Transcript
JEE Main FULL TEST : ID - 001
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PCM : TEST PAPER XII – JEE MAINS
1 2
1.
The value of definite integral
n(1 n(1 2x) 2x) dx,equal 1 4x2
0
(1)
2.
n2
(2)
8
If f (x)
n2 4
2sin x, x 2 a cos(x) b, x 0 2 is 2 cos x, x, 0 x 2 csin x, x, x 2
(3)
n2
(4)
32
n2 16
continuous in [, ] ,then number of points at which f(x) is not
differentiable is /are (1) 0 3.
(2) 1
x2 y2 Tangent to the ellipse 32 18
(3) 2
1 having
slope
3 4
(4) 3
meet the coordinate axes in A and B the area of
AOB (O is origin) equals (1) 12 4.
(2) 8
(4) 32
In which one of the following of the functions, Rolle’s theorem is applicable? (1) f (x) x , in 2 x 2 2
(3) f (x) 5.
(3) 24
1 x 2 3 , in1 x 3
(2) f (x)
nx,in0 x tanx,in0
(4) f (x) x (x-2 )2 in 0
x2
A house of height 100m subtends a right angle at the window of an opposite house. If the height of the window is 64m,then the distance between the two house is (1) 48m
(2) 36m
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(3) 54m
(4) 72m Page 1
JEE-MAINS TEST PAPER PAPER
6.
The area of the triangle inscribed in an ellipse bears the ratio 5 : 3 to the area of the triangle formed by joining the points on the auxiliary circle corresponding
to the vertices of the first triangle, then the
eccentricity of the ellipse is (1) 7.
1 5
If y cos1
(1) 9.
(2)
3 4
(3)
5 3
(4)
The distance between the origin and the normal to the curve y e2x (1)
8.
2 3
(2)
1 x2 1 2 1 x2
1 1 x2
, then
(2)
2 5
(3)
2 3
3 5
x2at x 0, is
(4)
1 2
(4)
1 2(1 x2 )
dy is equal to dx 1 1 x2
(3)
1 2(1 x2 )
Let p be the statement ‘7 is not greater then 4’and q be the statement ‘paris is in France’ then
(p q) is
the statement
10.
(1) 7 is greater than 4 or Paris is not in France
(2) 7 is not greater than 4 or Paris is not in France.
(3) 7 is greater than 4 or Paris is in France
(4) 7 is greater than 4 or Paris is not in France
Let
f (t) t 2for 0 t 1 and
g (t) t for 0 t 1the 3
value
of
c
with
0 c 1 and
at
which
f(1 f(1) f (0) f '(c) , is g(1 g(1) g(0 g(0) g'(c) g'(c) (1)
11.
2 3
(2)
1 3
(3)
B) Let A and B be two events such that p (A B)
1 2
(4)
1 6
1 1 1 P(A B) B) , and P (A) , where A stands for 4 6, 4
complement of event A. then, events A and B are (1) Mutually exclusive and independent.
(2) independent but not equally likely.
(3) equally likely but not independent.
(4) equally likely and mutually exclusive.
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JEE-MAINS TEST PAPER PAPER
12.
A chord is drawn through the focus of parabola y2
5 2
13.
If I
1
0
14.
If
3 2
(2)
dx
2
(3)
5
(4)
2 3
, then
1 x 2
loge 2 I
(1)
that its distance from the vertex of this
5 ,then its slope can be 2
parbola is
(1)
6x such
dx
4
(2) loge 2 I
(3) I
4
(4) I loge 2
1 k
sin1(ksinx) (ksinx) c,the ,then K2 (1 k2 )(1 k4 )(1 k2 k12) is
1 tan 2 x
equal to [note :c constant of
integration] (1) 2010
(2) 2012
(3) 2013 18
15.
If x1 ,x 2,...x18 are observations such that
j I
(4) 2014
18
(x 8)
(x j 8) 9and
j I
2
J
45, then the standard deviation of
observations is (1)
18 34
(2) 5 10
16.
The sum
(r
2
(3)
5
(4)
3 2
1) (r!) r!) is equal to
r l
(1) 101 x (10!)
(2) (11)!
(3) 10 x (11)!
(4) 11 x (11!)
k 3 off (3 - x) (4 - y) (3x + 4y) 4y) is ,where K is equal to (0,3)a )an nd y (0,4) (0,4),, then maximum value o 17. If x x (0,3 12 (1) 18.
25 3
(2)
25 6
(3)
25 2
(4)
25 12
n : n I 3
(4)
2n : n I 3
The set S {x R : cos(2 s(2x) 2co 2cos2 (x) (x) 2}, is equal to (1)
2n : n I 3
(2)
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n : n I 6
(3)
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JEE-MAINS TEST PAPER PAPER
19.
z 2 0 is z 1
The locus of P(z) where z = x + iy and satisfying Re (1) { x, x, y R2 | x2 y2 — 3y (3) { x, y R 2 | x 2 y2
20.
2 0}
3x 2 0}
(2) { x, y R 2 | x 2 y2
3x 2 0}
(4) none of above
Hat W contains two white balls and one black ball. Hat B contains two black balls and one white ball. At random, one of the following strategies is selected: Two different balls are drawn from hat W. Two different balls are drawn drawn from hat B One ball is drawn drawn from each each hat. The probability probability of getting at least least one white ball, ball, is
(1)
21.
1 2
(2)
1 4
(3)
Let y f (x (x) satisfies the differential equation (1 x2 )
22 27
(4)
21 27
dy and f (0 (0) 2 then the number of 2xy 2x an dx
integers in the range of f (x) is (1) 1 22.
(2) 2
(3) 3
(4) 4
On the set N of all natural numbers, define the relation R by aRb if and only if the greatest common divisor of a and b is 2, then R is
23.
(1) reflexive but not symmetric
(2) symmetric only
(3) reflexive and transitive
(4) equivalence
Let a, b, c be non zero real numbers if the system of equations y z a 2x , x z
x y c 2z 2z is consistent and b = 4a +
2y , b 2y
c , then the absolute value of sum of roots of the equation 4
ax2 bx c 0 , is equal to (1) 1
(2) 2
(3) 3
(4) 4 9
24.
Let the term independent of x in the expansion of
x2 1 x
has the value p and q be the sum of the
coefficients of its middle terms then (p -q) equals (1) 0
(2) 2.9 C4
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(3)
9
C5
(4)
9
C3
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25.
Consider the ten numbers ar,ar 2,ar 3,.......ar 10 if their sum is 18 and the the sum of their reciprocals is 6 then the product of these ten number, is (1) 324
26.
(2) 343
If A is a square matrix such that
(1) 256
27.
For
(3) 243
4 A (adj. A) = 0 0
(2) 64
x R, x 0, x 1,
letf0 (x)
0 0
4 0 , then
(4) 729
adj(adj.A)
0 4
adj.A
is equal to
(3) 32
1 1 x
and
(4) 16
fn 1 (x) (x) f0 (fn (x) (x)),n 0,1,2... ,2..... ..
then
the
value
of
2 f 3 is equal to 2 3 2
f100 (3) f1
(1)
28.
8 3
(2)
If the parabola y2
5 3
(3)
1 3
2ax(a 0) 0) meets the rectangular hyperbola
(4)
4 3
xy 4 2 orthogonally then the value of
‘a’ is (1)
29.
2
(2) 2
(3) 2 2
(4) 4
4 1 , then which of the following will not be an element of B100? 9 2
Let B = (1) 300
(2) 301
(3) -299
(4) 100
30. Number of ways in which three distinct numbers can be selected between 1 and 20 both inclusive i nclusive whose
sum is even is (1) 120
(2) 450
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(3) 570
(4) 620
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31.
If time period measured are 8.01sec and 8.41 sec using a stop watch having least count 0.01 sec then find best reported time in second. second. (1) 8.2 0.2
32.
(2) 8.41 8.41 0.01 0.01
(3) 8.01 8.01 0.01 0.01
(4) 8.2 0.01 .01
Five identical capacitor plates, each of area A are arranged such that adjacent plates are at a distance d apart, the plates are connected to a source of emf V as shown. The charge on plate 4 is
(1) 33.
20AV d
(2)
20AV d
(3)
0 AV d
(4)
0AV d
Choose correct statement regarding straight line motion while symbols have their usual meaning: (1) if a =- 3ms-2 then the motion must be retarded motion (2) If a particle is project project vertically up towards positive y-axis than acceleration will be negative at the time of ascent and positive at the time of its decent. (3) When velocity is zero acceleration must be be zero. (4) motion is said to be be retarded motion when a and v have opposite sign.
34.
A rectangular loop carrying a current I is situated near a long straight wire, such that the wire is parallel to one of the sides of the loop and is in the plane of the loop. If steady current I is established in the wire as shown in the figure, the loop will:
(1) rotate about an axis parallel to wire
(2) Move Move away from the wire
(3) Move towards the wire
(4) remain stationary
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JEE-MAINS TEST PAPER PAPER
35.
Find the value of ‘R’ for which current in 6 resistor will be zero
(1) 36.
16 5
(2)
15 4
(3)
14 3
(4)
13 3
What is the minimum energy required to launch a satellite of mass ‘m’ and radius ‘R’ in a circular orbit at an altitude ‘3R’ (1)
37.
GMm 3R
(2)
GMm 4R
7GMm 8R
(4)
8GMm 7R
The amplitude of a damped oscillator decreases to half of its original length in 3 sec. then in next 4sec. it becomes times of original amplitude where (1)
38.
(3)
1 8
(2)
will be:
1 4
(3)
1 16
A wall is moving with velocity u and a source of sound moves with velocity
(4)
1 32
u in the same direction as 2
shown in the figure. Assuming that the sound travels with velocity10u. The ratio of incident sound wavelength on the wall to the reflected sound wavelength by the wall, is equal to:
(1) 9:11 39.
(2) 11:9
(3) 4:5
(4) 5:4
A thin semicircular conducting ring of radius R is falling with its plane vertical in a horizontal magnetic induction B At the position MNQ the speed of the of the ring is v and the potential difference developed across the ring is : (1) zero (3)
BRv and Q is at higher potential
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(2) BvR2 /2 and M is at higher potential (4) 2RBv and Q is at higher higher potential Page 7
JEE-MAINS TEST PAPER PAPER
40.
A block of ice at
10 C is slowly heated and converted to steam at 100 C which of the following curves o
o
represent the phenomena qualitatively [T=temperature, H =Heat applied]
(1)
41.
(2)
(3)
(4)
The magnitude of potential energy per unit mass of the object at the surface of the earth is E and the escape velocity of the object is V e find the correct graph
(1)
42.
(2)
(3)
(4)
A bullet of mass m and charge q is fired towards a fixed solid uniformly charged sphere of radius R and total charge + q. If it strikes the surface of sphere with speed u. Find the minimum speed u so that it can penetrate through the sphere,(neglect sphere,(neglect all resistance or friction acting on bullet except except electrostatic force)
(1)
43.
q 20 mR
(2)
q 40 mR
(3)
3q 20 mR
(4)
3q 40mR
In a region of space magnetic field exists in a cylindrical region having axis of the cylinder parallel to the z axis, of radius a centered at origin. the field is given by: B B0 t k the force experienced by a stationary charge q placed at (r,0,0) where r > a is: (1)
qB0
qB0a 2 (2) 2r
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(3)
q,B0 r 2
(4) zero
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JEE-MAINS TEST PAPER PAPER
44.
A metallic metallic rod rod of of length length ( ) is tied tied to a string string of of length length (3 ) and made to rotate with constant angular velocity () on horizontal table with one end of the string is fixed. There is a vertical magnetic field B in the region, the emf induced across the ends of the rod rod is: (1)
45.
46.
B V
2
2
7B 2 (3) 2
5B 2 (4) 2
In the circuit shown, the current through:
(1) the 3 resistor is 0.50A
(2) the 3 resistor is 0.25A
(3) the 4 resistor is 0.50A
(4) the 4 resistor is 0.25A
An unpolarised beam of light of intensity I is incident on a set of four polarising plates such that each plate makes an angle of (1)
47.
(2)
B
1 64
The intensity of light / 3 with preceding sheet. The (2)
1 128 128
(3)
transmitted through the combination is:
1 32
(4)
1 256
In figure s is a monochromatic source emitting light of wavelength 500 500 nm and a thin lens of focal length 0.10 m is cut into identical halves. The two halves are placed symmetrically about the central axis So with a gap of d =0.5 mm. the distance of the lens from S is 0.15 m and that from O is 1.30 m if the third intensity maximum occurs at a point A on the screen (Perpendicular (Perpendicular to So), So), find the distance distance OA.
(1) 0.5 mm 48.
(2) 1.0 mm
(3) 1.5 mm
(4) 2.0mm
A radioactive sample P having activity 10 C ha twice the number of nuclei as another sample Q which has an activity 20 C the half lives of P and Q can be: (1) 20 years and 5 years respectively
(2) 20 years and 10 years respectively
(3) 10 years each
(4) 5 years each
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JEE-MAINS TEST PAPER PAPER
49.
A proton when accelerated through 24000V has wavelength associated with it An Particle in order to have the same wave length must be accelerated through: (1) 24000V
50.
(2) 9600V
(3) 12000V
(4) 3000V
In a hydrogen atom, the binding energy of electron in the ground state is E1 ,then the frequency of revolution of the electron in the nth orbit is: (1)
51.
2E1 n3h
2E1n3 (2) h
(3)
2mE 2mE1 n3 h
E1n 2 (4) h
An X ray tube is operated at 6.6KV in the continuous spectrum of the emitted X-rays which of the following frequency will be missing. (1)
52.
0.10 0.1018 Hz
(2) 1.51018 Hz
(3) 1.21018 Hz
(4) 1.61018 Hz
A transistor is connected connected in common common emitter configuration. configuration. The collector supply is 8V and the voltage drop across a resister of 800
in the collector circuit is 0.5 V if the current gain factor is 0.96,then the
base currents is: (1) 53.
20A
(2) 26A
(3) 30A
(4) 35A
A light emitting diode has a voltage drop of volt across it and passes a current of 10 mA when it operates with 6 volt battery through a limiting resistor R. the value of R is (1)
54.
40
(2) 4K
(3) 200 200
(4) 400 400
There is a spherical cavity of radius R / 2 in uniformly uniformly charged charged spherical spherical region having having charge charge q 0 is released at point C, centre of the cavity then it will collide with the wall of the cavity with kinetic energy
(1) 55.
R 2q0 30
(2)
R 2q0 60
(3)
R 2q0 40
(4)
R 2q0 120
If the TV-Telecast is cover a radius of 120km then the height of the transmitting antenna is (use radius of the earth R e = 6400km) (1) 1900 m
(2) 1125 m
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(3) 900 m
(4) 80 m Page 10
JEE-MAINS TEST PAPER PAPER
56.
An emf of 15 volt is applied in a circuit containing 5 Henry inductance and 10 current at time t = (1)
57.
e1/2 1/2
e
1
resistance. the ratio of the
and t =1 sec. is :
(2)
e2 2
e
1
(3) 1 e1
(4) e1
An LCR LCR series circuit with a resistance of 100 5 is connected to an AC-source of 200 V when the capacitor is removed from the circuit, current lags behind emf by 45o when the inductor is removed is removed from the circuit, keeping capacitor and resistor in the circuit current leads by an angle of
1 .then the current in the LCR circuit will be: 2
tan tan1
(1) 2A 58.
(2) 0.8A
(3) 5A
(4) 0.1A
The graph as shown represents the variation of temperature (T) of the bodies X and Y having same surface area with time (t) due to emission of radiation. Find the correct r elation between emissivity and absorptivity power of the two bodies.
(1) 59.
60.
Ex
Ey and a x a y (2)
Ex
Ey and ax a y
(3) Ex
Ey and ax a y (4)
Ex
Ey and ax a y
Soft iron is preferred as the core of transformers due to its: (1) high retentivity, high coercivity
(2) high retentivity, low coercivity
(3) low retentivity, high coercivity
(4) low retentivity, low coercivity
EM wave can be Produced by: (1) stationary charge
(2) charge moving with constant velocity
(3) Oscillating charge
(4) None
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JEE-MAINS TEST PAPER PAPER
61.
In an fcc crystal, which of the following shaded planes contains the following type of arrangement of atoms?
(1)
62.
(2)
(3)
(4)
Calculate the e. m. f. (in V) of the Galvanic cell: Pt | H2 (g) | BOH aq aq || HA aq aq | H 2 g | Pt; 0.1bar
1M
0.1M
1bar
Given; K a (H (HA) 107 ,K b (BO (BOH) 10 5 ] (1) 0.39V 63.
(2) 0.36V
(3) 0.93V
(4) 0.63V
A purified pepsin (Protein containing several amino acids) isolated from bovine preparation was introduced in the amino acid analysis. It was seen that 0.43 g of lysine (mol.wt = 146) was present in 100g of pepsin. Therefore minimum molecular weight of approximately is : (1) 34000
64.
(2) 39000
(3) 40,000
(4) 46000
A particular state of system is arrived at starting from a given state in two different ways (1) through reversible path and (2) irreversible path. Which of the following rel ations would be correct if the process are isothermal?
65.
(1)
Srev Sirrev
(3)
Srev Sirrev
(2)
qrev T
(4)
qrev qirrev Sirrev
qirrev T
Srev
The order with respect to a reaction having the following data is
(1) Zero
t (s)
0
50
100
Conc.(mol L-1)
0.68
0.34
0.17
(2) 1
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(3) 2
(4) 3 Page 12
JEE-MAINS TEST PAPER PAPER
66.
A liquid mixture having composition corresponding to point Z in the figure shown is subjected to distillation at constant pressure. Which of the following statement is correct about the process?
(1) the composition composition of of distillate differs from the mixture. (2) the boiling point goes on changing (3) the mixture has highest highest vapour pressure than for any other composition (4) Composition of an azeotrope alters on changing the external pressure. pressure. 67.
The gas A2 in the left glass bulb allowed to t o react with gas B2 present in right glass bulb as shown in figure:
A2(g) B2( 2 ( g)
2AB(g) ; Kc
4at 27o C
What is the concentration of AB(g) when equilibrium is established (1) 1.33M 68.
(2) 2.66M
(3) 0.66M
(4) 0.33M
Which of the following molecules is most suitable to disperse benzene in water
(1)
(2)
(3)
(4)
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JEE-MAINS TEST PAPER PAPER
69.
Consider the given figure showing the formation of H2 ion depending on internuclear distance versus potential energy of the system. Select the correct statement: (1) Curve 1 represents the most stable state of the system of H2 ion (2) Curve 2 represents the most stable state of the system of H2 ion (3) Curve 1 indicates that the molecular hydrogen hydrogen ion is formed (4) Curve 2 represents the energy level of the antibonding antibonding region region
70.
Which of the following is not obtained by direct reaction of constituent elements? (1)
71.
XeF2
(2) XeF4
(3) XeO XeO3
(4) XeF XeF6
The Ellingham diagram for zinc, magnesium and carbon converting into corresponding oxides is shown below
At 11000 C, which reaction is spontaneous to a maximum extent?
72.
(1)
Mg CO MgO C
(2) ZnO C Zn CO
(3)
Mg ZnO MgO Zn
(4) ZnO Mg MgO Zn
(Y) CO2 (x) K2CO3 Air Heat
(Z)Pink KCl (Y) Cl 2
which of the following is correct? (1)
X black,Mn k,MnO2 ,Y Blue, K2CrO4 , Z KMnO4
(2)
X gree reen,Cr n,Cr2O3 ,Y Yellow, K2CrO4 ,Z K2Cr2O7
(3)
X black,Mn k,MnO2 ,Y gree reen,K2MnO4 ,Z KMnO4
(4)
X bla black; Bi 2O3 , Y Colo olourle urless ss,KB ,KBiO iO2 , Z KBiO3
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JEE-MAINS TEST PAPER PAPER
73.
n
How many geometrical isomers are possible for complex Mab(AB)2 (1) 5
74.
(2) 4
(3) 3
(4) 6
In which of the following transformations, the bond order has increased and the magnetic behavior has changed? (1)
75.
C2
C2
(2) NO NO
NO
(3) O2
O2
(4) N2
N2
X3Y2 (i 5) When reacted with A2 B3 (i 5) in aqueous gives brown colour. These are separated by a semipermeable membrane AB as shown. Due to osmosis there is (1) brown colour formation in side X (2) brown colour formation in side Y (3) formation in in both of the sides X and Y (4) no brown colour formation
76.
Wave function of an orbital is plotted against the distance from nucleus. The graphical representation is for ____ orbital:
(1) 1s 77.
(2) 2s
(3) 3s
(4) 2P
The percentage of ammonia obtained, if equilibrium were to be established during the Haber’s process, p rocess, is plotted against the operating pressure for two temperatures, 400o C and 500o C .Which of the following graph correctly represents the process?
(1)
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(2)
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JEE-MAINS TEST PAPER PAPER
(3)
78.
A gas expands adiabatically at constant pressure such that T (1) 1.30
79.
(4)
(2) 1.50
V
, The value of the gas is
(3) 1.70
(4) 2
In which of the following arrangements, arrangements, the order order is not correct according according to the property indicated against against it:
(1) Increasing size: Al3
Mg2 Na F
(3) Increasing E.A.1: I Br F Cl 80.
1
(2) Increasing I.E.1: B C N O (4) Increasing metallic radius: Li Na K Rb
The straight chain polymer is formed by: (1) Hydrolysis of (CH3 )SiCl 2 followed by condensation polymerization. (2) Hydrolysis of (CH3 ) 3SiCl followed by condensation polymerization. (3) Hydrolysis of CH3SiCl3 followed by condensation polymerization. (4) Hydrolysis of (CH3 )4Si by addition polymerization
81.
In given compound which of the following electronic effects is absent:
(1) Inductive effect
(2) Resonance effect
(3) Hyperconjugative effect
(4) Negative mesomeric effect
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JEE-MAINS TEST PAPER PAPER
82.
Butaclamol is potent antipsychotic that has been used clinically in the treatment of schiz ophrenia. Although patints are given a racemic racemic mixture of the drug, only the (+) – (+) – enantiomer enantiomer has pharmacological pharmacological activity. How many chiral centres does butaclamol have?
(1) 1 83.
(2) 2
(3) 3
(4) 4
In the Newman projection for 2,2 -Dichlorobutane
Which one statement is correct?
84.
(1) If ‘X’ is H then ‘Y’ will be CH3
(2) If ‘X’ is H then ‘Y’ will be Cl
(3) If ‘X’ is H then ‘Y’ will be C2 H5
(4) If ‘X’ is Cl then ‘Y’ will be CH3
Consider the following carbocation,
If we assume that all possible rearrangements are taking place by various shifts, then which of the following rearranged carbocation cannot be formed,
(1)
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(2)
(3)
(4)
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85.
S N 2 reaction will be observes in
(1)
(2)
(3)
(4)
(racemisation in reaction mixture) 86.
The structure of product (P) is
(1)
(2)
(3)
(4)
87.
In cannizzaro cannizzaro reaction given below 2PhCH PhCH2OH PhCO2 the slowest step is: hCHO :OH :OH
(1) the transfer transfer of hydride to the carbonyl group (2) the abstraction abstraction of proton from from the carboxylic group (3) the deprotonation of PhCH2OH
(4) the attack of : OH at the carboxyl group 88.
The most basic ‘N’ is
(1) p
(2) q
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(3) r
(4) s Page 18
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89.
The following compound on hydrolysis will give
(1) A pair of anomers
(2) A pair of enantiomers
(3) A pair of epimers
(4) A pair of molecules having common tautomer
condensation polymerization of : 90. Nylon 6,10 is prepared by the condensation (1) adipic acid and hexamethylene diamine
(2) sebacic acid and hexamethylene diamine
(3) sebacic acid and hexamethylene amine
(4) adipic acid and hexamethylene amine
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DATE :-
04 / 04 2018
ANSWER & SOLUTION
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