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FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 26515949, 26569493, Fax 26513942 website: www.fiitjee.com.
PHYSICS, CHEMISTRY & MATHEMATICS JEE Main 2019 Mock Tests-1 (Code:100365.1)
Time Allotted: 3 Hours Maximum Marks: 360
Do not open this Test Booklet until you are asked to do so. Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.
Important Instructions:
1. Immediately fill in the particulars on this page of the Test Booklet with Blue / Black Ball Point Pen. Use of pencil is strictly prohibited.
2. The Answer Sheet is kept inside this Test Booklet. When you are directed to open the Test Booklet, take out the
Answer Sheet and fill in the particulars carefully. 3. The test is of 3 hours duration. 4. The Test Booklet consists of 90 questions. The maximum marks are 360. 5. There are three parts in the question paper A, B, C consisting of Physics, Chemistry and Mathematics having
30 questions in each part of equal weightage. Each question is allotted 4 (four) marks for correct response. 6. Candidates will be awarded marks as stated above in instruction No.5 for correct response of each question. ¼
(one fourth) marks will be deducted for indicating incorrect response of each question. No deduction from the total score will be made if no response is indicated for an item in the answer sheet.
7. There is only one correct response for each question. Filling up more than one response in any question will be
treated as wrong response and marks for wrong response will be deducted accordingly as per instruction 6 above. 8. Use Blue / Black Ball Point Pen only for writing particulars / marking responses on Side-1 and Side-2 of the
Answer Sheet. Use of pencil is strictly prohibited. 9. No candidate is allowed to carry any textual material, printed or written, bits of papers, pager, mobile phone, any
electronic device, etc. except the Admit Card inside the examination hall / room. 10. On completion of the test, the candidate must hand over the Answer Sheet to the Invigilator on duty in the Room /
Hall. However, the candidates are allowed to take away this Test Booklet with them. 11. Do not fold or make any stray marks on the Answer Sheet.
Atomic No.: H=1, He=2, Li=3, Be=4, B=5, C=6, N=7, O=8, F=9, Na=11, Mg=12, Al = 13, Si = 14, 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, Si = 21, Sn = 50, Ti = 22,I = 53, Xe = 54, Ba = 56, Pb = 82, U = 92, V = 50. 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.
Name of the Candidate (in Capital Letters) :_____________________________________
Enrolment Number :_________________________________________________________
Batch :________________________ Date of Examination : ________________________
FIITJEE - JEE (Main)
FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 26515949, 26569493, Fax 26513942 website: www.fiitjee.com.
IT2019JEE Main 2019 Mock Test-1-(100365.1)-PCM2
PPPAAARRRTTT ––– III ::: PPPHHHYYYSSSIIICCCSSS
(Single Correct Answer Type)
This part contains 30 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. 1. One end of a massless rope, which passes over a massless
and frictionless pulley P is tied to a hook C while the other end is free. Maximum tension that the rope can bear is 360 N. With what value of minimum safe acceleration (in ms–2) can a monkey of 60 kg move down on the rope
(A) 16 (B) 6 (C) 4 (D) 8
P
C
2. A particle moves on a rough horizontal ground with some initial velocity say v0. If (3/4)th of its kinetic
energy is lost due to friction in time t0, then coefficient of friction between the particle and the ground is
(A) 0
0
v2gt
(B) 0
0
v4gt
(C) 0
0
3v4gt
(D) 0
0
vgt
3. A source is moving on a circle of radius 3 m with constant angular velocity
= 5 rad/s. If the observer is at a distance 5 m from the centre of circle, the time interval between maximum and minimum frequency received by the observer is
(A) 5 (B) 12 3cos
5 4
(C) 12 3cos5 5
(D) 12 3sin5 5
source
observer 3m
4. A spherical conductor A of radius r is placed concentrically inside a conducting shell B of radius
R(R > r). A charge Q is given to A, and then A is joined to B by a metal wire. The charge flowing from A to B will be
(A) Q RR r
(B) rQR r
(C) Q (D) zero
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IT2019JEE Main 2019 Mock Test-1-(100365.1)-PCM3
5. A homogeneous rod of mass 3 kg is pushed along the smooth horizontal
surface by a horizontal force F equals to 40 N. The angle for which rod has pure translation motion is (g = 10 m/s2)
(A) 45 (B) 37 (C) 53 (D) 60
F=40 N
6. At a moment (t = 0), when the charge on capacitor C1 is zero, the switch is
closed. If I0 be the current through inductor at t = 0 , for t > 0 (initially C2 is uncharged)
(A) maximum current through inductor equals I0/2.
(B) maximum current through inductor equals 1 0
1 2
C IC C
.
C2
C1
L
S
(C) maximum charge on 1 0 21
1 2
C I LCC
C C
.
(D) maximum charge on 1 1 01 2
LC C IC C
.
7. A heated body emits radiation which has maximum intensity near frequency 0. The emissivity of
material is 0.5, if absolute temperature of body is doubled, the maximum intensity of radiation will be near the frequency.
(A) 0/2 (B) 20 (C) 80 (D) 160 8. The Boolean equation for the circuit shown in the figure is (A) Y A B C (B) Y A (B C)
(C) Y A (B C)
(D) Y A (B C)
A
B Y
C
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IT2019JEE Main 2019 Mock Test-1-(100365.1)-PCM4
9. Radius of a circular ring is changing with time and the ring is
placed in a uniform magnetic field perpendicular to its plane. The variation of r with time t is as shown in the figure. The magnitude of induced emf (e) is best represented by
r
t (A) e
t
(B) e
t (C) e
t
(D) e
t 10. For a telescope, the diameter of objective lens to be 6 cm and wavelength of light used to be 540 nm.
The resolving power of telescope is (A) 3.2 104 (B) 4 104 (C) 7.7 104 (D) 9.1 104 11. An atom of atomic number Z = 11 emits K wavelength which is . Find the atomic number for an
atom that emits K radiation with wavelength 4 (an integer). (A) 2 (B) 4 (C) 6 (D) 8 12. In the figure shown, a conducting wire PQ of length 1 m is
moving in a uniform magnetic field B = 3T with constant velocity v = 2m/sec towards right. R = 2, C = 1F and L = 2H. The currents through inductor at time t = 2 sec is
(A) 2A (B) 4A (C) 6A (D) 8A
R B C
Q
P
L
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IT2019JEE Main 2019 Mock Test-1-(100365.1)-PCM5
13. An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of the escape velocity from the earth. If the satellite is stopped suddenly in its orbit and allowed to fall freely, onto the earth, find the speed (in km/sec) with which it hits the surface of the earth (g = 10 m/s2 and R = 6400 km).
(A) 8 km/sec (B) 16 km/sec (C) 2 km/sec (D) 4 km/sec 14. A cube of mass 20 gm wettable by water floats on the surface of water. Each face of the cube is 3 cm
long. The distance between lower face of cube and surface of water is (surface tension of water = 70 dyne/cm, g = 10 m/s2, assume contact angle is 0)
(A) 1.012 cm (B) 1.631 cm (C) 2.315 cm (D) 2.52 cm 15. An amount Q of heat is added to a monoatomic ideal gas in a process in which the gas performs a
work Q/2 to its surrounding. The molar heat capacity for the process is (A) R (B) 2R (C) 3R (D) 4R 16. The figure shows a long straight wire of a circular cross-section (radius a) carrying
steady current I. The current I is uniformly distributed across this cross-section. The ratio of magnetic fields at a distance a/2 and 2a from the axis is
(A) 2 : 1 (B) 1 : 2 (C) 4 : 1 (D) 1 : 1
I
a
wire
17. A plane electromagnetic wave of frequency 25 MHz travels in free space along the x-direction. At a
particular point in space and time, E
= 6.3 j V/m. What is B
at this point?
(A) 2.1 × 108 T ˆ( k) (B) 2.1 × 108 T ˆ(k)
(C) 2.1 × 108 T ˆ( j) (D) 2.1 × 108 T ˆ( i)
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IT2019JEE Main 2019 Mock Test-1-(100365.1)-PCM6
18. Light with an energy flux of 18 W/cm2 falls on a nonreflecting surface at normal incidence. If the surface has an area of 20 cm2, the average force exerted on the surface during a half hour time span, will be
(A) 2.16 103 N (B) 6.48 105 N (C) 1.2 106 N (D) 360 N 19. A steel rod 100 cm long is clamped at its middle. The fundamental frequency of longitudinal vibrations
of the rod are given to be 2.53 kHz. What is the speed of sound in steel? (A) 10.06 km s–1 (B) 5.06 km s–1
(C) 15.06 km s–1 (D) 0.06 km s–1
20. The ratio of free electron densities in copper and gold is given by Cu
Au
n1.4
n , and the ratio of the mean
free times of their free electrons is given by Cu
Au
5049
. The ratio of their conductivities is
(A) 107
(B) 710
(C) 250343
(D) 343250
21. A block of mass 1 kg is pulled along the curve path ACB by a
tangential force as shown in figure. The work done by the frictional force when the block moves from A to B is
(A) 5 J (B) 10 J (C) 20 J (D) none of these
=0.2 C
A B X=10m
22. A particle starts moving with velocity v i (m/s), and acceleration a i j
(m/s2). Find the radius
of curvature of the particle at t = 1sec. (A) 5 m (B) 5 5 m (C) 6 5 m (D) none
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IT2019JEE Main 2019 Mock Test-1-(100365.1)-PCM7
23. Energy stored in the capacitor in it’s steady state is
(A) CV (B) CV2
(C) 1QV2
(D) zero
C R
R E
24. A stone of mass m tied to one end of thread of length . The diameter of thread is ‘d’ and it is
suspended vertically. The stone is now rotated in horizontal plane and makes an angle ‘’ with vertical. The increase in length of wire is (young’s modulus of wire is y)
(A) 24mg
d ycos (B) 2
4mgd ysin
(C) 24mg
d y (D) 2
4mgd y sec
25. A rigid circular loop of radius 3.5 m and mass 11 kg lies at rest in x-y
horizontal plane, when a current is flowing through it. The magnetic field ˆ ˆB 5i 8k (T)
is present in space. Find the value of current. (g = 10 m/s2)
(A) 2A (B) 4A (C) 6A (D) 8A 26. In the Young’s double–slit experiment, when a glass plate ( = 1.5) of thickness t is introduced in the
path of one of the interfering beams (wavelength ), the intensity at the position where the central maximum occurred previously remains unchanged. The minimum thickness of the glass plate is
(A) 2 (B) 23
(C) 3 (D)
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IT2019JEE Main 2019 Mock Test-1-(100365.1)-PCM8
27. The potential deference across the resistor as measured by a
voltmeter is 60 1.5V and the current through the resistor as measured by an ammeter is 2 0.01 A. What is the maximum % error in the measured value of R?
(A) 3% (B) 1.5% (C) 2.5% (D) None of these
V
R
V
A 28. Two identical thermally insulated conducting rods AB and
CD are connected to a circular conducting and thermally insulated ring at two diametrically opposite points B and C. The radius of the ring is equal to the length of rods AB and CD each. The area of cross-section and thermal conductivity of the rod and ring are equal. Points A and D are maintained at temperatures of 100ºC and 0ºC. Temperature of point C
will be 227
A B C D100ºC 0ºC
(A) 62ºC (B) 37ºC (C) 28ºC (D) 45ºC 29. A conducting shell having inner radius 1R and outer radius
2R contains a charge + q which is placed at a distance x from its centre. Field at an exterior point P which is situated at a distance r from centre of shell 2r R
(A) depends on x (B) depends on 1R and 2R (C) depends only or r (D) None.
r R1
R2
+q
P
30. A glass hemisphere of radius R and of material having
refractive index 1.5 is silvered on its flat face as shown in fig. A small object of height h is located at a distance 2R from the surface of hemisphere as shown in the figure. The final image will form
2R
h
(A) at a distance of R from silvered surface, on the right side (B) on the object itself (C) at hemisphere surface (D) at a distance of 2R from the silvered surface, on left side.
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IT2019JEE Main 2019 Mock Test-1-(100365.1)-PCM9
PPPAAARRRTTT ––– IIIIII ::: CCCHHHEEEMMMIIISSSTTTRRRYYY
(Single Correct Answer Type)
This part contains 30 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. 1. The wave number of the spectral line in the emission spectrum of hydrogen will be equal to 8/9 times
the Rydberg’s constant if the electron jumps from (A) n = 3, n = 1 (B) n = 10 to n = 1 (C) n = 9 to n = 1 (D) n = 2 to n = 1 2. If two compounds have same empirical formula but different molecular formula, they must have (A) same viscosity (B) same vapour density (VD) (C) different molecular weight (D) different percentage composition 3. For CO, isotherm is of the type as shown. Near the point A, compressibility factor Z is
A
pVCO
B Ideal
p
(A) b1V
(B) b1V
(C) a1RT V
(D) a1
RT V
4. Depression of freezing point of 0.01 molal aq. CH3COOH solution is 0.02046°. 1 molal urea solution
freezes at –1.86°C. Assuming molality equal to molarity, pH of CH3COOH is 23.0 Torr at 25°C, is (A) 0.25 (B) 0.75 (C) 0.50 (D) 0.66 5. The unstable nucleus 212
82 Pb decays with -particle emission, having a half-life of 10 h. From this it follows that the
I. mass number of the product is 212 II. atomic number of the product is 81 III. fraction of the original isotope remaining after 20 h is 1/4 IV. nucleus formed is stable (A) I, II and III (B) I and III (C) II and IV (D) IV
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IT2019JEE Main 2019 Mock Test-1-(100365.1)-PCM10
6. In the reaction, P Q R S the time taken for 75% reaction of P is twice the time taken for 50% reaction of P. The concentration of Q varies with reaction time as shown in the figure. The overall order of the reaction is
Time
[Q]
0[Q]
(A) 2 (B) 3 (C) 0 (D) 1
7. 2 2 32SO O 2SO . Starting with 2 mole SO2 and 1 mole O2 in 1 L flask, mixture required 0.4
mole MnO4– in acidic medium. Hence, KC is
(A) 2 (B) 0.4 (C) 1.6 (D) 2.6 8. When con entreated HCl is added to a, solution of [Co(H2O)6]4– ion, an intense blue colour develops
due to the formation which one of the following ? (A) [CoCl6]4– (B) [CoCl4]2– (C) [CoCl2(H2O)4] (D) [CoCl(H2O)5]+ 9. A container of 1.0 L capacity filled with 1.0 mole of ideal gas is connected to an evaculated vessel of
9.0 L. Calculate the change in entropy. (R = 1.987 cal) (A) 0.188 cal K–1 mol–1 (B) 0.4576 cal K–1 mol–1 (C) 4.576 cal K–1 mol–1 (D) 4.366 cal K–1 mol–1 10. The standard enthalpy of formation of NH3 is –46.0 kJ mol–1. If the enthalpy of formation of H2 from its
atoms is –436 kJ mol–1 and that of N2 is –712 kJ mol–1, the average bond enthalpy of N–H bond in NH3 is
(A) –964 kJ mol–1 (B) +352 kJ mol–1 (C) +1056 kJ mol–1 (D) –1102 kJ mol–1 11. Mg2C3 reacts with water forming propyne. 4
3C has (A) two sigma an tow pi bonds (B) three sigma and one pi bonds (C) two sigma and one pi bonds (D) two sigma and three pi bonds 12. AgNO3 (aqueous) was added to an aqueous KCl solution gradually and the conductivity of the
solution was measured. The plot of conductance () versus the volume of AgNO3 is
volume(P) (Q)
volume(R)
volume volume(S)
(A) (P) (B) (Q) (C) (R) (D) (S)
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IT2019JEE Main 2019 Mock Test-1-(100365.1)-PCM11
13. Ferrimagnetism is in (A) (B) (C) (D) None of these 14. For the half-cell
OH
OH
O
O
2H 2e ; E 1.30 V
At pH = 2, electrode potential is (A) 1.36 V (B) 1.30 V (C) 1.42 V (D) 1.20 V 15. Select the incorrect order of size of ions/atoms. (A) I I I (B) Fe Co Ni (C) Ni < Cu < Zn (D) None is incorrect 16. In the following reaction,
OH
OH
O
O
acid or base
( = 13C) product formed is
(A)
OH
OH
O
O
(B)
OH
OH
O
O
(C)
OH
OH
O
O
(D)
OH
OH
O
O
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IT2019JEE Main 2019 Mock Test-1-(100365.1)-PCM12
17. CO
O
2NO Product of
This reaction by single SE reaction
(A) CO
ONO2
(B) CO
O
NO2
(C) CO
O
O2N
(D) CO
O
NO2
18. The first ionisation potential of Na is 5.1 eV. The value of electron gain enthalpy of Na+ will be (A) –2.55 eV (B) –5.1 eV (C) –10.2 eV (D) +2.55 eV
19. 3 2 3 2
3 2
3|
CH CH ONa CH CH OH3(CH CH OH) |(major ) (major )
3
CH
CHB CH C Br A
A and B are
(A) 3
|
3 2 3|
3
CH
CHCH C OCH CH in both case (B)
3|
3 2
CH
CH C CH in both case
(C)
2
3 3| |
3 2 3 3| ||
3
CH CH
CH CHCH C OCH CH and CH –C (D)
2
3 3| |
3 3 2 3|| |
3
CH CH
CH CHCH –C and CH C OCH CH
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IT2019JEE Main 2019 Mock Test-1-(100365.1)-PCM13
20.
O
3CH MgBr 3
3
H O HBr Mg/ether HCHOH O
A B C D, D is
(A) CH3 CH2OH
(B) CH3
CH2OH
(C)
CH3
CH3
OH
(D)
CH2OH 21. Which is the incorrect statement about silicones ? (A) They are repeating units (SiO4) in silicates (B) They are synthetic polymers containing repeated R2SiO2 units (C) They are formed by hydrolysis of R2SiCl2 (D) All the above are incorrect statements
22. 2 3||
NaNH /CH IHO OH H3 2
O
CH CCH C CH A, A is
(A) ||
3 2 2 2 3
O
CH CCH CH CH CH (B) ||
3 2 2 2 3
O
CH CH CCH CH CH
(C) ||
3 2 3
O
CH CCH C CCH (D) ||
3 2 3
O
CH CCH HC CHCH 23. Which sequence represents the best synthesis of hexanal ? 3 2 2 2 2CH CH CH CH CH CH O hexanal
(A)
3 2 2 21. CH CH CH CH Br NaC CH
2 2 4 42. H O, H SO , HgSO
(B) ||
3 2 2 2 3
O
1. CH CH CH CH CCH
||
3
O
2. CH COOH 43. LiAlH
24. H O 2 25. PCC, CH Cl
(C) ||
3 2 2 2 3
O
1. CH CH CH CH CH CH COOH 32. CH MgBr, diethyl ether
33. H O 2 24. PCC, CH Cl
(D)
3 2 2 21. CH CH CH CH MgBr H2C CH2
O 32. H O
2 23. PCC, CH Cl
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IT2019JEE Main 2019 Mock Test-1-(100365.1)-PCM14
24. The interhalogen compound not obtained is (A) ICI (B) IF5 (C) BrF5 (D) BrCl7
25.
OC CH
3 2
2 2
BH .THF I /NaOHH O , OH H
X,
X is
(A)
OCOOH
(B)
OCOCH3
(C)
OCH2CHO
(D)
O
26. AgCl and NaCl are colourless. NaBr and NaI are also colourless but AgBr and AgI are coloured. This
is due to (A) Ag+ polarises Br– and I– (B) Ag+ has unpaired d-orbital (C) Ag+ depolarises Br– and I– (D) None of the above is correct 27. (Gly-Ala) has structures
(A) H3NCH2CNHCHCO2
CH3
O
(B) H3NCHC NHCH2CO2
CH3
O
(C) O2CCHNH CCH2NH3
CH3
O
(D) O2CCHNH CCHNH3
CH3
O
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IT2019JEE Main 2019 Mock Test-1-(100365.1)-PCM15
28. Which one of the following is not correctly matched ?
(A) Neoprene [ 2 2 n||
Cl
CH C CHCH ] (B)
|| ||
2 6 2 4
n
O O
Nylon - 66 NH(CH ) NHC(CH ) C
(C) Terylene OCH2CH2C C
OO
n
(D) PMMAn
CCH2
CH3
COCH3
O 29. The process used for purification Al2O3.2H2O is (A) magnetic separation (B) froth floatation (C) leaching (D) liquation 30. Consider following pairs of organic compounds
CCH3
O
CH2C H
O
I :
II : CH3OH CH3CH2OH
III : CH3CCH3 HCHO
O
A test that can make distinction between each pair is (A) Lucas test (B) Silver-mirror test (C) Victor Meyrer’s test (D) Iodoform test
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IT2019JEE Main 2019 Mock Test-1-(100365.1)-PCM16
PPPAAARRRTTT ––– IIIIIIIII ::: MMMAAATTTHHHEEEMMMAAATTTIIICCCSSS
Straight Objective Type
This section contains 30 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which only ONE option is correct 1. If f(x) = x2 + bx + 3 is not injective for values of x in the interval, 0 x 1, then the interval in
which b lies (A) (–, ) (B) (–2, ) (C) (–2, 0) (D) (–, 2)
2. 1/3 1/2
2x 0
cosx cos xlim
sin x
is
(A) 112
(B) 16
(C) 13
(D) 12
3. Tangents are drawn from the origin to the curve y = sin x, then their point of contact lie on
the curve
(A) 2 21 1 1y x
(B) 2 21 1 1x y
(C) x2 – y2 = 1 (D) x2 + y2 = 1 4. 1 2cot x cot x cosec x dx is
(A) x2ln cos c2
(B) x2ln sin c2
(C) 1 xln cos c2 2
(D) ln(sin x) – ln(cosec x – cot x) + c
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IT2019JEE Main 2019 Mock Test-1-(100365.1)-PCM17
5. For 0,2
, the value of
0
ln 1 tan tanx dx
is equal to
(A) ln(sec ) (B) ln(cosec )
(C) ln22
(D) 2 ln(sec )
6. Area bounded by 21y
x 2x 2
and x-axis is (in square units)
(A) 2 (B) 2
(C) 2 (D) 7. The solution of differential equation ex(x + 1)dx + (yey – xex) dy = 0, if f(0) = 0 (A) xex + 2y2ey = 0 (B) 2xex + y2ey = 0 (C) xex – 2y2ey = 0 (D) 2xex – y2ey = 0 8. The point at which the origin be shifted so that the equation x2 + y2 – 5x + 2y – 5 = 0 has no
first degree terms,
(A) 5 , 12
(B) 5, 12
(C) 51,2
(D) 51,2
9. The circle x2 + y2 – 4x – 8y + 16 = 0 rolls up the tangent to it at 2 3, 3 by 2 units,
assuming the x-axis as horizontal, then the equation of circle in the new position is (A) x2 + y2 – 6x – 2 4 3 y + 24 + 8 3 = 0
(B) x2 + y2 – 6x + 2 4 3 y + 24 + 8 3 = 0
(C) x2 + y2 + 6x – 2 4 3 y + 24 + 8 3 = 0 (D) none of these
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IT2019JEE Main 2019 Mock Test-1-(100365.1)-PCM18
10. If the incident ray from the point (–3, 2) parallel to the axis of parabola y2 = 4x strike the parabola, then the equation of reflected ray is
(A) x + 1 = 0 (B) x – 1 = 0 (C) y = 0 (D) y – 1 = 0
11. If 2
2atan tanb
, then the chord joining two points and an the ellipse 2 2
2 2x y 1a b
will
subtend a right angle at (A) focus (B) centre (C) end of major axis (D) none of these 12. If 5x2 + y2 = 20 represents a rectangular hyperbola then equals (A) 5 (B) 4 (C) –5 (D) none of these 13. If a, b, c, d and p are distinct real numbers such that (a2 + b2 + c2)p2 – 2(ab + bc + cd)p + (b2 + c2 + d2) 0, then a, b, c, d are in (A) A.P. (B) G.P. (C) H.P. (D) none of these 14. If a > 0, b > 0, c > 0 and the minimum value of a(b2 + c2) + b(c2 + a2) + c(a2 + b2) is abc,
then is (A) 2 (B) 1 (C) 6 (D) 3 15. The number of real roots of (6 – x)4 + (8 – x)4 = 16 is (A) 0 (B) 2 (C) 4 (D) none of these 16. The coefficient of x65 in the expansion of (1 + x)131(x2 – x + 1)130 is (A) 130C65 + 129C66 (B) 130C65 + 129C55 (C) 130C66 + 129C65 (D) none of these
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IT2019JEE Main 2019 Mock Test-1-(100365.1)-PCM19
17. If 2001 i
1 i
= x + iy, the sin–1 x + cos–1 y is equal to
(A) 2 (B)
(C) 32 (D) none of these
18. A polygon has 9 diagonals. The number of its sides is (A) 3 (B) 6 (C) 9 (D) none of these
19. If maximum and minimum values of the determinant
2 2
2 2
2 2
1 sin x cos x sin2x
sin x 1 cos x sin2x
sin x cos x 1 sin2x
are and
, then (A) + 99 = 5 (B) 3 - 17 = 25 (C) (2n – 2n) is always an even integer for nN (D) a triangle can be constructed having it’s sides as , and –
20. Let A =
2
2
2
x 6 8
3 y 9
4 5 z
, B = 2x 3 52 2y 61 4 2z 3
. If trace A = trace B then x + y + z is equal to
(A) 0 (B) 6 (C) 5 (D) none of these
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IT2019JEE Main 2019 Mock Test-1-(100365.1)-PCM20
21. The odds against an event A are 5 : 2 and odds in favour of another independent event B are 6 : 5 the chance that neither A nor B occurs is
(A) 5277
(B) 2577
(C) 1077
(D) 1277
22. The vectors a
and b
are non-zero and non-collinear. The value of x for which vector c = (x – 2)a
+ b
and d
= (2x + 1)a – b
are collinear
(A) 1 (B) 1/2 (C) 1/3 (D) 2 23. If vectors ax ˆ ˆ ˆi 3 j 5k and x ˆ ˆ ˆi 2 j 2axk make an acute angle with each other, for all x R,
then a belongs to the interval
(A) 1,04
(B) (0, 1)
(C) 60,25
(D) 3 ,025
24. The distance between the parallel planes 2x – y + 2z + 3 = 0 and 4x – 2y + 4z + 5 = 0 is
(A) 18
(B) 116
(C) 16
(D) none of these
25. The number of solutions of the equation sin x2 3
= x2 – 2 3 x + 4 is
(A) 0 (B) 2 (C) 1 (D) none of these
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IT2019JEE Main 2019 Mock Test-1-(100365.1)-PCM21
26. If (tan–1x)2 + (cot–1x)2 = 25
8 , then x equals
(A) –1 (B) 1 (C) 0 (D) none of these 27. AB is a vertical pole. The end A is on the level ground. C is the middle point of AB, P is a
point on the level ground. The portion BC subtends an angle at P. If AP = nAB, then the tan is equal to
(A) 2n
2n 1 (B) 2
nn 1
(C) 2n
n 1 (D) none of these
28. If X = {4n 3n 1 : n N} and Y = {9(n 1) : n N}, then (A) X Y (B) X = Y (C) Y X (D) none of these 29. The statement (p ~q) p is logically equivalent to (A) p (B) ~p (C) q (D) ~q 30. S.D. of a data is 6. When each observation is increased by 1, then the S.D. of new data is (A) 5 (B) 7 (C) 6 (D) 8
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IT2019JEE Main 2019 Mock Test-1-(100365.1)-PCM22
PHYSICS, CHEMISTRY & MATHEMATICS JEE Main 2019 Mock Tests-1 (Code:100365.1)
ANSWER KEY PHYSICS (PART-I) 1. C 2. A 3. C 4. C
5. B 6. D 7. B 8. D 9. B 10. D 11. C 12. C 13. A 14. C 15. C 16. D 17. B 18. C 19. B 20. A 21. C 22. B 23. D 24. A 25. A 26. A 27. A 28. C
29. C 30. B
CHEMISTRY (PART-II) 1. A 2. C 3. D 4. B
5. B 6. D 7. A 8. A
9. D 10. B 11. A 12. D
13. C 14. C 15. D 16. A
17. C 18. B 19. C 20. D
21. A 22. C 23. D 24. D
25. D 26. A 27. A 28. C
29. C 30. D
MATHEMATICS (PART-III) 1. C 2. A 3. A 4. D
5. A 6. D 7. B 8. A
9. A 10. B 11. B 12. C
13. B 14. C 15. B 16. D
17. B 18. B 19. C 20. D
21. B 22. C 23. C 24. C
25. C 26. A 27. A 28. A
29. A 30. C
FIITJEE - JEE (Main)
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IT2019JEE Main 2019 Mock Test-1-(100365.1)-PCM23
HINTS AND SOLUTIONS
PHYSICS (PART-I) 1. 600 T = ma
min600 360a 4
60
m/s2
2. 00 0
mvmgt mv
2
0
0
v2gt
3. Maximum will be corresponding to source position A
and minimum to source friction B.
So, time interval =
1 32cos2 5
5
C
A
B
O
4. As A and B will be at same potential so
charge flown equal to Q.
A Q
r
R
B
5. N = Mg
L NLF sin cos2 2
mg 3tanF 4
F
N
mg
6. 2
20
1 2
1 q 1LI2 (C C ) 2
1 2 0q L C C I
1 1 1 0
1 2 1 2
q Lq C C IC C C C
7. 1T1 = 2T2
1 1
0
T 2T
= 20 8.
A
B Y
C
A
(B+C)
A .(B+C)
9. e = B(dA/dt) = B(2r)(dr/dt)
10. 4aR 9.1 101.22
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IT2019JEE Main 2019 Mock Test-1-(100365.1)-PCM24
11. 2
1 22
2 1
(z 1)(z 1)
2
22
(z 1)14 (11 1)
On solving z2 = 6 12. V = Bv = (3) (2) (1) = 6V VR = VC = VL = 6V (all are in parallel)
LdiV Ldt
6 = di2dt
di 3dt
A/sec, After 2 sec, current will be 6A
13. Given v0 = ve/2
1/2 1/2GM 1 2GMR h 2 R
On solving h = R From law of conservation of energy,
2GMm 1 GMmmv(R h) 2 R
or 21 GMm GMm GMmmv2 R 2R 2R
or GMv gRR
= [(10) (6.4 106)]1/2 = 8 km/sec 14. mg + T 4a = (a)2xg
x = 2
mg 4Taa g
15. U = Q/2 dU = dW CvdT = PdV
32
(PdV + VdP) = PdV
PdV + 3VdP = 0 PV1/3 = constant
C = Cv + R
1 1 3 = 3R.
16. 0 01 2
I Ia aB B(at r )2 2 4 a2 a
B2 = B(at r = 2a)
0 0I I2 (2a) 4 a
Ratio of the fields, B1/B2 = 1 : 1 17 The magnitude of B is
88
E 6.3 V / mB 2.1 10c 3 10 m / s
T
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IT2019JEE Main 2019 Mock Test-1-(100365.1)-PCM25
To find the direction, we note that E
is along y-direction and the wave propagates along x-axis. Therefore, B
should be in a direction perpendicular to both x- and y-axes. Using vector algebra,
E B
should be along x-direction. Since, ˆ ˆ ˆj k i , B is along the z-direction.
Thus, B = 2.1 × 108 kT . 18. The total energy falling on the surface is U = (18 W/cm2) × (20 cm2) × (30 × 60) J = 6.48 × 105 J Therefore, the total momentum delivered (for complete absorption) is
5
38
U 6.48 10 Jp 2.16 10c 3 10 m / s
kg m/s
The average force exerted on the surface is
3
64
p 2.16 10F 1.2 10 Nt 0.18 10
19. 1002 cm, = 200 cm
v = f = 2 2.53 103 = 5.06 103 m/s 20. we know
2ne
m
Cu Cu Cu
Au Au Au
501.449
= 10/7
21. Work done by friction x
0
dxF ds mgcoscos
= mg x = 20 J
N
f
mg dxcosds
dx
dy ds
22.
22
n
5VR 5 5m1a5
23. Potential across capacitor is zero, hence energy stored is zero.
24. TyA
, T mgLAy Aycos
25. In critical condition, torque on loop is equal to gravitational torque about an axis tangent to the loop, g = mgr xB is contributing a torque,
2xM B MBsin90 r iB
1/ms at t = 0
at t = 1sec
5
1/ms
2/ms
1m/s2
1m/s2
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IT2019JEE Main 2019 Mock Test-1-(100365.1)-PCM26
x
mg 7 11 10i 2ArB 22 3.5 5
26. Path difference due to slab should be integral multiple of x = n ( – 1)t = n, n = 1, 2, …..
nt1
For minimum value of t, n = 1
t = n 21 1.5 1
27. R V IR V I
R V I100 100 100R V I
3%
28. AB CDR RKA
eq BCR
2KA
we have, CT 0100 02KA 2KA KA
TC = 28C
29. Apply gaus theorem
2 in
0
qE 4 r
2 20
q 1E E4 r r
field depends only on r. 30. Here, three optical phenomena take place-first refraction, then reflection,
and finally refraction.
For 1st refraction, 1.5 1 1.5 1v 2R R
1.5 0 vv
i.e. rays after refraction get parallel to the axis and strike the mirror normally, get retraced back, and final image is formed at the same place where the object is kept.
2R
h =1.5
CHEMISTRY (Part-II)
1. A Wave number of spectral line in emission spectrum of hydrogen,
H 2 21 2
1 1Rn n
…(i)
Given, H8 R9
On putting the value of in eq. (i), we get
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IT2019JEE Main 2019 Mock Test-1-(100365.1)-PCM27
H H 2 21 2
8 1 1R R9 n n
2 22
8 1 19 (1) n
22
8 119 n
n2 = 3 Hence, electron jumps from n2 = 3 to n1 = 1 2. C Same empirical formula, it means ratio of atoms is identical. Hence, they differ in molecular weight. 3. D At point a near low pressure region volume is very high thur (V – b) V
2ap V RT
V
apV RTV
pV aZ 1RT RT V
4. B
3CH COOH f( T) K 0.01 i 0.02046
urea f( T) K 1 1.86 i 1.1 (1 x) x = 0.1 3
3[H ] in CH COOH Cx 1 10 M pH = 3 5. B 0212 212
82 83 1( )
Pb Bi e
y 2
00 0
N1 1N N N2 2 4
total time 20where, y 2half - life 10
Thus, I and III are true 6. D 7. A SO2 is oxidised by MnO4
– in acidic medium. 2 2
2 4 45SO 2MnO 2Mn 5SO 2mol MnO4
– 5 mol SO2 Hence, 0.4 mol MnO4
– 1 mol SO2
2 2 32SO O 2SO (2–2x) (1–x) 2x (2 – 2x) = 1 mol (as determined by MnO4
–) x = 0.5
32x[SO ] 1MV
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IT2019JEE Main 2019 Mock Test-1-(100365.1)-PCM28
22 2x[SO ] 0.5M
V
21 x[O ] 0.5 M
V
2
3c 2
2 2
[SO ]K 2
[SO ] [O ]
8. A 2 4
2 6 6 2[Co(H O) ] 6Cl [CoCl ] 6H O Cl– replace H2O ligands and intense blue colour is developed. 9. D
2
1
VS 2.303 Rlog
V
9S 2.303 1.987log1
1 1S 2.303 1.987 0.9542 4.366 cal K mol 10. B Given, 1
22H H H 436 kJmol
122N N H 712 kJmol
o 12 2 3 f
3 1H N NH , H 46 kJmol2 2
Thus, 1
(H H)(BE) 436 kJ mol
1(N N)(BE) 712 kJ mol
(N H)(BE) ?
Based on (BE) values of
H H N N N H3 1(BE) (BE) 3(BE)2 2
3 1436 712 3x 462 2
1N Hx(BE ) 352 kJ mol
11. A 2 3 2 3Mg C H O CH C CH
C C C
,
Two and two bond 12. D 13. C 14. C In this electrode [A] = [B] in quinhydrone electrode
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IT2019JEE Main 2019 Mock Test-1-(100365.1)-PCM29
OH
OH
O
O
2H 2e
(A) (B) Hence, Q = [H+]2
20.0591E E log[H ]2
E 0.0591pH = E° + 0.0591 pH = 1.30 + 0.0591 2 1.42 V 15. D A true, B true, C true 16. A There is enolisation of the keto ring
OH
OH
O
O
OH
OH
O
O
OH
OH
O
O
17. C
CO
O
A B
activation deactivation, thus, attacks ring (A)2NO
but at p-site due to avoid steric effect.
18. B 19. C 20. D
O
3
3
CH MgBrH O
CH3 OH
HBr
CH3 OH2
CH3
2H O
1, 2-methyl shiftring expansionBr
Br
MgBr
Mg / ether
3
(i) HCHO(ii) H O
CH2OH
3 carbocation
predominant 21. A 22. C
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IT2019JEE Main 2019 Mock Test-1-(100365.1)-PCM30
Glycol blocks carbonyl group
2 3NaNH /CH I3 2 3 2 3CH CCH C CH CH CCH C C – CH
OO OO
||H
3 2 3
O
CH CCH C CCH
23. D
3
(i)
3 2 2 2 3 2 2 2 2 2(ii) H OCH CH CH CH MgBr CH CH CH CH CH CH OH
H2C CH2O
oxid PCC, CH2Cl2
3 2 2 2 2CH CH CH CH CH CHO 24. D Due to steric effect 25. D
OC CH
OCCH3
OOO
COOH3
2 2
BH /THFH O /OH
2(i) I /NaOH(ii) H
26. A 27. A 28. C 29. C 30. D
I II III Lucas test No No No Silver mirror test Yes No Yes Victor Meryer’s Test No No Yes Iodoform test Yes Yes Yes
MATHEMATICS (PART-III) 1. f(x) is not one-one then atleast one horizontal line should intersect it at two points
b0 12
b (–2, 0)
2. Let cos x = y
1/3 1/2
2y 1
y ylim1 y
=
1/3 1/2
2y 1
y 1 y 1y 1 y 1
limy 1y 1
= 1 1
13 22 12
3. y = sin x
dy cosxdx
0 cos0
..... (1)
= sin ..... (2) Squaring and adding (1) and (2), we get
y
O
y = sin x
P(, )
x
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IT2019JEE Main 2019 Mock Test-1-(100365.1)-PCM31
2
2 2 2cos sin 2 2
1 11
2 21 1 1
2 21 1 1y x
4. 2I 1 2cosec x cot x 2cot x dx
= 2 2cosec x 2 cosec x cot x cot x dx
= cosec x cot x dx = ln(sin x) – ln(cosec x – cot x)
5. 0
I ln 1 tan tan x dx
I = ln sec
6. Area = 21
12 dxx 2x 2
= 11
2 tan x 1
= 2 02
sq. units
y
x n = 1 O
7. xex = t
x x dx dte xedy dy
; ydt y e t 0dy
ydt t yedy
I.F. = 1 dy ye e
2
y y y yt e ye e dy c2
xex – y = 2y c
2
x = y = 0 c = 0 2xex + y2ey = 0
8. 2
25 49x y 12 4
9. Equation of tangent at P x 2 3 y 3 2 x 2 3 4 y 3 16 0
3x y 2 3 0 B = (2 + 2 cos 60º, 4 + 2 sin 60º) = 3, 4 3
22 2x 3 y 4 3 2
A(2, 4)
B
P 2 3, 3 60º
Q
10. incident ray passes through focus 11. mOA·mOB = –1
A(a cos , b sin ) B(a cos , b sin )
x
y
O
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IT2019JEE Main 2019 Mock Test-1-(100365.1)-PCM32
12. Since the general equation of the second degree represents a rectangular hyperbola, if 0, h2 > ab and a + b = 0
Therefore the given equation represents a rectangular hyperbola, if + 5 = 0 = –5 13. The given inequality can be re-written as (ap – b)2 + (bp – c)2 + (cp – d)2 0 ap – b = bp – c = cp – d = 0
a b c 1b c d p a, b, c, d are in G.P.
14. Using AM G.M.
12 2 2 2 2 2
2 2 2 2 2 2 6ab ac bc ba ca cb ab .ac .bc .ba .ca .cb6
a(b2 + c2) + b(c2 + a2) + c(a2 + b2) 6abc Hence = 6 15. Let y = 7 – x. Then the given equation becomes (y + 1)4 + (y –1)4 = 16 y4 + 6y2 – 7 = 0 (y2 – 1)(y2 + 7) = 0 y2 – 1 = 0 [ y2 + 7 0] y = 1 7 – x = 1 x = 6, 8 16. (1 + x)131(x2 – x + 1)130 = (1 + x)(1 + x3)130 = (1 + x3)130 + x(1 + x3)130 Hence coefficient of x65 is zero
17. 2002i
2
= (i)200 = 1 x = 1, y = 0
18. nC2 – n = 9 n n 1n 9
2
n2 – 3n – 18 = 0 n = 6
19. Applying C1 C1 + C2, we get
2
2
2
2 cos x sin2x
2 1 cos x sin2x
1 cos x 1 sin2x
Applying R2 R2 – R1 and R3 R3 – R1, we get
22 cos x sin2x0 1 01 0 1
= 2 + sin 2x
Since the maximum value of sin 2x is 1, and min value of sin 2x is (–1) Therefore = 3, = 1
20. x2 + y2 + z2 = 2x + 2y + 2z – 3 x2 – 2x + 1 + y2 – 2y + 1 + z2 – 2z + 1 = 0 (x – 1)2 + (y – 1)2 + (z – 1)2 = 0 x = 1, y = 1, z = 1 x + y + z = 3
21. Given P (A) = 27
and P (B) = 611
Required probability = P (A B) = (1 – P(A)) · (1 – P(B)) 22. Since c
and d
are collinear We have pc qd
= 0 where p + q = 0 for some scalars p and q
p{(x – 2)a + b
} + q{(2a
+ 1)a – b
} = 0
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IT2019JEE Main 2019 Mock Test-1-(100365.1)-PCM33
p(x – 2) = –q(2x + 1) and pb
= qb
(since a, b are
non-collinear) p(x – 2) = –p(2x + 1) x = 1/3 23. Since vectors make an acute angle with each other so Wtheir dot product must be positive. i.e. ax2 – 10 ax + 6 > 0 x R –ax2 + 10ax – 6 < 0 x R –a < 0 and 100a2
< 24a 24. Let P(x1, y1, z1) be any point on 2x – y + 2z + 3 = 0, then 2x1 – y1 + 2z1 + 3 = 0 ..... (1) The length of perpendicular from P(x1, y1, z1) to 4x – 2y + 4z + 5 = 0 is
1 1 11 1 12 2 2
2 2x y 2z 54x 2y 4z 5 16364 ( 2) 4
(Using equation (1))
25. sin x2 3
= (x – 3 )2 + 1 which can hold only if x = 3
26. y2 + 2 25y
2 8
, where y = tan–1x y = tan–1x = –
4 , 3
4 x = tan 1
4
27. Let APC = . Then tan =
AC AC AB 1AP nAB 2nAB 2n
In APB, tan ( + ) = AB AB 1AP nAB n
Now, = + –
tan = tan( ) tan1 tan( )tan
= 2
1 1 nn 2n1 1 2n 11 n 2n
B
AP
C
Hence (A) is the correct answer 28. Here, 4n 3n 1 = (1 + 3)n 3n 1 = nC0 + nC1 3 + nC2 3
2 + + nCn 3n 3n 1
= 32 {nC2 + nC33 + + nCn 3n2} which is a multiple of 9. Hence, X Y
29.
p q ~ q p ~ q (p ~ q) p T T F F T T F T T T F T F F F F F T F F
Hence p is logically equal to statement p��~ q) ��statement (p 30. S.D. (and variance) of a data is not changed when each observation is increased (or decreased) by the same constant