FIITJEE MOCK TEST-5 I I I I T T – – J J E E E E , , 2 2 0 0 1 1 9 9 PAPER-I Time: 3 Hours Maximum Marks: 210 A. Question Paper Format: 1. The question paper consists of 3 Parts (Chemistry-Part-I, Mathematics-Part-II and Physics-Part-III). 2. Section A(i) contains 10 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which only one is correct. 3. Section A(ii) contains 5 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. 4. Section C contains 5 questions. The answer to each of the questions is a single – digit integer, ranging from 0 to 9. The answer will have to be appropriately bubbled in the ORS as per the instructions given at the beginning of the section. B. Marking Scheme: 5. For each question in Section A(i) you will be awarded 3 marks if you darken the bubble corresponding to the correct answer and zero mark if no bubble is darkened. In case of bubbling of incorrect answer, minus one (-1) mark will be awarded. 6. For each question in Section A(ii), you will be awarded 4 marks if you darken the bubble(s) corresponding to the correct choice(s) for the answer, and zero mark if no bubble is darkened. In all other cases, Minus one (-1) mark will be awarded. 7. For each question in Section C, you will be awarded 4 marks if you darken the bubble corresponding to the correct answer and zero mark if no bubble is darkened. In all other cases, minus one (-1) mark will be awarded. Enrolment No. : Name : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Batch : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Date:. . . . . . . . . . . . . . . . . . . . Paper Code 100392.1
Transcript
FIITJEE MOCK TEST-5 IIIITT –– JJEEEE,, 22001199
PAPER-I
Time: 3 Hours Maximum Marks: 210
A. Question Paper Format: 1. The question paper consists of 3 Parts (Chemistry-Part-I, Mathematics-Part-II and Physics-Part-III). 2. Section A(i) contains 10 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its
answer, out of which only one is correct. 3. Section A(ii) contains 5 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. 4. Section C contains 5 questions. The answer to each of the questions is a single – digit integer, ranging from 0 to 9.
The answer will have to be appropriately bubbled in the ORS as per the instructions given at the beginning of the section.
B. Marking Scheme: 5. For each question in Section A(i) you will be awarded 3 marks if you darken the bubble corresponding to the
correct answer and zero mark if no bubble is darkened. In case of bubbling of incorrect answer, minus one (-1) mark will be awarded.
6. For each question in Section A(ii), you will be awarded 4 marks if you darken the bubble(s) corresponding to the correct choice(s) for the answer, and zero mark if no bubble is darkened. In all other cases, Minus one (-1) mark will be awarded.
7. For each question in Section C, you will be awarded 4 marks if you darken the bubble corresponding to the correct answer and zero mark if no bubble is darkened. In all other cases, minus one (-1) mark will be awarded.
Single Correct Choice Type This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 1. What is the major product of the following reaction?
3H O ?
(A)
OH
(B)
(C)
(D)
Et Et
2. A sample of copper (II) ore weighing 2.132 gm is dissolved in acid and copper is completely
electrolysed for 8.04 minutes by using a constant current of 2.00 A. What is the % of Cu in the sample? (At. wt. of Cu = 63.55)
3. What is the resultant product of the following reaction?
OCOOH H ?
(A) OH
CHO (B) CHO
(C)
OH
COOH
(D)
OH
4. According to Maxwell’s distribution of velocities of gaseous particles, on increasing temperature (A) Fraction of molecules having low velocity increases (B) Fraction of molecules having ump increases (C) Fraction of molecules having urms increases (D) Fraction of molecules having higher velocity increases
6. Which of the following expression does not give rms velocity?
(A) 1/23RT
M
(B) 123P
dM
(C) 1/23P
d
(D) 123PV
M
7. An adiabatic container with a movable adiabatic piston (operating at 1 atm) is filled with 2 litre of 2 M
H2O2 solution at 300 K. If H2O2 dissociates following first order decay with half life of 10 min then magnitude of change in internal energy in first 20 min will be... (Given R = 2 cal/mol – K)
(A) 900 cal (B) 450 cal (C) 1800 cal (D) 225 cal 8. Which of the following discard the presence of free –CHO group in glucose? (A) it react with HIO4 (B) glucose pentaacetate does not react with NH2OH (C) formation of osazone with excess of C6 H5 NHNH2 (D) formation of glucose oxime by reaction of NH2OH with glucose
9. For the equilibrium
2
5 3 2 pRTPCl PCl Cl ; K
1 V
Which one of the following statement is true at constant temperature? (A) KP increases with increase in volume (B) KP increases with decrease in volume (C) KP does not change with change in volume (D) KP may increase or decrease with change in volume 10. The self ionization constant of liquid ammonia is 10-30 at – 20oC, while density is 0.85 g/ml. What is
ionic product of NH3 at the same temperature? (A) 5 × 10-29 M2 (B) 2.5 × 10-28 M2
Multiple Correct Answer(s) Type This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct. 11. Which of the following statement(s) is/are correct? (A) CCl4 do not hydrolysed in usual conditions (B) HCl gas is one of the products formed due to hydrolysis of NCl3 (C) BiCl3 is partially hydrolysed while PCl3 is completely hydrolysed (D) During the hydrolysis of hypophosphoric acid (H4P2O6) both the ‘P’ atoms are electrophilic 12. Which of the following statements for a meso compound is/are correct? (A) The meso compound has either a plane or a point of symmetry (B) The meso compound has at least one pair of similar stereocentres (C) The meso compound is achiral (D) The meso compound is formed when equal amounts of two enantiomers are mixed 13. A reaction proceeds as follows’ which of the following is/are correct?
4colddil.KMnO A 4HIO B OH C
(A) (A) is OO (B) (B) is OH
(C) (A) is OHOH (D) (C) is
O
14. Which one of the following statements is/are true? (A) Work is a path function (B) Entropy is a state function (C) Entropy is an extensive property (D) Gibbs free energy per mole is an intensive property 15. Rate of NS 2 reaction will be negligible in the following substrates
This section contains 5 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive). 1. What is the number of optically active isomers of [Co(NH3)2Cl2(NO)(OH)]? 2. 500 ml of H2O at 4oC is saturated by NH3 which becomes 74.5% w
w of NH3, with density 0.98
gm/ml. What is the volume of resultant solution (in litre)? 3. No. of molecules which are non-linear among the following molecules will be 2 2 3 2 2 2 2 2ICl , AsF , NOF, N , CO , COS, H O, OF , SCl , SO 4. How many optically active isomers of dichlorocyclopentane are possible 5. Hydrogen atoms in the ground state are excited by means of monochromatic radiation of wavelength
970.6Å. How many different lines are possible in the resulting emission spectrum?
Single Correct Choice Type This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 1. A 3–digit number is divisible by 11 and the quotient obtained is the sum of squares of its digits. The
number of such possible numbers is/are (A) 1 (B) 2 (C) 0 (D) 3 2. Triangle ABC has side length a, b, c. If 2a + 3b + 4c = 4 2a 2 6 3b 3 8 4c 4 20 then
ABC is (A) acute angled (B) isosceles but not right angled (C) right angled but not isosceles (D) equilateral
3. Let
/ 4
e0
f x log 1 x tant dt then
1 1f f2 3
is equal to
(A) e
4log8 3
(B) e
5log8 3
(C) e
9log8 8
(D) e
3log8 2
4. The number of integral values of ‘a’ for which the equation (3 sin x – 4 cos x)2 – (a2 + a + 5) |3 sin x – 4 cos x| + a3 + 3a2 + 2a + 6 = 0 has a real solution is (A) 5 (B) 6 (C) 2 (D) 4
n n 1 n 21 2 n 1f x x a x a x ..... a x 1 has non–negative coefficients and
n–real roots. The polynomial 5 4 3 2f x x ax bx cx dx 1 has all coefficients non–negative. If the equation f(x) = 0 has all roots real then minimum value of f(2) is
(A) 25 (B) 35 (C) 36 (D) 26
7. The value of n
nlim sin 2 3
; n N equals
(A) does not exist (B) 1 (C) –1 (D) 0 8. n–distinct objects (n 3) are placed on the circumference of a circle. The probability that objects lie
on a semi–circle is
(A) nn2
(B) n
n2n
(C) n 1n
2 (D)
n 1
n 12n
9. Let f : {0, 1, 2, ….., 100} {0, 1, 2, …., 100} be a function such that |f(x) – f(y)| |x – y| for all x, y {0, 1, 2, ….., 100}. Then f(50) equals (A) 0 (B) 100 (C) 50 (D) 5 10. The area of equilateral triangle formed by points satisfying the equation x3 + 3xy + y3 = 1 is
Multiple Correct Answer(s) Type This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.
11.
2 2
41 x 2 x dxxcosx sin x
equals
(A) 3 11 tan x cot xtan x cot x c
3
(B) 3 11 tan x cot xtan x cot x c
3
(C) 31 1 x tanx 1 x tan x c
3 x tanx x tan x
(D) 31 1 x tan x 1 x tanx c
3 x tanx x tan x
12. Let f be continuous on [a, b] and differentiable on (a, b). If f(a) = a and f(b) = b, then (A) f(c1) + f(c2) = 2 for some c1, c2 (a, b)
(B) 1 2
1 1 2f ' c f ' c
for some c1, c2 (a, b)
(C) 1 1f ' cb c a c
for some c (a, b)
(D) none of these
13. Let A = 1 1 11 1 11 1 1
; B = 2 1 11 2 11 1 2
and C = 3A + 7B then
(A) (A + B)2013 = A2013 + B2013 (B) (A + B)2013 = 32012(A + B) (C) C2013 = 34025 A + 7.212012B (C) C2 = A2 + B2 14. If for all real values of u and v, 2f(u) cos v = f(u + v) + f(u – v) then
(A) 10
2
f x dx 0
(B) f( – x) + f(x) = –2b sin x (b = constant)
(C) f( – x) + f(x) = 2a cos x (a = constant) (D) f(x) + f(–x) = 2b cos x (b = constant)
15. The position vectors of the vertices A, B, C of a tetrahedron ABCD are ˆ ˆ ˆi j k , i , ˆ3i . The altitude from vertex D to opposite face ABC meets the median line AF of ABC at the point E. If AD = 4 and
volume of tetrahedron is 2 23
then E
is
(A) ˆ ˆ ˆ3i j k (B) ˆ ˆ ˆi 3 j 3k
(C) ˆ ˆ ˆ3i 3 j k (D) ˆ ˆ ˆi 3 j k
SECTION –C
Integer Answer Type This section contains 5 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive). 1. If the number of extreme points of the function f: R R f(x) = (x – 1)(x – 2)2(x – 3)3 …..
(x – 100)100 is , then the value of
2 (where [.] denotes the greatest integer function).] denotes the
greatest integer function is _____
2. The value of cos25º cos70º cos85º
sin70ºsin85º sin25ºsin85º sin25ºsin70º is equals to _____
3. Number of solution of the equation
x 2 xsin cos 24 4
_____
4. Let 2
0
f x x t dt , x > 0. Then minimum value of f(x) is _____
5. If for 0 x 2 , sin x + 2x k x (x + 1) and if M is maximum value of k, then [M] equals _____
Single Correct Choice Type This section contains 10 multiple choice questions. Each question has four 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 uniform wire of mass ‘3m’ and length ‘3l’ is bent in the
shape of three sides of a square and suspended from a horizontal axis XX’ in a vertical plane. A uniform vertical upward magnetic field ‘B’ is existing in the region. Now charge ‘Q’ is passed almost instantaneously through the wire frame.
The minimum value of ‘B’ required so that the wire frame will complete full rotation about the horizontal axis XX’, is
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. 7 th8
of nuclei have been disintegrated in 2 minutes after fresh sample was prepared. The half life of
the sample is (A) 30 seconds (B) 1 minute (C) 40 seconds (D) 20 seconds
8. 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
9. Two long rails are horizontal and parallel to each other. On one end, the rails are
connected by a resistance R and on the other end a capacitor of capacitance C is connected as shown in the figure. A connector of mass m and length can slide on the rails without friction. Uniform magnetic field B, perpendicular to the plane of the figure exist in space. A constant horizontal force F starts acting on the
connector. What is the acceleration of connector when its velocity is 34
of its
terminal velocity?
(A) 2 23F
4(m CB ) (B)
2 2F
(m CB )
(C) 2 2
F4(m CB )
(D) 2 24F
3(m CB )
R
m
F
C
B
10. Two small masses m1 and m2 are at rest on a frictionless,
fixed triangular wedge whose angles are 30° and 60° as shown. They are connected by a light inextensible string. The side BC of wedge is horizontal and both the masses are 1 metre vertically above the horizontal side BC of wedge. There is no friction between the wedge and both the masses. If the string
60 30
m1 m2
B C fixed wedge
is cut, which mass reaches the bottom of the wedge first? (Take g = 10m/s2) (A) Mass m1 reaches the bottom of the wedge first. (B) Mass m2 reaches the bottom of the wedge first. (C) Both reach the bottom of the wedge at the same time. (D) It’s impossible to determine from the given information.
Multiple Correct Answer(s) Type This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct. 11. 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. 12. A charge q is moving in a circle of radius ‘a’ with constant angular velocity (A) magnetic field at the centre of the ring will be constant (B) magnetic field on the axis of ring at a distance r from the centre will very with time (C) magnetic field on the axis of ring at a distance r from the centre will remain constant (D) direction of magnetic field on the axis of ring at a distance r from the centre will very with time. 13. 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
14. Three identical bodies are at temperature T1, T2 and T3
having e1, e2 and e3 as their respective emissivities. The thermal spectrum obtained for them is as shown in the diagram. Choose the correct order of temperatures and emissivities:
15. Monochromatic rays of intensity I are falling on a metal plate of
surface area A placed on a rough horizontal surface at certain angle as shown in figure. Choose correct statement (s) based on above information:
(A) There is a value of for which plate will not move however high the intensity of radiation is
(B) Plate will not move if plate is perfectly reflecting irrespective of the value of intensity. (C) If rays are falling perpendiculars to surface plate will not move (D) None of these
This section contains 5 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive). 1. A vessel is half filled with a liquid of refractive index . The other half of the vessel is filled with an
immiscible liquid of refractive index 1.5. The apparent depth of the vessel is 50% of the actual depth,
then is n3
. Find n.
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
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 ……………..
