10-01-15 Sr.iit-z (iz) Co-spark Jee Main Ctm-6 Q'paper 6z663y
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NARAYANA IIT ACADEMY INDIA
Sec:Sr.IIT-Z (IZ) CO-SPARK
REVISION CTMM-6
Dt: 10-01-15 Name of the Student: ___________________
I.D. NO:
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 test is of 3 hours duration.
3.
The Test Booklet consists of 90 questions. The maximum marks are 360.
4.
There are three parts in the question paper A, B, C consisting of Physics, Chemistry and Maths having 30 questions in each part of equal weightage. Each question is allotted 4 (four) marks for correct response.
5.
Candidates will be awarded marks as stated above in instruction No. 4 for correct response of each question. (1/4) (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.
Narayana IIT Academy SPARK_JEE MAIN_CTM-6 6.
10-01-15_Sr.IIT-Z (IZ) CO-
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 5 above.
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PHYSICS 1.
A diatomic ideal gas is heated at constant volume until the pressure is doubled and again heated at constant pressure until its volume is doubled. The average molar heat capacity for the whole process is : 1)
2.
3.
4.
13R 6
2)
19 R 6
3)
23R 6
4)
17 R 6
Two plane mirrors are ed together as shown in figure. Two point objects O 1 and O2 are placed symmetrically such that AO1 = AO2. The image of the two objects is common if :
1) = 60º 2) = 90º 3) = 30º 4) = 45º A half-wave rectifier is used to convert ‘n’ Hz a.c into d.c, then the number of pulses per second present in the rectified voltage is 1) n 2) n/2 3) 2n 4) 4n Which of the following logic gates the given truth table represents A 0 0 1 1
Sr.IIT-Z (IZ)_JEE-MAIN
B 0 1 0 1
Y 1 0 0 0 space for rough work
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5.
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1) XOR gate 2) NOR gate 3) AND gate 4) OR gate In the figure shown find the total magnification after two successive reflections first on M1 & then on M2
1) +1 6.
2) –2
3) +2
4) –1
The gate represented by the block diagram is :
A Y
B 1) AND 7.
2) NOT
3) NAND
4) NOR
Half-life of a radioactive substance A is two times the half-life of another radioactive substance B. Initially the number of nuclei of A and B are N A and N B respectively. After three half lives of A number of nuclei of both are equal. Then the ratio N A / N B is: 1) 1/4
Sr.IIT-Z (IZ)_JEE-MAIN
2) 1/8
3) 4/1 space for rough work
4) 8/1 Page 4
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8.
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A uniform rod of length L is moved with constant velocity V in a uniform magnetic field over the rails as shown in fig. Which of the following directions represents the direction of magnetic force on an electron moving along the rod.( Uniform magnetic field is into the plane of the paper).
B R
1) 9.
2)
V
3)
4)
On an X temperature scale, water freezes at – 125.0 o X and boils at 375.0o X. On a Y temperature scale, water freezes at – 70.0o Y and boils at – 30.0o Y. The value of temperature on X-scale to the temperature of 50.0o Y on Y-scale is : 1) 455.0o X
10.
2) –125.0o X
3) 1375.0o X
4) 1500.0o X
The current through a coil of self – inductance L 2mH is given by How long it will take to make the emf zero? 1) 1 s 2) 2 s 3) 3 s
Sr.IIT-Z (IZ)_JEE-MAIN
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I t 2 e t at
time t.
4) 4 s
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11.
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The voltage applied to an X-ray tube is 18KV. The maximum mass of photon emitted by the X-ray tube will be: 1) 2 X 10–13kg
12.
2) 3.2 X 10–36kg 3) 3.2 X 10–32kg 4) 9.1 X 10–31kg
In a photoelectric experiment, with light of wavelength , the fastest electron has speed v. If the exciting wavelength is changed to
3 4
the speed of the fastest emitted electron
will become 1) 13.
v
3 4
2)
v
4 3
3) less than
v
3 4
4) greater than
v
4 3
P-T diagram is shown below then choose the corresponding V-T diagram
1) Sr.IIT-Z (IZ)_JEE-MAIN
2)
3) space for rough work
4) Page 6
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14.
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A heavy nucleus having mass number 200 gets disintegrated into two small fragments of mass number 80 and 120. If binding energy per nucleon for parent atom is 6.5 MeV and for daughter nuclei is 7 MeV and 8 MeV respectively, then the energy released in the decay will be: 1) 200 MeV
15.
2) –220 MeV
3) 220 MeV
4) 180 MeV
Switch S is closed for a long time, and at t = 0 it is opened, then :
LV 2 R2 R1 1 LV 2 is 2 2 R R1 R2
1) total heat produced in resistor R after opening the switch is 2) total heat produced in resistor R1 after opening the switch 3) heat produced in resistor R1 after opening the switch is 16.
1 R2LV 2 2 R1 R2 R 2
4) no heat will be produced in R1. A vertical rod of length l is moved with constant velocity v towards East. The vertical component of the earth's magnetic field is B and the angle of dip is . The induced e.m.f. in the rod is: 1) B
l
v cot
Sr.IIT-Z (IZ)_JEE-MAIN
2) B l v sin
3) B l v tan space for rough work
4) B l v cos Page 7
Narayana IIT Academy SPARK_JEE MAIN_CTM-6
17.
18.
19.
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All electrons ejected from a surface by incident light of wavelength 200 nm can be stopped before travelling 1 m in the direction of uniform electric field of 4 N/C. The work function of the surface is : 1) 4 eV 2) 6.2 eV 3) 2 eV 4) 2.2 eV Which of the following frequencies will be suitable for beyond the horizon communication using sky waves? 1) 10 KHz 2) 10 MHz 3) 1 GHz 4) 1000 GHz In a uniform magnetic field of induction B a wire in the form of a semicircular loop of radius r rotates about the diameter of the circle with constant angular frequency . The axis of rotation is perpendicular to the field . If the total resistance of the semicircular loop is R, the mean electric power generated per period of rotation is : ( B r 2 ) 2 ( B r ) 2 ( B r 2 ) 2 B r 2 1) 2) 3) 4) 2R
20.
8R
2R
8R
A circuit containing capacitors C1 and C2 as shown in the figure are in steady state with key K1 closed and K2 is opened. At the instant t = 0, if K 1 is opened and K2 is closed then the maximum current in the circuit will be :
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1) 1 A 21.
2)
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1 A 2
3) 2A
4)
3 A 2
One mole of an ideal gas is taken from state A to state B by three different processes, a) ACB (b) ADB (c) AEB as shown in the P – V diagram. The heat absorbed by the gas is: B
P C
D
E A
22.
V
1) greater in process (b) then in (a)
2) the least in process (b)
3) the same in (a) and (c)
4) less in (c) then in (b)
In the figure shown, the image of a real object O is formed at point I. AB is the principal axis of the mirror, the mirror must be:
1) concave & placed towards right of I 2) concave & placed towards left of I 3) convex & placed towards right of I 4) convex & placed towards left of I 23.
If the ratio of the intensity of two coherent sources is 4 then the visibility
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[(Imax–Imin)/(Imax+Imin)] of the fringes is 1) 4 24.
2) 4/5
3) 3/5
4) 9
Interference fringes were produced using a light of wavelength 4800 A0 in a double slit arrangement. When sheet of uniform thickness of refractive index 1.6 (relative to air) is placed in the path of light from one of the slits, the central fringe moves some distance. This distance is equal to the width of 30 interference bands. The thickness (in m ) of sheet is:
25.
1) 90 2) 12 3) 14 4) 24 Electrons with energy 80 keV are incident on the tungsten target of an X-ray tube. K – shell electrons of tungsten have 72.5 keV energy. X-rays emitted by the tube contain only: 1) a continuous X-ray spectrum (Bremsstrahlung) with a minimum wavelength of 0
0.155 A
2) a continuous X-ray spectrum (Bremsstrahlung) with all wavelengths 3) the characteristic X-ray spectrum of tungsten
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4) a continuous X-ray spectrum (Bremsstrahlung) with a minimum wavelength of 0
0.155 A and the characteristic X-ray spectrum of tungsten
26.
27.
In a L-R growth circuit, inductance and resistance used are 1 H and 20 respectively. If at t = 50 millisecond, current in the circuit is 3.165 A then applied direct current emf is: 1) 200 V 2) 100 V 3) 50 V 4) Data is insufficient to find out the value. A bulb is rated at 100V, 100W, it can be treated as a resistor. Find out the inductance of an inductor (called choke coil) that should be connected in series with the bulb to operate the bulb at its rated power with the help of an source of 200V and 50 Hz. 1)
28.
H 3
2) 100 H
3)
2 H
4)
3 H
The value of current in two series LCR circuits at resonance is same when connected across the same sinusoidal voltage source. Then: 1) both circuits must be having same value of capacitance and inductor 2) in both circuits ratio of L and C will be same 3) for both the circuits XL/XC must be same at resonance frequency 4) both circuits must have same impedance at all frequencies.
29.
The secondary coil of an ideal step down transformer is delivering 500 watt power at 12.5 A current. If the ratio of turns in the primary to the secondary is 5: 1, then the current flowing in the primary coil will be : 1) 62.5 A
Sr.IIT-Z (IZ)_JEE-MAIN
2) 2.5 A
3) 6 A space for rough work
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30.
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A particle of mass M at rest decays into two particles of masses m1 and m2 having nonzero velocities. The ratio of the de-Broglie wave lengths of the particles 1 / 2 is: 1) m1 / m2
2) m2 / m1
3) 1
4) m2 / m1
MATHEMATICS
31. 32.
2 4 The value of Sec 2 Sec 2 Sec 2 is 7 7 7
1) 22 2) 24 3) 26 4) 28 Let f n 2 cos nx n N , then f 1 f n 1 f n equals 1) f n 3
2) f n 2
3) f n 1 f 2
4) f n 2 f 2
33.
The number of solutions of the equation x3 x 2 2 x sin x 0 in 2 , 2 is 1) 1 2) 2 3) 3 4) 4
34.
The number of positive integral values of ‘n’ satisfying the equation sin is 1) 1
35.
36.
2) 2
3) 3 ab 1
4) 4 bc 1
ca 1
1 1 1 If a b c 0 , then the value of cot cot cot c a a b b c 1) 0 2) 3) 4) 2
If
n cos 2n 2n 2
is
x 1 x 2 1 x 1 , then cos 1 x cos 1 2 2
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1) 2 cos 1 x 37.
4
2) 2 cos 1 x
3) 0
4)
4
The remainder when 2147 1 divided by 343 is 1) 0
38.
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2) 48
3) 102
4) 342
In a triangle ABC, if the median AD makes an angle with AC and AB = 2AD then sin
39.
1) sin A 2) sin B 3) sin C 4) 2sin A If D is a point of the base BC of an isosceles triangle ABC such that AD is perpendicular to AC, then a =
1 sin A AD cos B If x1 , x2 , x3 ,.....xn are in A.P. whose common difference is , then the value of
1) 2b 40.
2) 2b cos B
3)
1 cos A AD sin B
4)
sin [sec x1 sec x2 sec x2 sec x3 ..... sec xn 1 sec xn ] =
1)
sin n cos xn cos x1
2) sin(n 1)
3) sin(n 1)
4) cos(n 1)
cos xn cos x1
cos xn cos x1
cos xn cos x1
10
41.
Sum of the series 1 r 0
1)
2 1 220 10
n
42.
If an r 0
n 2
1) an 43.
r
1 3r 2 r is r 2 2 220 1 3) 20 2
Cr
10
210 1 220 n 1 r , then equals n n Cr r 0 Cr n 2) an 4
2)
3) nan
4)
220 1 220
4) n 1 an
If 2sinx – cos2x = 1, then cos2x + cos4x is equal to
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1) 1 44.
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2) -1
3)
5
4)
5
The sum of the factors of 9! Which are odd and are of the form 3m 2 , where m is a natural number is 1) 40
45.
2) 45 2) 33 n
Sum of the series 1) n 1 !
47.
4) 44
The remainder when x 1! 2! 3! 4! .... 100! is divided by 240, is 1) 153
46.
3) 51
r r 1
2
3) 73
4) 187
3) n n 1 !
4) n 1 ! 1
1 r ! is
2) n 2 ! 1
The number of ways of selecting 4 cards of an ordinary pack of playing cards so that exactly 3 of them are of the same denomination is 1) 2496
48.
2) 13C3 4C3 48
3) 52C3 48
4) 2296
If three six-faced fair dice are thrown together, the probability that the sum of the numbers appearing on the dice is 16 is 1) 1/36
49.
2) 1/11
3) 1/2
4) 5/36
Out of 21 tickets marked with numbers 1,2, ....,21, three are drawn at random without replacement. The probability that these numbers are in A.P. is 1)
10 133
Sr.IIT-Z (IZ)_JEE-MAIN
2)
9 15
3)
14 261
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4)
13 261 Page 14
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50.
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While shuffling a pack of playing cards, four are accidently dropped. The probability that the cards that are dropped are one from each suit is 1)
51.
1 20825
2)
2197 20825
3)
1 256
4)
2197 499800
The number of points inside or on the circle x 2 y 2 4 satisfying tan 4 x cot 4 x 1 3sin 2 y is
1) 1 52.
2) 2
4) 4
If ‘m’ is a natural number such that m 5 , then the probability that the quadratic 1 2
equation x 2 mx 1)1/5 53.
3) 3
m 0 has real roots is? 2
2) 2/3
3) 3/5
4) 1/5
The least number of times a fair coin must be tossed so that the probability of getting at least one head is at least 0.95 is 1) 5
54.
2) 6
3) 7
4) 12
If three positive real numbers a, b, c are in A.P. such that abc = 4, then the minimum possible value of ‘b’ is 1) 23/2
Sr.IIT-Z (IZ)_JEE-MAIN
2) 22/3
3) 21/3 space for rough work
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55.
1 1 1 1 1 1 2 .... If 2 2 2 upto , then value of 2 2 2 .... up to is 1 2 3 1 3 5 6
1) 56.
2 4
2) 1
If an 1 1 a
n
2 6
3)
2 8
4)
2 12
2001 for n 1 and a3 a1 , then a2001 equals
1) -1 57.
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2) 1
3) 0
4) 2
If a, b, c are real and a b , then the roots of the equation 2 a b x 2 11 a b c x 3 a b 0 (are)
58.
59.
1) real and equal
2) real and unequal
3) purely imaginary
4) Cannot be decided
Let a > 0, b > 0 and c > 0. Then both the roots of the equation 2ax 2 3bx 5c 0 . 1) are real and negative
2) have negative real parts
3) have positive real parts
4) Cannot be decided
Let , be the roots of x 2 x p 0 and , be the roots of x 2 4 x q 0 . If , , , are in G.P. then the integral values of p and q respectively, are
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1) -2, -32 60.
61.
3) -6, 3
4) -6, -32
If a b c d , then the equation 3 x a x c 5 x b x d 0 has 1) real and distinct roots
2) real and equal roots
3) purely imaginary roots
4) Non real roots
CHEMISTRY Which alkene will give only optically active product upon catalytic hydrogenation H 2 / Pd ?
1) 62.
2) -2, 3
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2)
3)
4)
Predict the product of the reaction of 1-pentyne and excess HCl in the presence of hydrogen peroxide. 1) 1,1- dichloropentane
2) 1,2-dichloropentane
3) 2,2-dichloropentane
4) 2-chloro-1-pentene
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O K C elctroysiM aAjor
Narayana IIT Academy SPARK_JEE MAIN_CTM-6
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;
Major-product (A) is:
63.
O C O
64.
gS2O C H 4 H O H
1) 2) 3) 4) What is the major organic product of the following reaction?
O H N H N a b c
1) 65.
2)
H H O
H O 3)
4)
O
O
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Compare rate of EAS : 1) a b c
l AlC3 C H 66.
Cumene
1)
67.
2) a c b
3) b a c
4) c a b
l AlC3 C
is prepared by :
2)
3) 4) All of these Which of the following isomeric hexachlorocylohexanes is least reactive in
lC l C lC lC
lC l C lC lC
-dehydrochlorination on treatment with strong base?
1)
Sr.IIT-Z (IZ)_JEE-MAIN
2)
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lC l C lC lC
3) 68.
4) All three are equally reactive
B r
Compare rate of reaction with Ag NO3 :
B r
B r
i)
ii)
iii)
1) i iii ii
2) i ii iii
3) iii i ii
C H O H 2 O XmolesofHBr
4) ii i iii
69.
value of (x ) is
1) 1
2) 2
3) 3
4) 4
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H 2 P hC H 3 P hC C H 2 h H It? O ea 1)
71.
2)
P h H 3 P hO E tC
3) 4) What are the major products from the following reaction ?
1)
72.
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H IC 2O O C H I 2O
2)
O H C H 2I O C H H 2IO
3) 4) Which of the following reactions can be used to prepare 3-methyl-3-hexanol,
H C H C H 32O 23 32C ?
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1)
O gB r M g B r 33 2M 33 H H C C H H 3O 2C 23 1.C 32C 2C 2H 3 1.C 2H.H O 2H.H O H H gB r 32 2C 2M C H H 3O 2C 3 1.C .H 3O 2)
E t H3O O 3)
4) all of these
73.
O H
Product obtained in above reaction are:
EtOH
1)
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O
,
O CH 3 CHO
2)
O
,
CH 3CO2 H
3)
,
O 10%NaOH,2O 74.
4) EtOH,
What is the product of the following reaction?
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H OO
O H O 1)
75.
H O O
3N O HH 4H.52
3) 4) What is the product of the following reaction?
C H 3N H 76.
2)
H OO
H O N H 2
C H 3 N
C H 3 O H N
1) 2) 3) 4) Which of the following compounds is the least reactive towards nucleophilic acyl substitution?
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O R C N H 2 H H M eO 2iO iOHNO iO
O R C H 3
O R C l
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O O R C C R
77.
1) 2) 3) 4) The Keq values in HCN addition to following aldehydes are in the order:
78.
1) i ii iii 2) ii iii i 3) iii ii i What is the product of the following reaction?
O H O O H H Heat O
OO O H H 1)
79.
O
?
O H O H O
2)
OO H
4) ii i iii
3) 4) What is the product of the following reaction?
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18 H ? O H 2O
1)
18H 18C H O H H C 22C 22O O 18H H O C 2H 2C 2H 2C
3)
O 18C H O H H H 22C 22C 2) 4) All of these
the reaction O O H N C l 2 H h e r X i s : 80. Consider X ; N H 2
O H N H 2N 1)
O H
3) Sr.IIT-Z (IZ)_JEE-MAIN
O H N H 2N
2)
O H N
4) space for rough work
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Narayana IIT Academy SPARK_JEE MAIN_CTM-6
81.
O 15H C N 2 C H 3
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O C N H 2 O C H 3
O C N H 2 N O 2
Which of the following is most reactive towards Hoffmann bromamide reaction?
N H 2 H C C m olle H N H 2 21 1)
2)
O C N H 2
3)
4)
82.
Product formed in the reaction is:
lC N H 3C H N H 2 2
1) Sr.IIT-Z (IZ)_JEE-MAIN
N H 2 C H l N 3C
N H 2 C H N H l 2 3C 2)
3) space for rough work
N H 2 N H l 3C 4) Page 26
Narayana IIT Academy SPARK_JEE MAIN_CTM-6
83.
N H O 2O H H
N H 3O O
2)
N H 2O O
3) 4) Which of the following compounds is a nonreducing sugar?
1) i 85.
N H O 2O H
What is the major structure of aspartic acid present at pH = 7 in aqueous solution having PKa1=2.10, PKa2=3.86 and PKa3=9.82?
1)
84.
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2) ii
3) iii
4) iv
Which of the following pair will form same osazone? 1) D-Glucose, D-Allose
Sr.IIT-Z (IZ)_JEE-MAIN
2) D-Glucose, D-Altrose space for rough work
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3) D-allose, D-Altrose 86.
4) D-Fructose, D-Galactose
In elastomer, intermolecular forces are: 1) Nil
87.
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2) Weak
3) Strong
4) Very strong
Which of the following polymer, not having C - C bond formation during polymerisation. 1) Teflon
88.
2) Bakelite
3) Natural rubber 4) Buna-s
Absolute alcohol cannot be obtained by simple fractional distillation because: 1) Pure C2 H 5OH is unstable 2) C2 H 5OH do not form hydrogen bonds with water 3) Boiling point C2 H 5OH is very close to that of water 4) Constant boiling azeotropic mixture is formed with water
89.
Histamine stimulates the secretion of pepsin and hydrochloric acid and antihistamines are used to prevent the action of histamines. Among the following which are antihistamines?
SO N H R H 2NO
1) Ranitidine
2) Terfenadine
3) Brompheniramine
4) All of these
90. Above drug is an example of: Sr.IIT-Z (IZ)_JEE-MAIN
space for rough work
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Narayana IIT Academy SPARK_JEE MAIN_CTM-6
1) Sulpha drug
Sr.IIT-Z (IZ)_JEE-MAIN
2) Morphine
10-01-15_Sr.IIT-Z (IZ) CO-
3) Analgesic
space for rough work
4) Tranquilizer
Page 29
Sec:Sr.IIT-Z (IZ) CO-SPARK
REVISION CTMM-6
Dt: 10-01-15 Name of the Student: ___________________
I.D. NO:
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 test is of 3 hours duration.
3.
The Test Booklet consists of 90 questions. The maximum marks are 360.
4.
There are three parts in the question paper A, B, C consisting of Physics, Chemistry and Maths having 30 questions in each part of equal weightage. Each question is allotted 4 (four) marks for correct response.
5.
Candidates will be awarded marks as stated above in instruction No. 4 for correct response of each question. (1/4) (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.
Narayana IIT Academy SPARK_JEE MAIN_CTM-6 6.
10-01-15_Sr.IIT-Z (IZ) CO-
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 5 above.
Sr.IIT-Z (IZ)_JEE-MAIN
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10-01-15_Sr.IIT-Z (IZ) CO-
PHYSICS 1.
A diatomic ideal gas is heated at constant volume until the pressure is doubled and again heated at constant pressure until its volume is doubled. The average molar heat capacity for the whole process is : 1)
2.
3.
4.
13R 6
2)
19 R 6
3)
23R 6
4)
17 R 6
Two plane mirrors are ed together as shown in figure. Two point objects O 1 and O2 are placed symmetrically such that AO1 = AO2. The image of the two objects is common if :
1) = 60º 2) = 90º 3) = 30º 4) = 45º A half-wave rectifier is used to convert ‘n’ Hz a.c into d.c, then the number of pulses per second present in the rectified voltage is 1) n 2) n/2 3) 2n 4) 4n Which of the following logic gates the given truth table represents A 0 0 1 1
Sr.IIT-Z (IZ)_JEE-MAIN
B 0 1 0 1
Y 1 0 0 0 space for rough work
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Narayana IIT Academy SPARK_JEE MAIN_CTM-6
5.
10-01-15_Sr.IIT-Z (IZ) CO-
1) XOR gate 2) NOR gate 3) AND gate 4) OR gate In the figure shown find the total magnification after two successive reflections first on M1 & then on M2
1) +1 6.
2) –2
3) +2
4) –1
The gate represented by the block diagram is :
A Y
B 1) AND 7.
2) NOT
3) NAND
4) NOR
Half-life of a radioactive substance A is two times the half-life of another radioactive substance B. Initially the number of nuclei of A and B are N A and N B respectively. After three half lives of A number of nuclei of both are equal. Then the ratio N A / N B is: 1) 1/4
Sr.IIT-Z (IZ)_JEE-MAIN
2) 1/8
3) 4/1 space for rough work
4) 8/1 Page 4
Narayana IIT Academy SPARK_JEE MAIN_CTM-6
8.
10-01-15_Sr.IIT-Z (IZ) CO-
A uniform rod of length L is moved with constant velocity V in a uniform magnetic field over the rails as shown in fig. Which of the following directions represents the direction of magnetic force on an electron moving along the rod.( Uniform magnetic field is into the plane of the paper).
B R
1) 9.
2)
V
3)
4)
On an X temperature scale, water freezes at – 125.0 o X and boils at 375.0o X. On a Y temperature scale, water freezes at – 70.0o Y and boils at – 30.0o Y. The value of temperature on X-scale to the temperature of 50.0o Y on Y-scale is : 1) 455.0o X
10.
2) –125.0o X
3) 1375.0o X
4) 1500.0o X
The current through a coil of self – inductance L 2mH is given by How long it will take to make the emf zero? 1) 1 s 2) 2 s 3) 3 s
Sr.IIT-Z (IZ)_JEE-MAIN
space for rough work
I t 2 e t at
time t.
4) 4 s
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Narayana IIT Academy SPARK_JEE MAIN_CTM-6
11.
10-01-15_Sr.IIT-Z (IZ) CO-
The voltage applied to an X-ray tube is 18KV. The maximum mass of photon emitted by the X-ray tube will be: 1) 2 X 10–13kg
12.
2) 3.2 X 10–36kg 3) 3.2 X 10–32kg 4) 9.1 X 10–31kg
In a photoelectric experiment, with light of wavelength , the fastest electron has speed v. If the exciting wavelength is changed to
3 4
the speed of the fastest emitted electron
will become 1) 13.
v
3 4
2)
v
4 3
3) less than
v
3 4
4) greater than
v
4 3
P-T diagram is shown below then choose the corresponding V-T diagram
1) Sr.IIT-Z (IZ)_JEE-MAIN
2)
3) space for rough work
4) Page 6
Narayana IIT Academy SPARK_JEE MAIN_CTM-6
14.
10-01-15_Sr.IIT-Z (IZ) CO-
A heavy nucleus having mass number 200 gets disintegrated into two small fragments of mass number 80 and 120. If binding energy per nucleon for parent atom is 6.5 MeV and for daughter nuclei is 7 MeV and 8 MeV respectively, then the energy released in the decay will be: 1) 200 MeV
15.
2) –220 MeV
3) 220 MeV
4) 180 MeV
Switch S is closed for a long time, and at t = 0 it is opened, then :
LV 2 R2 R1 1 LV 2 is 2 2 R R1 R2
1) total heat produced in resistor R after opening the switch is 2) total heat produced in resistor R1 after opening the switch 3) heat produced in resistor R1 after opening the switch is 16.
1 R2LV 2 2 R1 R2 R 2
4) no heat will be produced in R1. A vertical rod of length l is moved with constant velocity v towards East. The vertical component of the earth's magnetic field is B and the angle of dip is . The induced e.m.f. in the rod is: 1) B
l
v cot
Sr.IIT-Z (IZ)_JEE-MAIN
2) B l v sin
3) B l v tan space for rough work
4) B l v cos Page 7
Narayana IIT Academy SPARK_JEE MAIN_CTM-6
17.
18.
19.
10-01-15_Sr.IIT-Z (IZ) CO-
All electrons ejected from a surface by incident light of wavelength 200 nm can be stopped before travelling 1 m in the direction of uniform electric field of 4 N/C. The work function of the surface is : 1) 4 eV 2) 6.2 eV 3) 2 eV 4) 2.2 eV Which of the following frequencies will be suitable for beyond the horizon communication using sky waves? 1) 10 KHz 2) 10 MHz 3) 1 GHz 4) 1000 GHz In a uniform magnetic field of induction B a wire in the form of a semicircular loop of radius r rotates about the diameter of the circle with constant angular frequency . The axis of rotation is perpendicular to the field . If the total resistance of the semicircular loop is R, the mean electric power generated per period of rotation is : ( B r 2 ) 2 ( B r ) 2 ( B r 2 ) 2 B r 2 1) 2) 3) 4) 2R
20.
8R
2R
8R
A circuit containing capacitors C1 and C2 as shown in the figure are in steady state with key K1 closed and K2 is opened. At the instant t = 0, if K 1 is opened and K2 is closed then the maximum current in the circuit will be :
Sr.IIT-Z (IZ)_JEE-MAIN
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Narayana IIT Academy SPARK_JEE MAIN_CTM-6
1) 1 A 21.
2)
10-01-15_Sr.IIT-Z (IZ) CO-
1 A 2
3) 2A
4)
3 A 2
One mole of an ideal gas is taken from state A to state B by three different processes, a) ACB (b) ADB (c) AEB as shown in the P – V diagram. The heat absorbed by the gas is: B
P C
D
E A
22.
V
1) greater in process (b) then in (a)
2) the least in process (b)
3) the same in (a) and (c)
4) less in (c) then in (b)
In the figure shown, the image of a real object O is formed at point I. AB is the principal axis of the mirror, the mirror must be:
1) concave & placed towards right of I 2) concave & placed towards left of I 3) convex & placed towards right of I 4) convex & placed towards left of I 23.
If the ratio of the intensity of two coherent sources is 4 then the visibility
Sr.IIT-Z (IZ)_JEE-MAIN
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Narayana IIT Academy SPARK_JEE MAIN_CTM-6
10-01-15_Sr.IIT-Z (IZ) CO-
[(Imax–Imin)/(Imax+Imin)] of the fringes is 1) 4 24.
2) 4/5
3) 3/5
4) 9
Interference fringes were produced using a light of wavelength 4800 A0 in a double slit arrangement. When sheet of uniform thickness of refractive index 1.6 (relative to air) is placed in the path of light from one of the slits, the central fringe moves some distance. This distance is equal to the width of 30 interference bands. The thickness (in m ) of sheet is:
25.
1) 90 2) 12 3) 14 4) 24 Electrons with energy 80 keV are incident on the tungsten target of an X-ray tube. K – shell electrons of tungsten have 72.5 keV energy. X-rays emitted by the tube contain only: 1) a continuous X-ray spectrum (Bremsstrahlung) with a minimum wavelength of 0
0.155 A
2) a continuous X-ray spectrum (Bremsstrahlung) with all wavelengths 3) the characteristic X-ray spectrum of tungsten
Sr.IIT-Z (IZ)_JEE-MAIN
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10-01-15_Sr.IIT-Z (IZ) CO-
4) a continuous X-ray spectrum (Bremsstrahlung) with a minimum wavelength of 0
0.155 A and the characteristic X-ray spectrum of tungsten
26.
27.
In a L-R growth circuit, inductance and resistance used are 1 H and 20 respectively. If at t = 50 millisecond, current in the circuit is 3.165 A then applied direct current emf is: 1) 200 V 2) 100 V 3) 50 V 4) Data is insufficient to find out the value. A bulb is rated at 100V, 100W, it can be treated as a resistor. Find out the inductance of an inductor (called choke coil) that should be connected in series with the bulb to operate the bulb at its rated power with the help of an source of 200V and 50 Hz. 1)
28.
H 3
2) 100 H
3)
2 H
4)
3 H
The value of current in two series LCR circuits at resonance is same when connected across the same sinusoidal voltage source. Then: 1) both circuits must be having same value of capacitance and inductor 2) in both circuits ratio of L and C will be same 3) for both the circuits XL/XC must be same at resonance frequency 4) both circuits must have same impedance at all frequencies.
29.
The secondary coil of an ideal step down transformer is delivering 500 watt power at 12.5 A current. If the ratio of turns in the primary to the secondary is 5: 1, then the current flowing in the primary coil will be : 1) 62.5 A
Sr.IIT-Z (IZ)_JEE-MAIN
2) 2.5 A
3) 6 A space for rough work
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Narayana IIT Academy SPARK_JEE MAIN_CTM-6
30.
10-01-15_Sr.IIT-Z (IZ) CO-
A particle of mass M at rest decays into two particles of masses m1 and m2 having nonzero velocities. The ratio of the de-Broglie wave lengths of the particles 1 / 2 is: 1) m1 / m2
2) m2 / m1
3) 1
4) m2 / m1
MATHEMATICS
31. 32.
2 4 The value of Sec 2 Sec 2 Sec 2 is 7 7 7
1) 22 2) 24 3) 26 4) 28 Let f n 2 cos nx n N , then f 1 f n 1 f n equals 1) f n 3
2) f n 2
3) f n 1 f 2
4) f n 2 f 2
33.
The number of solutions of the equation x3 x 2 2 x sin x 0 in 2 , 2 is 1) 1 2) 2 3) 3 4) 4
34.
The number of positive integral values of ‘n’ satisfying the equation sin is 1) 1
35.
36.
2) 2
3) 3 ab 1
4) 4 bc 1
ca 1
1 1 1 If a b c 0 , then the value of cot cot cot c a a b b c 1) 0 2) 3) 4) 2
If
n cos 2n 2n 2
is
x 1 x 2 1 x 1 , then cos 1 x cos 1 2 2
Sr.IIT-Z (IZ)_JEE-MAIN
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Narayana IIT Academy SPARK_JEE MAIN_CTM-6
1) 2 cos 1 x 37.
4
2) 2 cos 1 x
3) 0
4)
4
The remainder when 2147 1 divided by 343 is 1) 0
38.
10-01-15_Sr.IIT-Z (IZ) CO-
2) 48
3) 102
4) 342
In a triangle ABC, if the median AD makes an angle with AC and AB = 2AD then sin
39.
1) sin A 2) sin B 3) sin C 4) 2sin A If D is a point of the base BC of an isosceles triangle ABC such that AD is perpendicular to AC, then a =
1 sin A AD cos B If x1 , x2 , x3 ,.....xn are in A.P. whose common difference is , then the value of
1) 2b 40.
2) 2b cos B
3)
1 cos A AD sin B
4)
sin [sec x1 sec x2 sec x2 sec x3 ..... sec xn 1 sec xn ] =
1)
sin n cos xn cos x1
2) sin(n 1)
3) sin(n 1)
4) cos(n 1)
cos xn cos x1
cos xn cos x1
cos xn cos x1
10
41.
Sum of the series 1 r 0
1)
2 1 220 10
n
42.
If an r 0
n 2
1) an 43.
r
1 3r 2 r is r 2 2 220 1 3) 20 2
Cr
10
210 1 220 n 1 r , then equals n n Cr r 0 Cr n 2) an 4
2)
3) nan
4)
220 1 220
4) n 1 an
If 2sinx – cos2x = 1, then cos2x + cos4x is equal to
Sr.IIT-Z (IZ)_JEE-MAIN
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Narayana IIT Academy SPARK_JEE MAIN_CTM-6
1) 1 44.
10-01-15_Sr.IIT-Z (IZ) CO-
2) -1
3)
5
4)
5
The sum of the factors of 9! Which are odd and are of the form 3m 2 , where m is a natural number is 1) 40
45.
2) 45 2) 33 n
Sum of the series 1) n 1 !
47.
4) 44
The remainder when x 1! 2! 3! 4! .... 100! is divided by 240, is 1) 153
46.
3) 51
r r 1
2
3) 73
4) 187
3) n n 1 !
4) n 1 ! 1
1 r ! is
2) n 2 ! 1
The number of ways of selecting 4 cards of an ordinary pack of playing cards so that exactly 3 of them are of the same denomination is 1) 2496
48.
2) 13C3 4C3 48
3) 52C3 48
4) 2296
If three six-faced fair dice are thrown together, the probability that the sum of the numbers appearing on the dice is 16 is 1) 1/36
49.
2) 1/11
3) 1/2
4) 5/36
Out of 21 tickets marked with numbers 1,2, ....,21, three are drawn at random without replacement. The probability that these numbers are in A.P. is 1)
10 133
Sr.IIT-Z (IZ)_JEE-MAIN
2)
9 15
3)
14 261
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4)
13 261 Page 14
Narayana IIT Academy SPARK_JEE MAIN_CTM-6
50.
10-01-15_Sr.IIT-Z (IZ) CO-
While shuffling a pack of playing cards, four are accidently dropped. The probability that the cards that are dropped are one from each suit is 1)
51.
1 20825
2)
2197 20825
3)
1 256
4)
2197 499800
The number of points inside or on the circle x 2 y 2 4 satisfying tan 4 x cot 4 x 1 3sin 2 y is
1) 1 52.
2) 2
4) 4
If ‘m’ is a natural number such that m 5 , then the probability that the quadratic 1 2
equation x 2 mx 1)1/5 53.
3) 3
m 0 has real roots is? 2
2) 2/3
3) 3/5
4) 1/5
The least number of times a fair coin must be tossed so that the probability of getting at least one head is at least 0.95 is 1) 5
54.
2) 6
3) 7
4) 12
If three positive real numbers a, b, c are in A.P. such that abc = 4, then the minimum possible value of ‘b’ is 1) 23/2
Sr.IIT-Z (IZ)_JEE-MAIN
2) 22/3
3) 21/3 space for rough work
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Narayana IIT Academy SPARK_JEE MAIN_CTM-6
55.
1 1 1 1 1 1 2 .... If 2 2 2 upto , then value of 2 2 2 .... up to is 1 2 3 1 3 5 6
1) 56.
2 4
2) 1
If an 1 1 a
n
2 6
3)
2 8
4)
2 12
2001 for n 1 and a3 a1 , then a2001 equals
1) -1 57.
10-01-15_Sr.IIT-Z (IZ) CO-
2) 1
3) 0
4) 2
If a, b, c are real and a b , then the roots of the equation 2 a b x 2 11 a b c x 3 a b 0 (are)
58.
59.
1) real and equal
2) real and unequal
3) purely imaginary
4) Cannot be decided
Let a > 0, b > 0 and c > 0. Then both the roots of the equation 2ax 2 3bx 5c 0 . 1) are real and negative
2) have negative real parts
3) have positive real parts
4) Cannot be decided
Let , be the roots of x 2 x p 0 and , be the roots of x 2 4 x q 0 . If , , , are in G.P. then the integral values of p and q respectively, are
Sr.IIT-Z (IZ)_JEE-MAIN
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Narayana IIT Academy SPARK_JEE MAIN_CTM-6
1) -2, -32 60.
61.
3) -6, 3
4) -6, -32
If a b c d , then the equation 3 x a x c 5 x b x d 0 has 1) real and distinct roots
2) real and equal roots
3) purely imaginary roots
4) Non real roots
CHEMISTRY Which alkene will give only optically active product upon catalytic hydrogenation H 2 / Pd ?
1) 62.
2) -2, 3
10-01-15_Sr.IIT-Z (IZ) CO-
2)
3)
4)
Predict the product of the reaction of 1-pentyne and excess HCl in the presence of hydrogen peroxide. 1) 1,1- dichloropentane
2) 1,2-dichloropentane
3) 2,2-dichloropentane
4) 2-chloro-1-pentene
Sr.IIT-Z (IZ)_JEE-MAIN
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O K C elctroysiM aAjor
Narayana IIT Academy SPARK_JEE MAIN_CTM-6
10-01-15_Sr.IIT-Z (IZ) CO-
;
Major-product (A) is:
63.
O C O
64.
gS2O C H 4 H O H
1) 2) 3) 4) What is the major organic product of the following reaction?
O H N H N a b c
1) 65.
2)
H H O
H O 3)
4)
O
O
Sr.IIT-Z (IZ)_JEE-MAIN
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10-01-15_Sr.IIT-Z (IZ) CO-
Compare rate of EAS : 1) a b c
l AlC3 C H 66.
Cumene
1)
67.
2) a c b
3) b a c
4) c a b
l AlC3 C
is prepared by :
2)
3) 4) All of these Which of the following isomeric hexachlorocylohexanes is least reactive in
lC l C lC lC
lC l C lC lC
-dehydrochlorination on treatment with strong base?
1)
Sr.IIT-Z (IZ)_JEE-MAIN
2)
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Narayana IIT Academy SPARK_JEE MAIN_CTM-6
10-01-15_Sr.IIT-Z (IZ) CO-
lC l C lC lC
3) 68.
4) All three are equally reactive
B r
Compare rate of reaction with Ag NO3 :
B r
B r
i)
ii)
iii)
1) i iii ii
2) i ii iii
3) iii i ii
C H O H 2 O XmolesofHBr
4) ii i iii
69.
value of (x ) is
1) 1
2) 2
3) 3
4) 4
70. Sr.IIT-Z (IZ)_JEE-MAIN
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Narayana IIT Academy SPARK_JEE MAIN_CTM-6
H 2 P hC H 3 P hC C H 2 h H It? O ea 1)
71.
2)
P h H 3 P hO E tC
3) 4) What are the major products from the following reaction ?
1)
72.
10-01-15_Sr.IIT-Z (IZ) CO-
H IC 2O O C H I 2O
2)
O H C H 2I O C H H 2IO
3) 4) Which of the following reactions can be used to prepare 3-methyl-3-hexanol,
H C H C H 32O 23 32C ?
Sr.IIT-Z (IZ)_JEE-MAIN
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Narayana IIT Academy SPARK_JEE MAIN_CTM-6
1)
O gB r M g B r 33 2M 33 H H C C H H 3O 2C 23 1.C 32C 2C 2H 3 1.C 2H.H O 2H.H O H H gB r 32 2C 2M C H H 3O 2C 3 1.C .H 3O 2)
E t H3O O 3)
4) all of these
73.
O H
Product obtained in above reaction are:
EtOH
1)
10-01-15_Sr.IIT-Z (IZ) CO-
O
,
O CH 3 CHO
2)
O
,
CH 3CO2 H
3)
,
O 10%NaOH,2O 74.
4) EtOH,
What is the product of the following reaction?
Sr.IIT-Z (IZ)_JEE-MAIN
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Narayana IIT Academy SPARK_JEE MAIN_CTM-6
10-01-15_Sr.IIT-Z (IZ) CO-
H OO
O H O 1)
75.
H O O
3N O HH 4H.52
3) 4) What is the product of the following reaction?
C H 3N H 76.
2)
H OO
H O N H 2
C H 3 N
C H 3 O H N
1) 2) 3) 4) Which of the following compounds is the least reactive towards nucleophilic acyl substitution?
Sr.IIT-Z (IZ)_JEE-MAIN
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Narayana IIT Academy SPARK_JEE MAIN_CTM-6
O R C N H 2 H H M eO 2iO iOHNO iO
O R C H 3
O R C l
10-01-15_Sr.IIT-Z (IZ) CO-
O O R C C R
77.
1) 2) 3) 4) The Keq values in HCN addition to following aldehydes are in the order:
78.
1) i ii iii 2) ii iii i 3) iii ii i What is the product of the following reaction?
O H O O H H Heat O
OO O H H 1)
79.
O
?
O H O H O
2)
OO H
4) ii i iii
3) 4) What is the product of the following reaction?
Sr.IIT-Z (IZ)_JEE-MAIN
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Narayana IIT Academy SPARK_JEE MAIN_CTM-6
10-01-15_Sr.IIT-Z (IZ) CO-
18 H ? O H 2O
1)
18H 18C H O H H C 22C 22O O 18H H O C 2H 2C 2H 2C
3)
O 18C H O H H H 22C 22C 2) 4) All of these
the reaction O O H N C l 2 H h e r X i s : 80. Consider X ; N H 2
O H N H 2N 1)
O H
3) Sr.IIT-Z (IZ)_JEE-MAIN
O H N H 2N
2)
O H N
4) space for rough work
Page 25
Narayana IIT Academy SPARK_JEE MAIN_CTM-6
81.
O 15H C N 2 C H 3
10-01-15_Sr.IIT-Z (IZ) CO-
O C N H 2 O C H 3
O C N H 2 N O 2
Which of the following is most reactive towards Hoffmann bromamide reaction?
N H 2 H C C m olle H N H 2 21 1)
2)
O C N H 2
3)
4)
82.
Product formed in the reaction is:
lC N H 3C H N H 2 2
1) Sr.IIT-Z (IZ)_JEE-MAIN
N H 2 C H l N 3C
N H 2 C H N H l 2 3C 2)
3) space for rough work
N H 2 N H l 3C 4) Page 26
Narayana IIT Academy SPARK_JEE MAIN_CTM-6
83.
N H O 2O H H
N H 3O O
2)
N H 2O O
3) 4) Which of the following compounds is a nonreducing sugar?
1) i 85.
N H O 2O H
What is the major structure of aspartic acid present at pH = 7 in aqueous solution having PKa1=2.10, PKa2=3.86 and PKa3=9.82?
1)
84.
10-01-15_Sr.IIT-Z (IZ) CO-
2) ii
3) iii
4) iv
Which of the following pair will form same osazone? 1) D-Glucose, D-Allose
Sr.IIT-Z (IZ)_JEE-MAIN
2) D-Glucose, D-Altrose space for rough work
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Narayana IIT Academy SPARK_JEE MAIN_CTM-6
3) D-allose, D-Altrose 86.
4) D-Fructose, D-Galactose
In elastomer, intermolecular forces are: 1) Nil
87.
10-01-15_Sr.IIT-Z (IZ) CO-
2) Weak
3) Strong
4) Very strong
Which of the following polymer, not having C - C bond formation during polymerisation. 1) Teflon
88.
2) Bakelite
3) Natural rubber 4) Buna-s
Absolute alcohol cannot be obtained by simple fractional distillation because: 1) Pure C2 H 5OH is unstable 2) C2 H 5OH do not form hydrogen bonds with water 3) Boiling point C2 H 5OH is very close to that of water 4) Constant boiling azeotropic mixture is formed with water
89.
Histamine stimulates the secretion of pepsin and hydrochloric acid and antihistamines are used to prevent the action of histamines. Among the following which are antihistamines?
SO N H R H 2NO
1) Ranitidine
2) Terfenadine
3) Brompheniramine
4) All of these
90. Above drug is an example of: Sr.IIT-Z (IZ)_JEE-MAIN
space for rough work
Page 28
Narayana IIT Academy SPARK_JEE MAIN_CTM-6
1) Sulpha drug
Sr.IIT-Z (IZ)_JEE-MAIN
2) Morphine
10-01-15_Sr.IIT-Z (IZ) CO-
3) Analgesic
space for rough work
4) Tranquilizer
Page 29
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