaneous, exothermic (C) spontaneous, endothermic (D) spontaneous, exothermic
Multiple Correct Choice Type
This section contains 4 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONE OR MORE is/are correct 8. Which of the following carbocation will be relatively more stable than benzyl carbocation?
(A) CH2
(B) Ph2CH
(C)
(D)
C
CH3
Ph CH3
Space for rough work
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9. Which of the following molecules/species contains atleast one atom with sp3 hybridization? (A) ClO2
(B) SO32
(C) BO33 (D) H3PO3
10. Which of the following is correct about the given reaction sequence?
3 22 2
4
Hg OCOCH /THF, H OBr /h alc. KOH NaOINaBH , OH
A B C D E F
3H O
(A) Molecular weight of (F) is nth multiple of weight of a methyl radical (where n = positive integer) (B) Compound (C) on heating with conc. H2SO4 gives (B) (C) Compound (B) can not exhibit position isomerism (D) Compound (A) can exhibit position isomerism 11. Chlorine gas is prepared in laboratory by the reaction: 2 2 7 3 2 2K Cr O HCl KCl CrCl Cl H O If a 61.3 g sample of 96% K2Cr2O7 is allowed to react with 320 ml of hydrochloric acid solution having
density 1.15 g/ml and containing 30% HCl by mass. Now select the correct statement (s) among the following:
(A) the mass of Cl2 generated is 42.63 g (B) equivalent weight of K2Cr2O7 is 49 g (C) equivalent weight of HCl is 85.16 g (D) the stoichiometric coefficient of HCl is 14
Comprehension Type
This section contains 2 paragraphs. Based upon one of paragraphs 2 multiple choice questions and based on the other paragraph 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct
Paragraph for Question Nos. 12 to 13 The decomposition of N2O5 is according to the equation:
2 5 2 22N O g 4NO O g is a first order reaction. After 30 minutes from the start of the decomposition in a closed vessel, the total pressure is found to be 294.5 mm Hg. On complete decomposition the total pressure is 594.5 mm Hg. An inert gas with partial pressure 10 mm Hg has always been present in vessel during decomposition of N2O5. 12. What is the pressure of the vessel before the beginning of decomposition of N2O5? (A) 223.8 mm (B) 233.8 mm (C) 243.8 mm (D) 253.8 mm 13. What is the pressure of NO2 after 30 minutes? (A) 67.6 mm (B) 66.6 mm (C) 65.6 mm (D) 64.6 mm
Space for rough work
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Paragraph for Question Nos. 14 to 16 Study following molecules before answering questions:
CH3 H
CH3 CH3
HCH3 H
CH3 CH3
H H
CH3 CH3
H
14. What is the molecular formula of isomer of any of these molecules? (A) C5H10 (B) C5H12 (C) C5H14 (D) C4H10 15. The number of pairs of diastereomers are (A) 1 (B) 2 (C) 3 (D) 4 16. One of the seven cyclic isomers is missing. What is the number of C atom constituting the cyclic ring? (A) 3 member ring, hence 3 C atoms (B) 4 members ring, hence 4 C atoms (C) 5 member ring, hence 5 C atoms (D) 6 member ring, hence 6 C atoms
Space for rough work
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16
SECTION – B
(Matrix-Match Type) This section contains 2 questions. Each question contains statements given in two columns which have to be matched. Statements (A, B, C, D) in column I have to be matched with statements (p, q, r, s, t) in column II. The answers to these questions have to be appropriately bubbled as illustrated in the following example.
If the correct match are A-p, A-s, B-q, B-r, C-p, C-q and D-s, then the correctly bubbled 4 4 matrix should be as follows:
p q r s
p q r s
p q r s
p q r s
p q r s
D
C
B
A t
t
t
t
t
1. Match the following column – I and column – II:
Column – I (bond Order)
Column – II (Molecule)
(A) 0 (p) N2+
(B) 1.5 (q) N2 (C) 2.5 (r) CO (D) 3 (s) O2
(t) He2
2. Match the following:
Column – I (Quantity)
Column – II (Dimensions)
(T = Time, L = length, M = mol, W = mass) (A) Degree of dissociation (p) T1 (B) Pre-exponential factor (Arrhenius
equation) (q) L0T0
(C) Rate of reaction (r) M0L0 (D) Activation energy (s)
M1L3T1
(t) W1L2T2
Space for rough work
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SECTION – C
Integer Answer Type
This section contains 6 questions. The answer to each of the questions is a single-digit integer, ranging from 0 to 9. The appropriate bubbles below the respective question numbers in the ORS have to be darkened. For example, if the correct answers to question numbers X, Y, Z and W (say) are 6, 0, 9 and 2, respectively, then the correct darkening of bubbles will look like the as shown
0 0 0 0
1 1 1 1
2 2 2 2
3 3 3 3
4 4 4 4
5 5 5 5
7 7 7 7
8 8 8 8
9 9 9 9
6 6 6 6
X Y Z W
1. Number of possible cyclic alcohols with formula C5H10O (excluding stereoisomer) is x than what is
x/2? 2. The number of pure sigma bonds in Cr2O7
2 will be. 3. Which number of hydrogen will be having least bond energy
with carbon in given below compound? H HH
HH
(2) (1)
(4)
(3)
(5)
4. Calculate the number of protons present in an acid whose 0.45 g requires 40 ml of N/2 KOH solution.
(MW = 90) 5. The pH of blood stream is maintained by a proper balance of H2CO3 and NaHCO3 concentration. The
volume of 10 M NaHCO3 solution which is mixed with 10 mL sample of blood which is 4 M in H2CO3 in order to maintain a pH of 7.4 is x mL. Ka for H2CO3 in blood is 4 107. What will be the value of x/10?
6. If a mixture of 3 mol of H2 and 1 mole of N2 is completely converted in to NH3, what would be the ratio
of the initial and final volume at same temperature and pressure?
Space for rough work
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MMaatthheemmaattiiccss PART – III
SECTION – A
Straight Objective Type
This section contains 7 multiple choice questions numbered 1 to 7. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct
1. Two consecutive sides of a parallelogram are 4x + 5y = 0 & 7x + 2y = 0. If one diagonal is 11x + 7y = 9, then equation of other diagonal is
(A) x + 2y = 0 (B) 2x + y = 0 (C) x – y = 0 (D) none of these.
2. The curve x3 + y3 = 3axy is symmetric about (A) x-axis (B) y-axis (C) y = x (D) none of these.
3. If ii
1m ,m
i = 1, 2, 3, 4 are con-cyclic points, then the value of m1 m2 m3 m4 is
(A) 1 (B) – 1 (C) 0 (D) none of these.
4. Coefficient of xr in the expansion of (1 – 2x)–1/2 is
(A) 22r !
r! (B)
2r
2r !
2 r!
(C) 2 2r
2r !
r! 2 (D) none of these.
Space for rough work
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5. If w is a complex cube root of unity then w + 1 3 9 27 ...2 8 32 128w
is
(A) – 1 (B) 0 (C) 9 (D) i.
6. If 1 + a + a2 + a3 + … + ax = (1 + a)(1 + a2)(1 + a4) then x is (A) 3 (B) 5 (C) 7 (D) 9.
7. Ten persons, amongst whom are A, B and C to speak at a function. The number of ways in which it can be done if A wants to speak before B and B wants to speak before C is
(A) 10!6
(B) 3! 7!
(C) 10P3 . 7! (D) none of these.
Multiple Correct Choice Type
This section contains 4 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONE OR MORE is/are correct
8. If (1+ x + x2)n = a0 + a1x + a2x2 + …+a2n x2n, then the value of a0 + a3 + a6 + .... is (A) a1+ a4 +a7 + ... (B) a2+ a5 +a8 + ... (C) 3n-1 (D) none of these.
9. One vertex of the triangle of maximum area that can be inscribed in the curve |z – 2 i| =2,is 2 +2i , remaining vertices is / are
(A) -1+ i( 2 + 3 ) (B) –1– i( 2 + 3 ) (C) -1+ i( 2 – 3 ) (D) –1– i( 2 – 3 )
10. If a, b, c be three unequal positive quantities in H.P. then (A) a100 + c100 > 2b100 (B) a3+c3 > 2b3 (C) a5 + c5 > 2b5 (D) a2 + c2 > 2b2
11. If 1 sinA = sin A2
– cos A2
, then A2 4
could lie in quadrant
(A) first (B) second (C) third (D) fourth
Space for rough work
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Comprehension Type
This section contains 2 paragraphs. Based upon one of paragraphs 2 multiple choice questions and based on the other paragraph 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct
Paragraph for Question Nos. 12 to 13
Read the following comprehension carefully:
Let f(n) denotes the number of different ways the positive integer n can be expressed as the sum of 1’s and 2’s. For example, f(3) = 3, since 3 = 1 + 1 + 1 = 1 + 2 = 2 + 1 f(4) = 5, since 4 = 1 + 1 + 1 + 1 = 1 + 1 + 2 = 1 + 2 + 1 = 2 + 1 + 1 = 2 + 2. Note that order of the appearance of 1’s and 2’s is important.
Now, answer the following questions:
12. The value of f(6) is (A) 6 (B) 11 (C) 13 (D) 15
13. f{f(6)} is equal to (A) 377 (B) 302 (C) 321 (D) 350
Space for rough work
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Paragraph for Question Nos. 14 to 16
Read the following comprehension carefully:
A coplanar beam of light emerging from a point source have equation x – y + 2(1 + ) = 0, R. the rays of the beam strike an elliptical surface and get reflected. The reflected rays form another convergent beam having equation x – y + 2(1 – ) = 0, R. Further it is found that the foot of the perpendicular from the point (2, 2) upon any tangent to the ellipse lies on the circle x2 + y2 – 4y – 5 = 0.
Now answer the following questions:
14. The eccentricity of the ellipse is equal to
(A) 13
(B) 13
(C) 23
(D) 12
15. The area of the largest triangle that an incident ray and the corresponding reflected ray can enclose
with the axis of the ellipse is equal to (A) 4 5 (B) 2 5 (C) 5 (D) none of these
16. Total distance travelled by an incident ray and the corresponding reflected ray is the least if the point of incidence coincides with
(A) an end of the minor axis (B) an end of the major axis (C) an end of the latus rectum (D) none of these
Space for rough work
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22
SECTION – B
(Matching List Type)
This section contains 2 multiple choice questions. Each question has matching Column(s). The codes for the Column(s) have choices (A), (B), (C) and (D) out of which only ONE OR MORE is/are correct
1. Match the following Column-I with Column-II
Column – I Column – II (A) f(z) is a complex valued function f(z) = (a + ib)z where a, b R
and |a + ib| = 12
. It has the property that f(z) is always
equidistant from 0 and z, then a – b =
(p) 5
(B) The number of all positive integers n = 2a 3b (a, b 0) such that n6 does not divide 6n is (q) 0
(C) A is the region of the complex plane {z: z/4 and 4/ z have real and imaginary part in (0, 1)}, then [p] (where p is the area of the region A and [.] denotes the greatest integer function) is
(r) 6
(D) If 3x + 4y + z = 5, where x, y, z R, then minimum value of26(x2 + y2 + z2 )is (s) 25
(t) 10
2. Match the following Column-I with Column-II
Column – I Column – II (A) sin cos x (p) x R
(B) 1cos sinx
(q) R – n
6
(C) tan( sinx) (r) x n , n2
(D) ln(tanx) (s) x 2n , 2n2 2
(t) x R n8
Space for rough work
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SECTION – C
Integer Answer Type This section contains 6 questions. The answer to each of the questions is a single-digit integer, ranging from 0 to 9. The appropriate bubbles below the respective question numbers in the ORS have to be darkened. For example, if the correct answers to question numbers X, Y, Z and W (say) are 6, 0, 9 and 2, respectively, then the correct darkening of bubbles will look like the as shown
0 0 0 0
1 1 1 1
2 2 2 2
3 3 3 3
4 4 4 4
5 5 5 5
7 7 7 7
8 8 8 8
9 9 9 9
6 6 6 6
X Y Z W
1. The value of blog xa when a = 0.2 b = 5 , 1 1 1x ...4 8 16
is ….
2. The value of ‘c’ for which 2 2 74
, where and are the roots of 2x2 + 7x + c = 0 is ….
3. If coefficient of x7 in 11
2 1axbx
is equal to coefficient of x–7 in 11
21ax
bx
, then ab = …..
4. In a ABC, a3cos(B – C) + b3 cos(C – A) + c3 cos (A – B) = (abc) k then k is ……
5. The line L passes through the points of intersection of the circles x2 + y2 = 25 and x2 + y2 – 8x + 7 = 0. The length of perpendicular from centre of second circle onto the line L is ….
6. If the lines ax + y + 1 = 0, x + by + 1 = 0 and x + y + c = 0 are concurrent then 1 1 11 a 1 b 1 c
…
(given a, b, c are distinct and different from 1)
Space for rough work