Transcript
FULL TEST : ID - 005
SPACE FOR ROUGH WORK
Page 1
PCM : TEST PAPER XII – JEE MAINS
1.
If a b 2c b c a 2c [a b c] c], then λ is equal to
(1) 2.
1
1 x The integral 1 2x2 e x (1) (2x 1)e
3.
(2) 1
x2
1 x
C
2
(3) 2 1 x
(4) 3
dx, is equal to [Note : C denotes constant of integration] x2
(2) (2x 1)e
1 x
C
x2
(3) xe
1 x
C
(4)
x2
xe
1 x
C
Let f (x (x) (a2 a 2)x2 (a 4)x 7, x R. If unity lies between the roots of equation f(x) = 0 then number of integral values of a is (1) 5
4.
(2) 4
(3) 3
(4) 2
A circle x2 y2 6x 16 0 cuts the x-axis at A and B and positive y-axis at the point D (0, d). The value of d equals (1) 2
5.
Let Sn
(2) 4
(4) 16
n2015 (1 22014 32014 32014 ..... n2014 ), then LimSn is
(1) 1
6.
(3) 9 n
1 2014
(2)
(3)
1 2015
(4)
2014 2015
x2 y2 The common tangent of parabola y 4x and hyperbola 1 touches them at P and Q 4 3 2
respectively, then Q can be (1) (4, 3) 7.
(2) (3, 4)
(3) (4, 3)
(4) (4, (4, 3)
For x (1,1 1,1), ), the number of solutions of the equation tan1(x x2 x3 x4 ....)
cot 1 (6 6x 6x2 ....) (1) 0
2
is
(2) 1
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(3) 2
(4) 4 Page 1
JEE-MAINS TEST PAPER PAPER
8.
If the smallest radius of a circle passing through the intersection of x2 y2 2x 0 and x y 0 , is r then the value of (10 r 2 ) is equal to (1) 2
9.
(2) 4
(3) 5
(4) 10
Three positive numbers form an increasing G.P. If the first term is doubled and second term is trebled, the new numbers are in A.P. Then the common ratio of the G.P. is (1) 3 7
10.
(2) 3 7
7
(4)
dy 1 y2 (1 x x2 ) given that when x = 1, y = 0 is The solution of the differential equation, xy 2 dx 1 x (1) ln 1 y2
l n(x) tan1 (x) 2
1 y2 (3) l n 2 2tan 2tan1 x x 4 11.
(3) 2
(2) l n
1 y2 2tan1(x) 2 2tan 2 x
1 y2 1 (4) l n tan ta n (x) 2 4 x
The plane x + y + z = 5 is rotated by 90 along the line of intersection with the plane x – x – y – y – z z = 2. If the equation of plane in new position is ax + by + cz + d = 0 where a, b, c, d I, then least value of
| a b c d | is (1) 10 12.
(2) 9
(3) 4
(4) 11
The sum of all value(s) of λ for which the lines 2x + y + 1 = 0 ; 3x + 2λy + 4 = 0 ; x + y – 3λ = 0 are concurrent, is (1)
13.
1 4
(2)
1 2
(3)
7 2
(4)
7 12
A line L in R passing through (1, 1) intersect lines L1 :12 :12x 5y 13 and L2 :12 :12x 5y 65 at A and B respectively. If AB = 5, then line L can be (1) 16x – 16x – 33y 33y + 17 = 0
14.
(2) 8x + 9y – 9y – 17 17 = 0
(3) 16x + 63y – 63y – 79 79 = 0
(4) 56x + 23y – 23y – 33 33 = 0
Let p and q be two t wo statements. Then, (~ p q) (~ p ~ q) q ) is a (1) tautology
(2) contradiction
(3) neither tautology nor contradiction
(4) either tautology or contradiction
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JEE-MAINS TEST PAPER PAPER
15.
x2 If the circle x y 2x 4y k 0 and director circle of ellipse y2 1 intersects orthogonally then 4 2
2
k equals (1) 0 16.
Length fo the normal chord of the parabola, y2 (1) 8
17.
(2) 5
(3) -5
4x, which makes an angle of
(2) 8 2
(3) 4
(4) 2
with the axis of x is 4 (4) 4 2
Let ABC be a variable triangle such that A is (1, 2), B and C lie on the line y = x + λ (where λ is a variable). The locus of the orthocentre of triangle ABC is a straight line whose y-intercept is equal to (1) 2
18.
(2) 3
(3) 4
(4) 5
zz iz iz b 0 and C2 : zz z z (1 i)z (1 i)z 4 0 where STATEMENT 1 : Consider two curves C1 : zz (b R, R, z x iy aan nd i 1) If C1 and and C2 intersects orthogonally then b = - 2. STATEMENT 2 : If two curves intersects orthogonally then the angle between the tangents at all their
points of intersection is
. 2
(1) Statement-1 is true, statement-2 is true and statement-2 is correct explanation explanation for statement-1. (2) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1. (3) Statement-1 is true, true, statement-2 statement-2 is false (4) Statement-1 is false, false, statement-2 statement-2 is true true 19.
Let A be a square matrix of order 3. If det. A = 2 then the value of det. (adj. A 3) is equal to (1) 23
(2) 26
(3) 29
(4) 212
2
20.
sin(4x)cot(x)dx is equal to 0
(1)
2
(2) 0
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(3)
2
(4) Page 3
JEE-MAINS TEST PAPER PAPER
21.
A circle S = 0 passes through points of intersection of circles x2 y2 2x 4y 1 and
x2 y2 4x 2y 2y 5 0 and cuts the circle x2 y2 4 0 orthogonally. Then the length of tangent from origin on circle S = 0, is (1) 3
(2) 2
(3) 1
(4) 4
x xdx sin xdx 0 Let f(x) , x 0 x3 k, x0 2
22.
If f(x) is continuous at x = 0 then k equals (1) 23.
1 3
2 3
(3)
The equation of common tangent to the curves y2 (1) 3y 9x 2
24.
(2)
(2) y 2x 1
Let y = y(x) satisfy the differential equation, x
4 3
(4) does not exist
8x and xy 1, is (3) y x 2
(4) 2y x 8
dy y x2. If y(1) = 0 then the area bounded by the curve dx
and the x-axis is (1) 25.
1 2
(2)
1 3
(3)
1 4
(4)
1 6
A function f is continuous and differentiable on R 0 and satisfies the condition x f '(x) f (x (x) 1 throughout its domain, with f (1) 2. Then the range of the function is (1) (, )
26.
(2) (,1) (1, )
Let g : [2, 2] 2] R where g(x) x
2015
(3) (0, )
(4) (1, )
x2 1 sgn(x) 2,2]] then the be an odd function for all x [2,2 p
smallest integral value of p is equal to [Note : [k] denote the greatest integer less than or equal to k.] (1) 6
(2) 5
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(3) 3
(4) 2 Page 4
JEE-MAINS TEST PAPER PAPER
27.
A function f is defined by f(x f(x) cost cos(x t)dt, 0 x 2 then the minimum value of f(x) is 0
(1)
28.
4
(2)
(3)
2
(4)
4
If f (x) x3 3x2 2x a, a R , then the real values of x satisfying f (x (x2 1) f (2 (2x2 2x 3) 3) will be (1) (, )
29.
2
(2) (0, )
(3) (, 0)
From the point (4, 6), a pair of tangent lines are drawn to the parabola y2
(4)
8x. The area of the triangle
formed by these pair of tangent lines and the t he chord of contact of the point (4, 6) is (1) 8 30.
(2) 4
(3) 2
(4) 6
Let A and B are two square matrices of order 3 such that det.(A) = 3 and det.(B) = 2, then the value of
det adj. B1A1
1
is equal to
[Note : adj M denotes the adjoint of a square matrix M.] (1) 6
(2) 9
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(3) 18
(4) 36
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JEE-MAINS TEST PAPER PAPER
31.
The edge of a square is l = = 1.5102 m then its area will be : (1) 2.25 .25 104 m2
32.
(2) 2.3104 m2
(3) 2.2104 m2
(4) 2.0 104 m2
0.04 kg of nitrogen is enclosed in a vessel at a temperature of 27C . How much heat has to be transferred to the gas to double the rms speed of its molecules [R = 2 cal/mol K] (1) 2250 cal
33.
(2) 2250 J
(3) 4500 J
(4) 6428 cal
Choose correct statement : (1) Dimensionally correct equation must be correct (2) Dimensionally correct equation may be correct (3) Dimensionless quantity must not have SI units units (4) The quantity which has SI units must must not be be dimensionless
34.
If the terminal speed of a sphere of gold (density = 19.5 kg/m 2) is 0.2 m/s in a viscous liquid (density = 1.5 kg/m2), find the terminal speed of a sphere of sliver (density = 10.5 kg/m 3) of the same size in the same liquid: (1) 0.4 m/s
35.
(3) 0.1 m/s
(4) 0.2 m/s
A particle is projected vertically up with 20 ms-1 then find average velocity in initial 3sec : (g 10 ms2 ) (1) 15m 15 ms1
36.
(2) 0.133 m/s
(2) 25/3ms1
(3) 5 ms1
(4) 15m 15 ms1
25 cm long closed organ pipe is in resonance with 330 Hz tuning fork in fundamental mode, find the minimum length of an open organ pipe which is also in resonance with same tuning fork (neglect end correction) (1) 50 cm
37.
(2) 75 cm
(3) 100 cm
(4) 150 cm
A uniform ring is released form rest and start rolling on an inclined plane having inclination 30. Find out the time taken by it to t o travel 5 m along the greatest slope of the inclined plane. (g = 10 -2) (1) 2sec
(2) 6sec
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(3) 3sec
(4) 1 sec Page 6
JEE-MAINS TEST PAPER PAPER
38.
If amplitude of a damped harmonic oscillator becomes half in initial one minute and it will become 1/x of initial amplitude after three minutes then the x is : (1) 2
39.
(2) 4
(3) 8
(4) 16
A 2kg block is thrown on a rough (coefficient of friction is 0.2 horizontal surface with 4 ms -1. Then work done by kinetic friction on the horizontal surface and on the block with respect to an observer moving with constant velocity 4m/sec parallel to the velocity of the block respectively will be: (1) 0 J, 16 J
40.
(2) 16 J, - 16 J
(3) 0 J, - 16 J
(4) - 16 J, 8 J
The amount of work required for increasing the length of a given wire of length l by by l will will be : (A = Area, Y = Young’s modulus of material of the t he wire) (1) YAl /2 /2
41.
(2) Yl /2A /2A
(3) Yl 2/2A
(4) None
Ratio of gravitational acceleration due to the earth at height R to the acceleration at the depth R/2 will be : (R is radius of the earth) (1)
42.
8 9
(2) 2
(3) 1/2
(4) 1
The length of a needle floating the surface of water is 2.5 cm. The minimum force needed to lift the needle above the surface of water will be : (T = 7.2 N/cm) (1) 3.6 N
43.
(2) 1.8 N
(3) 72 N
(4) 18 N
Two particles are executing SHM of the same amplitude A about same equilibrium position and having same frequency ω along along the x-axis. Initially one particle is at x = 0 and moving towards positive extreme and another at x = A. Find their phase difference : (1)
44.
2
(2)
(3)
3
(4)
4
A gas undergoes cyclic process as shown in the figure, 5-1 and 3-4 are adiabatic process, 1-2 and 4-5 are isochoric process, 2-3 is isobaric process. Find efficiency of the cycle.
(1) 15%
(2) 30%
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(3) 45%
(4) 60% Page 7
JEE-MAINS TEST PAPER PAPER
45.
When three progressive wave : Y1 4sin(2x 6t), y2
6 si sin(2x 6t ) and Y3 12 si sin(2x 6t 6 t ) are 2
superimposed then find amplitude of resultant wave (1) 6 46.
(2) 2
(3) 10
(4) 8
In Carnot engine the work done by working substance is equivalent to : (1) Heat taken by source (2) Heat given to sink (3) Difference between above two (4) Ratio of heat taken taken and and heat heat given given
47.
and 3i 4j ms1 respectively then centripetal If acceleration and velocity of a particle are 5ms-2 j and acceleration and radius of curvature are at that point of the path where particle is present will be : (1) 3ms2 ,
48.
25 m 3
(2) 4 ms2 ,
4 m 25
(3) 5 ms2 ,
1 m 25
(4) None
When photons of energy 4.25 eV strike the surface of a metal A, the ejected photoelectrons have max imum kinetic energy, T A expressed in eV and de-Broglie wavelength
A . The maximum kinetic energy of
photoelectrons liberated from another metal B by photons of energy 4.70 eV is i s TB de-Broglie wavelength of these photoelectrons is (1) the work function of A is 2.25 eV (3) TA 49.
2.75eV 5eV
(TA 1.50 eV). If the
B 2A , then (2) the work function of B is 2.25 eV (4) TB
5eV 1.25eV
The diameter of the outer conductor of a cylindrical capacitor is D 2. What should be the diameter of the core (inner cylinder) D1 of this capacitor be, so that for given potential difference between the outer conductor and the core, the electric field strength at t he core is minimum. (1)
2D2 e
(2)
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D2 e
(3)
D2 e2
(4) None of these
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JEE-MAINS TEST PAPER PAPER
50.
A hydrogen like atom (atomic number Z) is in a higher excited state a quantum number n. This excited atom can make a transition to the first excited state by successively emitting two photons of energies 10.2 eV and 16.8 eV respectively. Alternatively, the atom from the same excited state can make a transition to the second excited 4.25 eV and 5.95 eV respectively. The values of n and Z are respectively (Ground state energy of hydrogen atom is (1) 6 and 6
51.
13.6 13.6 eV) eV)
(2) 3 and 3
(3) 6 and 3
(4) 3 and 6
Two small identical balls lying on a horizontal plane are connected by a massless spring. One ball is fixed and the other is free. The balls are charged identically as a result of which the spring length increases two fold. Determine the factor by which frequency of small harmonic vibrations of the system will change. Assume that force constant of spring is constant. It does not change with length of spring. (1)
52.
3
(2) 2 2
(3) 3 2
(4)
2
For a carrier frequency of 100 kHz and a modulating frequency of 5 kHz, what is the band width of AM transmission? (1) 5 kHz
53.
(2) 10 kHz
(3) 20 kHz
(4) 200 kHz
A conducting disc of radius R is rotating with an angular velocity ω. Allowing for the fact that electrons are the current carries in a conductor, determine the potential difference between the centre of the disc and the edge. Mass of the electron is m and charge is e.
m2R 2 (1) e 54.
2m2 R 2 (2) e
m2R 2 (3) 2e
(4) None of these
If the voltage between the terminals A and B is 17 V and Zener breakdown voltage is 9V, then the potential voltage across R is : (1) 6 V
(2) 8 V
(3) 9 V
(4) 17 V
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JEE-MAINS TEST PAPER PAPER
55.
A concave mirror and a glass slab (μ = 1.5) are arranged as shown in the t he figure. A converging bundle of paraxial rays is incident on on the slab as shown. Find Find the position of the final image.
56.
(1) 21.3 cm from the mirror (towards right)
(2) 20 cm from the mirror (towards right)
(3) 3.21 cm from the mirror (towards right)
(4) none of these
Light ray is incident on a prism pri sm of refracting angle 4 degree and refractive index of its material is 1.5. Find the minimum angle of deviation. (1) 1 degree
57.
(2) 2 degree
(3) 3 degree
(4) 4 degree
A magnet of length 14 cm and magnetic moment M is broken into two parts of length 6 cm and 8 cm. cm . They are put at right angles to t o each other with the opposite poles together. The magnetic dipole moment of the combination is (1)
58.
M 1.4 1.4
(2) M
(3) 1.4 M
(4) 2.8 M
An induction coil has an impedance of 10 when an AC signal of frequency 1000 Hz is applied to the coil and the voltage leads the current by 45. Then the inductance of the coil is : (1)
59.
1 2
(2)
1 2 200
(3)
1 2 20
(4)
1 200 200
A particle of specific charge α (charge per unit mass) is released at time t = 0 from origin with an initial velocity of v v0 i in a uniform magnetic field B B0 k. Find the velocity of particle at any time t. (1) v0 cos(B0 (3)
60.
t)i v0 sin(B0 t)j
t)i v0 sin(B0 t)j v0 cos(B0 t)i
(2) v0 cos(B0
t)i v0 sin(B0 t)j t)i
(4) None of these
An AC voltage is given by V V0 V1 cos t. What is its rms value for one cycle ? (1)
V12 V 2 2 0
(2)
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V12 V 2 2 0
V12 (3) V 2 2 0
V12 (4) V02 2 Page 10
JEE-MAINS TEST PAPER PAPER
61.
If S represents
(1)
62.
then which conformation represent energy level R?
(2)
(3)
(4)
Consider the following compounds.
Arrange these compounds in decreasing order of their basicity. (1) 1 > 2 > 3 > 4
(2) 2 > 3 > 1 > 4
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(3) 4 > 1 > 3 > 2
(4) 4 > 1 > 2 > 3
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JEE-MAINS TEST PAPER PAPER
63.
64.
IUPAC name of the following compound is :
(1) 1,2-Dibromo-3-chlorocy 1,2-Dibromo-3-chlorocycloprop-1-ene cloprop-1-ene
(2) 1,3-Dibromo-2-chlorocy 1,3-Dibromo-2-chlorocycloprop-1-ene cloprop-1-ene
(3) 1,2 Dibromo-3-chlorocycloprop-2-ene Dibromo-3-chlorocycloprop-2-ene
(4) 2,3-Dibromo-1-chlorocy 2,3-Dibromo-1-chlorocycloprop-1-ene cloprop-1-ene
Antiseptics and disinfectants either kill or prevent growth of mi croorganism. Identify which of the following statements is not true. (1) Chlorine and and iodine are used strong disinfectants. disinfectants. (2) Dilute solutions of boric acid acid and hydrogen peroxide are strong antiseptics antiseptics (3) Disinfectants harm the living tissues (4) A 0.2% solution of phenol is an antiseptic while 1% solution acts as a disinfectant disinfectant
65.
The total number of basic group in the following form of lysine.
(1) 0 66.
(2) 1
(3) 2
(4) 3
The reaction below is an example of an intramolecular S N 2 substitution The stereochemistry of the product is
(1) meso form
(2) pair of enantiomers
(3) pair of diastereomers
(4) only one enantiomer
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JEE-MAINS TEST PAPER PAPER
67.
The final product Z is (1) 68.
(4)
(2)
(3)
(4)
The most probable product of the following sequence of reactions would be :
(1)
70.
(3)
The major product of following reaction is :
(1)
69.
(2)
(2)
(3)
(4)
What is true about the following carbohydrate :
(1) It anomerizes in solution phase (2) It is a reducing sugar (3) It shows the phenomenon of inversion of sugar in acidic medium (4) It shows mutarotation SPACE FOR ROUGH WORK
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JEE-MAINS TEST PAPER PAPER
71.
The structure shown here represents :
(1) Schottky defect 72.
(2) Frenkel defect
(3) Metal excess defect (4) None of these
Arrange the following electrolytes in the increasing order of coagulation power for the coagulation of
As2S3 sol : K2SO4 CaCl2 Na 3PO4 AlCl3 ( I)
(1) I < II < III < IV 73.
(2) I = III < II < IV
( II)
( III )
( IV )
(3) II < IV < I < II
(4) II < III < IV < I
According to Henry’s law, the partial pressure of gas (Pg ) is directly proportional to mole fraction of gas in liquid solution, Pgas
KH Xgas , where K H is Henry’s constant. Which is of the following statement i s
incorrect? (1) K H us characteristic constant for a given gas-solvent system (2) Higher is the value of K H , lower is solubility of gas for a given partial pressure of gas (3) K H has temperature dependence 74.
(4) K H decreases with increase of temperature
A schematic plot of n Keq Vs inverse of temperature for a reaction is shown below.
The reaction must be : (1) Exothermic
(2) Endothermic
(3) One with negligible enthalpy change
(4) Highly Highly spontaneous at ordinary temperature
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JEE-MAINS TEST PAPER PAPER
75.
V of two same charge particle A and B are plotted against de -Broglie wavelengths. Where V is the potential on the particles. Which of the following relation is correct about the mass of particle?
(1) mA 76.
mB
(2) mA
mB
(3) mA
mB
mB
(4) mA
A mixture of O2 and gas “Y” (mol. wt. 80) in the mole ratio a : b has a mean molecular weight 40. What would be mean molecular weight, if the gases are mixed in the ratio b : a under identical conditions? (gases are non-reacting) : (1) 40
77.
(2) 48
(3) 62
(4) 72
B C Consider the plots, given for the types of reaction nA
These plots respectively correspond to the reaction order : (1) 0, 1, 2 78.
(2) 1, 2, 0
(3) 1, 0, 2
(4) 0, 2, 1
A radioactive substance (parent) decays to it’s daughter element, the age of radioactive substance (t) is related to the daughter (d) parent (p) ratio by the equation : (1) t
79.
p ln 1 d 1
(2) t
d ln 1 p 1
(3) t
d ln p 1
(4) t
p ln d 1
The conductance of a salt solution (AB) measured by two parallel electrode of area 100 cm2 separated by 10 cm was found to be 0.00011. If volume enclosed between two electrode contain 0.1 mole of salt, what is the molar conductivity (Scm2 mol-1) of salt at same concentration : (1) 10
(2) 0.1
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(3) 1
(4) 0.01 Page 15
JEE-MAINS TEST PAPER PAPER
80.
Which is not correctly matched ?
(1)
Factors
Remarks
H 0, S 0
Process always spontaneous irrespective of temperature
81.
(2)
H 0, S 0
Process non-spontaneous at high temperature
(3)
H 0, S 0
Process spontaneous at low temperature
(4)
H 0, S 0
Always non-spontaneous irrespective of temperature
Which of the following is correctly matched ? Column-I
82.
Column-II
Column-III
(1) [Fe(CO)5 ]
Paramagnetic
Octahedral, sp3d2
(2) [Fe(CO)5 ]
Paramagnetic
Trigonal bipyramidal, sp3d
(3) [Co(CO)4 ]
Diamagnetic
Tetrahedral, sp3
(4) [Ni(CO)4 ]
Diamagnetic
Square planar, dsp dsp2
Borax is converted into crystalline boron by the following steps :
Borax X H3BO3 B2O3 Y B X and Y are respectively : (1) HCl, Mg 83.
(2) HCl, C
(3) C, Al
(4) HCl, Al
Match List-I with List-II and select the correct answer using the codes given below the lists : List-I (Compounds)
List-II (used in)
(1) BaSO4 ZnS
(1) Explosive
(2) NI3
(2) Oxidiser in rocket propellant
(3) N2O4
(3) Space capsule
(4) KO2
(4) Pigment
(1) (2) (2) (3) (4) (4) (1)
3
1
4
2
(1) (2) (2) (3) (4) (4) (2)
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4
1
2
3
(1) (2) (2) (3) (4) (4) (3)
3
4
1
2
(1) (2) (2) (3) (4) (4) (4)
4
3
2
1 Page 16
JEE-MAINS TEST PAPER PAPER
84.
When zeolite, which is hydrated sodium aluminum silicate, is teated with hard water the sodium ions are exchanged with : (1) H ion ions
85.
(2) Ca 2 ion ions
(3) Mg2 ion ions
(4) Both Ca 2 and Mg2
O2 H2O NaOH ; ' A' 4 Ba NaOH O2 ' A' H2O 00C t 25C
B is used for oxygenating in submarine. A and B are : (1) Na Na2O2 and and Na Na2O 86.
(3) Na Na2O2 and and O2
(4) Na Na2O and and O2
Lassaigne’s test for the detection detection of nitrogen will fail in case of : (1) NH NH2CON CONH2
87.
(2) Na Na 2O and and Na Na2O2
(2) H2NCONHNH2.HCl (3) H2N.NH2 2HCl
(4) C6H5NHNH2.2HCl
[CoCl2 (NH (NH3 )4 ] (NH3 )3 ] NH3. If in this reaction two isomers of the product are obtained, [CoCl3 (NH which is true for the initial (reactant) complex.
88.
89.
(1) Compound is in cis-from
(2) Compound is in trans-form
(3) Compound is in both (cis and trans) form
(4) Can’t be predicted
Which of the following substance acts as collector in froth floatation method? (1) Sodium xenate
(2) Sodium pyrophosphate
(3) Sodium nitroprusside
(4) Sodium ethyl xanthate
Which of the following statements is incorrect? (1) On heating potassium dichromate, dichromate, the gas gas evolved is oxygen (2) Compounds of La 3 are diamagnetic (3) Nd Nd3 has greater tendency to form complex compounds than Eu3 (4) Sm2 acts as reducing agent
90.
Among the following compounds, which one is not responsible for depletion of ozone layer? (1) Cl2
(2) CFCl3
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(3) NO
(4) CH4 Page 17
TEST : ID – 05 05 DATE :- ___-___-_____
ANSWER & SOLUTION
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