Transcript
FULL TEST : ID  004
SPACE FOR ROUGH WORK
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PCM : TEST PAPER XII – JEE MAINS
x2
1.
4
The value of Lim cos ec x x0
0
(1) 1 2.
n(1 n(1 4t) dt is t 2 1
(2) 2
(3) 3
(4) 4
3 2
Consider the matrix A t he determinant of B A I is . Then all possible values of λ such that the 4 1
1
0
0, where I and i 1, is 0 1 (1) 1 2i 3.
1 p
1 1 1 1 2 r p p q
2 q
2 r
(2)
4 r
(4) 5 6i
4 p
1 1 1 1 q r p q
If n (e 1)exy x 2 x 2 y2 , then (1) 0
5.
1 q
(3) 3 4i
The equation x2 x 0 has both the roots equal, then (1)
4.
(2) 2 3i
(3)
1 1 1 1 r p p q
(4)
1 1 1 1 r p q r
dy at (1, 0) is equal to [Note : e denotes Napier’s cons tant] dx
(2) 1
(3) 2
(4) 3
Let A [aij ]33 , B [bij ]33 where bi j 3ij ai j and C [ci j ]33, where ci j 4i j bi j be any three matrices. If det. A = 2, then det. B + det. C is equal to (1) 4
6.
(2) 3
(3) 2
(4) 1
For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is (1)
11 2
(2) 6
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(3)
13 2
(4)
5 2
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JEEMAINS TEST PAPER PAPER
7.
The locus of the foot of the perpendiculars drawn from the vertex on a variable tangent to the parabola
y2 4ax is
8.
(1) x (x2 y2 ) ay ay2 0
(2) y (x2 y2 ) ax ax2 0
(3) x (x2 y2 ) ay ay2 0
(4) x2 y2 ay2 0
Number of distinct real solutions of the equation x7 14x5 16x3 30x 42 420 0 is equal to (1) 0
9.
(2) 1
(3) 2
(4) 3
Let a = 8 and b = 3 9 and we define a sequence {un } as follows
1 u ; if u is multip tiple of 3 n u1 b, un1 3 n un a; a; otherwise then u500 u300 u 400 is equal to (1) 1 10.
(2) 3
(3) 5
(4) 7
Let f :( 1, 1,1) R be a differentiable function with f (0 (0) 1 and f '(0) 1. Let 2
g(x) f (2 (2f ( x) x) 2) , then g'(0) equals
(1) 4 11.
(2) 0
sin 2x 3 3
The maximum number of positive solutions of equation cos
(1) 0, 6 12.
(3) 2
(2) , 9 6
(3) , 9 3
(4) 4
, lies in 2
3, x 0,
(4) , 3 2
The equation to the locus of the middle mi ddle point of the portion of the tangent to the ellipse x 2 y2 16 9
1 included between the coordinate axes is the curve
(1) 9x2 16y2 4x2 y2 (2) 16x2 9y2 4x2 y2 (3) 3x2 4y2 4x2 y2 (4) 9x2 16y2 x2 y2 13.
Let P(a,b,c) be any point on the plane 3x 2y z 7 then the least value of (a2 b2 c2 ), is (1) 7
(2) 14
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(3)
7 2
(4) 4
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JEEMAINS TEST PAPER PAPER
14.
Given p and q are respectively the maximum and minimum value of f (x) 5sin 5sin(x) (x) 12co 2cos(x) (x) 1. If (p, q) is the centre of the circle ci rcle touching the xaxis then radius of the circle is (1) 14
(2) 12
(3) 13
(4) 11
3
15.
2sin3 x The value of the definite integral dx, dx, is equal to 5 cos x
4
(1) 1 16.
(2) 2
(3) 3
(4) 4
TP and TQ are tangents to the parabola y2 4ax at P and Q. If the chord PQ passes through the fixed point (a,b) then the locus of T is (1) ay 2b(x b)
17.
(2) bx 2a(y a)
(3) by 2a(x a)
(4) ab 2b(y b)
Tangents are drawn to the circle x2 y2 32 from a point A lying on the xaxis. The tangents cut the yaxis at point B and C, then the possible coordinates of A such that the area of ABC is minimum, are 2,0) (1) (8 2,0)
18.
(2) (12,0)
(3) (8,0)
(4) (8 2,0)
If the ellipse 4x2 9y2 36 and the hyperbola 2x2 y2 4 intersects orthogonally, then the value of can be (1) 5
19.
(2) 4
(3) 3
(4) 2
3 3 The upper th portion of a vertical pole subtends subtends an angle tan tan1 at a point in the horizontal plane 5 4 through its foot and at a distance 40m. from the foot. The height of vertical pole is (1) 20m
20.
(2) 40m
(3) 60 m
(4) 80 m
Let 3x y 8 0 be the equation of tangent to a parabola at the point (7, 13). If the focus of the parabola is at (1, 1), its directrix is (1) x 8y 19 19 0
21.
(2) 8x y 19 19 0
(3) 8x y 19 19 0
(4) x 8y 19 19 0
Consider the following statements P : Suman is brilliant
Q : Suman is rich
R : Suman is honest
The negation of the statement ‘Suman is brilliant and dishonest if and only if Suman is rich’ can be
expressed as (1) ~ Q (P ~ R) (2) ~ Q ~ P R SPACE FOR ROUGH WORK
(3) ~ (P (P ~ R) R) Q
(4) ~ P (Q ~ R) Page 3
JEEMAINS TEST PAPER PAPER
22.
The area (in sq. units) of tthe he region consisting of points (x, y) on xy plane which satisfy  x  1  y  and  y  1 is
(1) 4 23.
(2) 6
ax2 bx c If Lim x1 (x 1)2
(4) 12
2, then which of the following relation is correct?
(1) a2 b2 c2 12 24.
(3) 8
(3) a 2 c2 2b
(2) a c b
(4) b2 2(a2 c2 )
If the circle x2 y2 4x 22 of the circle x2 y2 2x 8y d 0 then 22y c 0 bisects the circumference of (c d) equals
(1) 50 25.
(2) 52
Let P be a variable point on the t he ellipse
(3) 54 x 2 y2 25 16
(4) 56
1 with foci at S1 and S2. If A is the area of triangle
PS1 S2 , then the maximum value of A is
(1) 12
(2) 24
(3) 36 1
26.
Let g(x) be a differentiable function on R and
(4) 48
g(x)d dx (1 sint), int), where t 0, . Then the value x g(x) 2 2
sint
1 equals 2
of g
(1)
1 2
(2) x2
27.
Let f (x)
0
1 2
(3) 2
(4) 1
t 2 1 dt. If a is the point of local maxima and b and c (b > c) are the points of the local et 1
minima, then (1) a b c 1
(2) a b c
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(3) a c b
(4) b c a Page 4
JEEMAINS TEST PAPER PAPER
28.
Let a i 2 j 3k; b i j 4k; c 4i 3j 6k; d 3i 6 j 5k then the value of a b c d is equal to (1) 214
29.
Consider two lines L1 :
(2) 342
(3) 392
(4) 476
x 7 y 7 z 3 x 1 y 1 z 1 and L2 : . 3 2 1 2 4 3
If a line L whose direction ratios are 2,2,1 intersect the lines L1 and L2 at A and B then distance AB is (1) 18 30.
(2) 24
(3) 36
If α and β are different di fferent complex numbers with 1, then then
(1) 0
(2)
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1 2
(4) 50
is equal to 1
(3) 1
(4) 2
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JEEMAINS TEST PAPER PAPER
31.
If mass of an element is 5.74 gm and its volume is 1.2 cm3. Its density will be : (1) 4.783 g/cm3
32.
(2) 4.78 g/cm3
(3) 4.7 g/cm3
(4) 4.8 g/cm3
The resistance and inductance of a coil are 1 ohm and 2 Henry respectively. A capacitor of 2F capacitor is discharged through the above coil. The frequency (n) and quality factor (Q) of LC circuit will be : (1) 59.5Hz, 59.5Hz,10 103
33.
(3) 79.5Hz, 79.5Hz,10 103
(4) 35.5Hz,102
If v Ax BeCt where v is velocity, x is distance, t is time then dimensions of A, B and C are : (1) LT1 ,L,T
34.
(2) 69.5Hz, 69.5Hz,10 103
(2) T1, L T1, T1
(3) L, LT1,T
(4) T, T, T
A neutral metallic sphere is present infront of a uniformly charged very large conducting plane force between sphere and plane plane is F and torque on sphere is ' ' then (1) F 0, 0
35.
(2) F 0, 0
(3) F 0, 0
(4) F 0, 0
A particle changes its velocity from 6 ms1 towards east to 6 ms1 towards north in 3 second. Then magnitude of its average acceleration will be : (1) 0
36.
37.
(2) 2 ms1
(3) 2 2 ms2
(4) 6 2 ms2
A rod is projected vertically up, such that it is rotating about its c.m. during its flight. Its angular velocity: (1) during ascent decreases
(2) during its flight decreases
(3) during ascent increases
(4) remain same
At what temperature does the rms speed of gas molecules will be double the rms speed at NTP (Pressure is assumed constant) : (1) 546 K
38.
(2) 273C
(3) 819C
(4) 1092C
If F yi x j is acting on particle during its displacement from (0, 0) to (2, 3) then find work done by the force (1) 6 J
(2) 4 J
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(3) 5 J
(4) data insufficient Page 6
JEEMAINS TEST PAPER PAPER
39.
If three tuning forks of frequencies 500, 501 and 502 Hz are ar e sounded together then the number of beats produced per second will be : (1) 2
40.
(2) 3
(3) 1
(4) 0
Two bodies of mass ‘m’ and 9m are placed at distance r. The gravitational potential at a point on the line
joining them where the gravitational gravitational field is zero is : (1) zero 41.
(2)
16Gm r
(3)
16Gm 3r
(4)
3Gm 16r 16r
A hydrogen atom and Li ion are both in i n the second excited state. If LH and LLi are their respective electronic angular momenta, and EH and ELi their respective energies, then :
42.
(1) LH LLiLi and EH ELi
(2) LH LLiLi and EH ELi
(3) LH LLiLi and EH ELi
(4) LH LLiLi and EH ELi
A particle of mass 2 kg has potential energy U 8x2 4x 4. Then its angular frequency for small oscillation about its equilibrium position will be : (1) 2 2 rad / sec
43.
(2) 2 rad/sec
(3) 1 rad/sec
(4) 4 rad/sec
One thousand small water drops of equal radii combine to form a big drop. The ratio of final surface energy to the total initial surface energy. (1) 1000 : 1
44.
(2) 1 : 1000
(3) 10 : 1
(4) 1 : 10
If three consecutive frequency produced by an organ pipe is 200 Hz, 250 Hz and 300 Hz then the organ pipe.
45.
(1) must be open pipe
(2) must be closed organ pipe
(3) may be closed organ pipe
(4) none
If the experiment of Newton’s l aw of cooling, the graph drawn between logarithm of excess of temperature
with the surroundings and the time is obtained as : (1) a straight line passing passing through through origin origin of positive gradient (2) a straight line line of positive positive gradient, not passing through origin (3) a straight line line of negative negative gradient, gradient, not passing passing through through origin (4) none of the above SPACE FOR ROUGH WORK
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JEEMAINS TEST PAPER PAPER
46.
At any instant, before its maximum height, power during ascent of a projectile on parabolic path must be (1) positive
47.
(2) negative
(3) zero
(4) data insufficient
An object is moving with a velocity of 5 cm/s at an angle of 60 with respect to the t he optic axis of a concave mirror of focal length 100 cm. The object is i s at a distance of 50 cm form the mirror. Find the velocity of image at the given instant.
48.
10i 5 3 j) cm/ s (1) (10
10i 5 3j)cm/s (2) (10
10i 5 3j)cm/s (3) (10i
10i 5 3j)cm/s (4) (10i
A carnot engine takes 840 J heat from the source. If its efficiency is 20%. How much heat will be rejected to sink. (1) 200 cal
49.
(2) 180 cal
(3) 42 cal
(4) 160 cal
A charged particle having some mass is resting in i n equilibrium at a height H above the centre of a uniformly charged nonconducting horizontal ring of radius R. The force of gravity acts downwards. The nature of equilibrium of the particle will be stable (1) for all values of H
50.
(2) only if H R / 2
(3) Only if H R / 2 (4) H R / 2
The work function of a metallic surface is 5.01 eV. Photoelectrons are emitted when light of wavelength 2000 Å falls on it. The potential difference required to stop the fastest photoelectrons is : (h 4.14 10 1015eVs)
(1) 1.2 V 51.
(2) 2.4 V
(3) 3.6 V
(4) 4.8 V
A person slides small ball with speed u along the smooth floor from point A. The ball returns to A after sliding on the circular smooth surface in the vertical plane from B to C and becoming a projectile at C. What is the minimum value of x for which the game could be planed if contact must be maintained at point C. neglect friction. (1) 2R
(2) 3R
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(3) 4R
(4) R Page 8
JEEMAINS TEST PAPER PAPER
52.
In Xray tube, when the accelerating voltage V is halved, the difference between the wavelengths of K line and minimum wavelength of continuous Xray spectrum.
53.
(1) remains constant
(2) becomes more than two times
(3) becomes half
(4) becomes less than two times
In the circuit diagram shown in figure, the capacitor of capacitance C is uncharged when the key k is open. The key is closed for time during which the capacitor becomes charged to a voltage V. Determine the amount of heat Q2 liberated during this time in the resistor of resistance R 2 if the emf of the source is E, and its internal resistance can be neglected.
54.
(1)
2R1CV (E V) (R1 R2 )
(2)
2R1CV (E V) 2(R1 R2 )
(3)
R1CV CV (E V) 2(R1 R2 )
(4)
R1CV CV (2E (2E V) 2(R1 R2 )
A bar of diamagnetic substance is placed in a magnetic field with its length making angle 30 with the direction of the magnetic field. How will the bar behave? (1) It will align itself parallel to the magnetic magnetic field (2) It will align itself perpendicular to the magnetic field field (3) It will remain remain as before (4) Its behavior cannot be predicted
55.
The current through 10 resistor in the circuit given below is (the diodes are ideal)
(1) zero 56.
(2) 80 mA
(3) 30 mA
(4) 20 mA
The magnetic field inside a current carrying toroidal solenoid is B. If its radius is doubled and the current through it is also doubled keeping the total number of turns same, the magnetic field inside the solenoid will be : (1) B/2
(2) B
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(3) 2 B
(4) 4B
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JEEMAINS TEST PAPER PAPER
57.
Two small balls having the same mass and charge are located on the same vertical line at height h 1 and h2. They are thrown simultaneously with the same velocity in the same direction along the horizontal. The first ball hits the ground at a distance distance l from from the initial vertical line. At what height will the second ball be at this instant (h1 h 2 ) 2
l (1) h1 h2 g v 58.
2
l (2) h1 h2 g v
l (3) h1 h2 g v
2
(4) None of these
If a carrier wave of 1000 kHz is used to carry the signal, the length of transmitting antenna will be equal to : (1) 3 m
59.
(2) 30 m
(3) 75 m
(4) 3000 m
You are given a parabolic mirror whose inner surface is silvered. The equation of the curve formed by its intersection with xy plane is given by y
x2 – y plane along line y = x + 3 it’s the . A ray travelling in x – y 4
mirror in second quadrant and gets reflected. Find the unit vector in the direction of reflected ray.
(1) 60.
1 (i j) 2
(2)
1 (i j) 2
(3)
1 2
i j
(4) None of these
As shown in figure, a convergent lens is placed inside a cell filled with liquid. The lens has focal length + 20 cm when in air and its material has refractive index 1.50. If the liquid has refractive index 1.60, the focal length of the system is : (1) + 80 cm
(2)  80 cm
(3)  24 cm
(4)  100 cm
SPACE FOR ROUGH WORK
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JEEMAINS TEST PAPER PAPER
61.
Select the correct statement about given square planar complex.
(1) It has no geometrical isomer (2) It is optically optically active because it does not have plane of symmetry (3) It is optically inactive inactive because because it has symmetric symmetric carbon (4) It is optically optically active because it has symmetric symmetric carbon 62.
In this sequence X, Y, Z are respectively :
(1) Acidified H2O2 ; Alkaline H2O2 ; Acidified H2O2 (2) Alkaline H2O2 ; Acidified H2O2 ; Zn/HCl (3) Acidified H2O2 ; Heat ; Alkaline H2O2 ; (4) Alkaline H2O2 ; Acidified H2O2 ; On standing 63.
Correct match of complex formed in the following methods are : (I) Mond’s process for purification of nickel (II) Removal of unreacted AgBr AgBr from photographic photographic plate. (III) Removal of lead poisoning from the body. SPACE FOR ROUGH WORK
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JEEMAINS TEST PAPER PAPER
64.
I (1) Ni(C Ni(CO) O)4
II [Ag(CN)2 ]
III [Pb(EDTA)]2
(2) Ni(C Ni(CO) O)4
[Ag(S2 O3 )2 ]3
[Pb(EDTA)]2
(3) Ni(CO Ni(CO))6
[Ag(S2 O3 )2 ]3
[Pb(EDTA)]4
(4) Ni(CO Ni(CO))6
[Ag(S2 O3 )]
[Pb(EDTA)]2
Select the incorrect statement about N2F4 and N2H4 : (I) In N2F4 , dorbitals are contracted by electronegative fluorine atoms, but dorbital contraction is not possible by Hatom in N2H4. (II) The NN bond energy energy in N2F4 is more NN bond energy in N2H4 (III) The NN bond length in N2F4 is more than that of in N2H4 (IV) The NN bond length in N2F4 is less than that of in N2H4 (1) I, II and III
(2) I and III
(3) II and IV
(4) II and III
65.
The incorrect statement regarding above reactions is :
66.
67.
(1) A shows amphoteric character
(2) Gas ‘P’ and ‘Q’ are different
(3) Both X and Y are water soluble
(4) Gas Q is inflammable
Select the correct match : (1) Bayer’s method

Na2CO3
(2) Matte
(3) van Arkel method

AgI
(4) Thomas slag

Raw material for cement industry

98% Cu 2S 2% FeS
In the reaction B2H6 2KOH 2X 2Y 6H2 , X and Y are respectively. (1) H2O, KBO2
(2) HCl, KBO3
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(3) H2O, KBO3
(4) H2, H 3BO3 Page 12
JEEMAINS TEST PAPER PAPER
68.
A red solid is insoluble i nsoluble in water. However, it becomes soluble if some KI is added to water. Heating the red solid in a test results in the liberation of some violet colored fumes and droplets of a metal appear on the cooler parts of the test tube. The red solid is : (1) (NH4 ) 2Cr2O7
69.
(2) HgI2
(3) HgO
The uncertainty in position for an electron is
(4) Pb3O4
where λ is the de Broglie wavelength. The uncertainty in 4
velocity will be : (1) 70.
(2) v
(3) 3v
(4)
v 4
At low pressure if RT 2 a. a.p, (a is van der Waals’ constant), then the volume occupied by a real gas is : (1)
71.
v 2
2RT P
2P RT
(2)
(3)
RT 2P
(4)
2RT P
In the following NaCl type structure : Salt
Anionanion distance
Cationanion distance
MT
2.40 Å
1.70 Å
MQ
1.63 Å
1.15 Å
RT
2.66 Å
1.88 Å
RQ
2.09 Å
1.48 Å
MT is represented as :
(1)
72.
(2)
(3)
(4)
Mixture of volatile components A and B total vapour pressure (in torr) p 254 254 119 119 XA
where xA is mole fraction of A in mixture. Hence poA and poB are (in torr) (1) 254, 119
(2) 135, 254
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(3) 119, 254
(4) 154, 119 Page 13
JEEMAINS TEST PAPER PAPER
73.
Given the standard oxidation potentials, 0.4V 0.8V Fe Fe2 (aq.) Fe3 (aq.)
(In acidic medium) medium) 0.9V 0.6V Fe Fe(OH)2 Fe(OH)3
(In Alkaline medium)
It is easier to oxidize Fe2 to Fe3 in :
74.
(1) Acid medium
(2) Neutral medium
(3) Alkaline medium
(4) Both in acidic and in alkaline mediums
A reaction (1) forms two products :
Ea2
2Ea
1
If frequency factors for both the reactions are equal. Therefore, /RT Ea1 /RT
(1) k2 k1e
(3) k1 Ak 2e 75.
(2) k2 k12 / A
/RT Ea1 /RT
(4) Both (1) and (2) are correct
The enthalpy of formation of H2O(l) is – 290 290 kJ/mol and enthalpy of neutralization of strong acid with wi th strong alkali is – 56 56 kJ/equiv. What is the enthalpy of formation of OH (aq)? Given f H(H ,aq) ,aq) 0 (1) 334 kJ / mol
76.
(2) 234 kJ / mol
(3) 346 kJ / mol
(4) 178 kJ / mol
A mixture of CH4 and C2H 2 occupied volume at a total pressure equal to 63 torr. The same gas mixture was burnt to CO2 and H2O(l). The CO2 (g) alone was collected in the same volume and at the same temperature, the pressure was found to be 69 torr. What was the mole fraction of CH4 in the original gas mixture? (1)
19 21
(2)
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19 20
(3)
17 18
(4)
15 16 Page 14
JEEMAINS TEST PAPER PAPER
77.
Plot of log (x/m) against log P is a straight line inclined at an angle of 45. When the pressure is 0.5 atm and Freundlich parameter k is 10, the amount of solute adsorbed per gram of adsorbent will be (log 5 = 0.6990) : (1) 1 g
78.
(3) 3 g
(4) 5 g
At constant pressure, addition of helium to the t he reaction system : N2 (g) 3H2 (g)
79.
(2) 2 g
2NH 2NH3
(1) Favour the formation of ammonia
(2) Reduces the formation of ammonia
(3) Does not effect the position of equilibrium
(4) Reduces the dissociation of ammonia
The solubility of AgCl in water, in 0.02 M CaCl2 in 0.01 M NaCl and a nd in 0.05M AgNO3 are S0 , S1 ,S2 and S3 respectively. Which of the following order of solubility is correct?
(1) S0 S1 S2 S3 80.
(2) S0 S2 S1 S3
(3) S0 S1 S2 S3
(4) S0 S2 S1 S1
In the following reaction Fe3O4 MnO4 Fe2O3 MnO2
the number of moles of OH liberated as per the t he balanced equation in the basic medium is (1) 1 81.
(2) 2
(3) 3
(4) 4
The correct IUPAC name of following compound is (1) 4Aminomethyl3hydroxycyclohex5ene1carbox 4Aminomethyl3hydroxycyclohex5ene1carboxylic ylic acid (2) 2Aminomethyl5carboxycyclohex3en1ol (3) 4Aminomethyl5hydroxycyclohex2ene1carbox 4Aminomethyl5hydroxycyclohex2ene1carboxylic ylic acid (4) 3Hydroxy4aminomethy 3Hydroxy4aminomethylcyclohex5en1oic lcyclohex5en1oic acid
82.
In which of the following delocalization of anion is not possible ? (1)
(2)
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(3)
(4)
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JEEMAINS TEST PAPER PAPER
83.
(1) Enantiomers 84.
(2) Geometrical isomers (3) Position isomers
(4) Conformers
In the given reaction,
[X] as the major product among the elimination product is :
(1)
85.
(2)
(3)
(4)
The major product (P) of the following reaction is :
(1)
(2)
(3)
(4)
86.
Product X & Y can be :
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JEEMAINS TEST PAPER PAPER
(1)
(2)
(3)
(4)
87.
X, Y and Z respectively are :
88.
(1)
(2)
(3)
(4)
In the following compound, the correct order of the acidity o f the position X, Y and Z is :
(1) X > Y > Z
(2) Z > X > Y
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(3) X > Z > Y
(4) Y > X > Z Page 17
JEEMAINS TEST PAPER PAPER
89.
90.
Which of the following is a nonreducing sugar?
(1)
(2)
(3)
(4)
The vitamin which is soluble neither in water nor in fat is : (1) Biotin
(2) Phylloquinone
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(3) Thiamine
(4) Ergocalciferol
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TEST : ID – 04 04 DATE : ___________
ANSWER & SOLUTION
Page 1